### Mastering Story: Screenplay Structure 101

**Mastering Story: Screenplay Structure 101**

**Bonus Material**: Beat Sheet Guide

Have you ever watched a movie and thought, “Hey, I could write this!”? Or had an idea that you thought would be just stellar on screen? As humans, we’re natural-born storytellers, and so it’s no wonder that you’ve probably had such thoughts.

The hard part isn’t about coming up with ideas – it’s about finding a way to organize those ideas into a story with a clear beginning, middle, and end.

As teenagers finish high school and start to look towards their futures, there is no skill more vital than clear communication.

Whether it’s cracking the college essay, figuring out how to sell themselves in an interview, or navigating new assignments, figuring out how to tell a compelling story is essential. Creative writing teaches students how to think in a new way that is readily transferable to all of the above scenarios and more.

To novice writers, though, an empty page can feel overwhelming. I mean, where do you even begin? How do you break a story? When do you introduce new plot developments? How do you know when the story’s done? The possibilities seem endless!

Thankfully, creative writing isn’t as freewheeling as most people assume. While writers are obviously allowed to go in any direction that moves them, there are certain tried-and-true frameworks that we keep coming back to. We’re going to dive into one such framework here.

Before we dive into the specifics, though, there are some basic things you should know up front.

**SCREENWRITING 101: THE BASICS**

Virtually any story can be summarized in this way: a likable character needs to overcome a series of increasingly difficult tasks in order to accomplish a compelling desire and grow as a human along the way.

It’s your job as a writer to invent that journey and to come up with obstacles that will enable your character to grow in a believable way. People grow when they’re faced with challenging situations that push them out of their comfort zones!

So how do we introduce those challenging situations?

As mentioned above, every story should have a beginning, middle, and end. In screenwriting, we think of these pieces in terms of **acts. **

- Act 1 is your “beginning.” This is where you show your protagonist in his/her “before world.” What does their status quo look like before undergoing the journey that will make up the bulk of your story? What flaws do they have that they might be unaware of? We should get a clear understanding of what’s missing in this person’s life and how they need to change.
- Act 1 should take up ~25% of your story

- Act 2 is the “middle” of your story. It begins with your protagonist choosing to pursue his/her goal, embarking on a journey in the process. Your protagonist’s status quo will start to be challenged as they’re faced with more and more obstacles, forcing that character to grow as they adapt to new circumstances.
- Act 2 should take up ~50% of your story

- Act 3 is the “end” of your story. After experiencing a moment of defeat at the end of Act 2, the protagonist considers giving up on their goal and returning to who they were at the beginning of the film, but they ultimately muster the strength to carry on. They use everything that they’ve learned to overcome their flaws and use their new strength to finally accomplish their goal.
- Act 3 should take up the last ~25% of your story

So that’s a nice basic framework, but how long is “25%,” exactly? The cool thing about screenwriting is that it’s formatted so that **each page of writing translates to one minute of screen time**.

- Since most movies are about 1.5 hours to 2.5 hours, most screenplays should be about 90 pages to 150 pages.
- The “ideal” screenplay is 110 pages.

Now that you have a basic idea of story, let’s look at that ideal 110-page screenplay to breakdown story even further.

**SCREENWRITING 101: STORY BEATS**

*Act 1 (Pages 1-25)*

- SET UP & THEME (Pages 1-10): The first impression of the story’s world and protagonist – a “before” snapshot of the person we’re about to follow on this adventure. It should present the main character’s world as it is and show us all of their problems. We should get a clear understanding of what’s missing in this person’s life and how they need to change. At some point during this beat, the theme of the movie should be explicitly stated, and that statement should serve as the movie’s thematic premise.
- CATALYST (Page 12): The inciting incident. This is the moment where life begins to change as your protagonist is faced with some form of life-changing event. It is allowing a monster onboard your ship, meeting the true love of your life, getting fired from your job, etc. It’s the moment that shakes up your “before” world. Usually, your character is posed with a choice: do they want to try to fix whatever calamity they’ve just encountered, or do they want to try to ignore it and carry on with business-as-usual?
- DEBATE (Pages 12-25): After experiencing the catalyst, the protagonist should doubt the journey that they must take. Change is scary. Can they really face the challenge that’s been put in front of them? It’s the moment of truth – will they embark on the journey or stay in their “before” world?

*Act 2 (Pages 25-85)*

- BREAK INTO 2 (Page 25): After the period of debate at the end of Act I, the protagonist ultimately decides to move forward with their quest. This is where the protagonist leaves their comfort zone and enters the upside-down world that is Act II.
- B-STORY (Page 30): This is where you want to introduce a new element of the story. For most screenplays, it’s "the love story." It is also the story that carries the theme of the movie.
- FUN AND GAMES (Pages 30-55): This is where you deliver on the “promise of the premise.” What kind of moments would people expect when they hear the concept of your film? It’s where most of the “trailer moments” will be found. It’s also where we’re concerned with forward progress of the journey – the character should begin to encounter obstacles, but generally things are going well for the protagonist as they’re having “fun” and moving along in the pursuit of their goal.
- MIDPOINT (Page 55): The midpoint is either an “up” where the hero seemingly peaks (though it is a false peak) or it is a “down” when the world collapses all around the hero (though it is a false collapse). The stakes are raised, the fun-and-games are over, and we’re back to the story. The protagonist’s strategy usually shifts after the midpoint as they begin to realize that things are more complicated than they may have seemed.
- CHALLENGES AND DECLINE (Pages 55-75): This is where the situation becomes much more difficult for the protagonist, and the forces that are aligned against them (internal and external) begin to tighten their grip. Doubt, jealousy, fear and foes regroup to defeat the main character’s goals. This is when the bad guys send in the heavy artillery.
- ALL IS LOST (Page 75): This is the moment where the hero loses everything they’ve gained, and the initial goal seems totally impossible. It is the opposite of the midpoint in terms of “up” or “down,” most often the hero’s lowest point. Usually, there is a symbolic or literal death here as the hero comes to feel that their journey was all for nothing.
- DARK NIGHT OF THE SOUL (Pages 75-85): After experiencing defeat, the hero should take some time to react. Typically, they wallow in hopelessness as they question their journey and wonder if it’s even worth it to keep carrying on in their pursuit.

*Act 3 (Pages 85-110)*

- BREAK INTO 3 (Page 85): Thanks to a fresh idea, new inspiration, or last-minute thematic advice from the B-story (usually the love interest), the main character chooses to try again. They’ve finally come to understand the theme of the film and have realized the solution to their problem as a result – now all they have to do is apply it.
- FINALE (Pages 85-110): This time around, the main character incorporates the theme – the nugget of truth that now makes sense – into the fight for the goal because they now have experience from the A-story and context from the B-story. Act 3 is all about synthesis! Thanks to what the protagonist has learned, they manage to defy the odds and accomplish their goal as a new person.
- FINAL IMAGE (Page 110): The very end of the story, where we get a snapshot of the protagonist’s new life that’s been born from the journey. Usually, it’s in direct contrast to whatever we saw at the beginning of the film.

**DOWNLOAD OUR FULL BEAT SHEET GUIDE**

If that felt like a lot to process, it’s because it is! Distilling the complex structure of a 110+ page work into just a few paragraphs inevitably means that a lot of information is getting jammed into a limited space.

That being said, nailing structure is fundamental to starting your journey as a storyteller. You can’t effectively build out character and theme until you have a strong story to layer onto!

To help you begin to organize your thoughts so that you can move into the writing stage, you can use our free **beat sheet guide, **which identifies what your major story “beats” (industry lingo for “developments”) should look like and where they should occur**.**

In addition to providing space for you to hone in on the key elements of your own story, we also break down a popular movie through the above lens to help you better understand what this template looks like in action.

### Annie

Annie is a graduate of Harvard University (B.A. in English). Originally from Connecticut, Annie now lives in Los Angeles and continues to mentor children across the country via online tutoring and college counseling. Over the last eight years, Annie has worked with hundreds of students to prepare them for all-things college, including SAT prep, ACT prep, application essays, subject tutoring, and general counseling. She is a Master tutor at Princeton Tutoring.

### Application Essentials for the Top 20 U.S. Private High Schools

**Application Essentials for the Top 20 U.S. Private High Schools**

Applying to private high schools can feel daunting. For many students, it’s the first time they’ve had to complete an application of this sort or take on serious standardized testing.

While the private school application process is definitely involved, it’s nothing that can’t be managed with a proper mindset, timeline, and study plan. We encourage families to start thinking about where they want to apply early and know the important deadlines for those schools.

Students should also begin studying for the SSAT plenty of time before their first official test date and be prepared to take the SSAT more than once. The first step towards independent school success is strong SSAT scores, and you want to put yourself in the best position possible to stand out.

To help with your planning, we've compiled a list of important dates, deadlines, and other application essentials for the top 20 private high schools in the U.S.

Here's what we cover in this post:

- The Private School Application in a Nutshell
- Application Essentials for the Top 20 U.S. Private High Schools
- Next Steps

**The Private School Application in a Nutshell**

Every private high school in the U.S. is different, but most applications require students to submit the same general materials, which typically involve the following:

- an academic transcript
- letters of recommendation
- SSAT scores
- an interview
- and/or essay or writing sample

Many competitive high schools have application components in addition to these general requirements, such as interviews, parent/guardian statements, supplementary letters of recommendation, portfolios, graded writing samples, and essay questions.

Some schools might have "optional" or "suggested" requirements, such as the SSAT Character Skills Snapshot.

We encourage families to familiarize themselves with *all *application requirements for each school of choice and to consider submitting optional components if possible. While this doesn't necessarily guarantee acceptance, these additional components can potentially provide admissions officers with greater insight into your student's potential.

If you have any questions about the application process for a specific school, feel free to contact the admissions office. Most school representatives are more than happy to provide further insight into SSAT score requirements, candidate statements, transcript submission, etc.

## Application Essentials for the Top 20 U.S. Private High Schools

The list below compiles application essentials for the most competitive U.S. private high schools in New England. There are numerous competitive private schools in this region, and their application standards are representative of most schools.

We update these details regularly for your convenience.

**Phillips Exeter Academy (Exeter, NH)**

- SSAT score submission deadline:
**January 15** - Application deadline:
**January 15** - Rolling Admissions: No
- Interviews: Yes (required)
- Application Portal: found here
- Additional application requirements: Essay questions, transcript report, principal/counselor recommendations, current English teacher recommendation, current Mathematics teacher recommendation, personal recommendation (optional), special interest recommendation (optional), SSAT character skills snapshot (optional)

**Phillips Academy Andover (Andover, MA)**

- SSAT score submission deadline:
**February 1**(February test scores accepted if all other materials are in prior to February 1) - Application deadline:
**February 1** - Rolling Admissions: No, but there is a “second round” admissions process for students applying after February 1. Call the admissions office for more information.
- Interviews: Yes (required)
- Application Portal: found here
- Additional application requirements: Graded writing sample, short answer and essay questions, parent/guardian statement, transcript report, principal/counselor recommendations, current English teacher recommendation, current Mathematics teacher recommendation, personal recommendation, special interest recommendation (optional)

**The Lawrenceville School (Lawrenceville, NJ)**

- SSAT score submission deadline:
**February 1** - Application deadline:
**January 15** - Rolling Admissions: No
- Interviews: Yes
- Application Portal: Apply with the SSAT Standard Application Online (more info)
- Additional application requirements: SSAT Standard Application Online forms, supplementary materials for athletics and art (encouraged), SSAT character skills snapshot (strongly recommended)

**Choate Rosemary Hall (Wallingford, CT)**

- SSAT score submission deadline:
**January 15** - Application deadline:
**January 15** - Rolling Admissions: No
- Interviews: Yes (strongly encouraged)
- Application Portal: found here
- Additional application requirements: Essay questions, parent/guardian statement, transcript report, principal/counselor recommendations, current English teacher recommendation, current Mathematics teacher recommendation, personal recommendation (optional), SSAT character skills snapshot (optional)

**Deerfield Academy (Deerfield, MA)**

- SSAT score submission deadline:
**January 15** - Application deadline:
**January 15** - Rolling Admissions: No, but there is a “late applicant” admissions process for students applying after January 15. Call the admissions office for more information.
- Interviews: Yes
- Application Portal: found here
- Additional application requirements: Graded writing sample, short answer and essay questions, transcript report, principal/counselor recommendations, current English teacher recommendation, current Mathematics teacher recommendation, current academic teacher recommendation (from a third teacher of the student’s choice)

**St. Paul’s School (Concord, NH)**

- SSAT score submission deadline:
**January 15** - Application deadline:
**January 15** - Rolling Admissions: No
- Interviews: Yes (required)
- Application Portal: found here
- Additional application requirements: Candidate statement, parent statement, transcript report, principal/counselor recommendations, current English teacher recommendation, current Mathematics teacher recommendation, personal recommendation, special interest recommendation (optional), supplementary materials for athletes/ballet dancers/musicians (optional)

**Groton School (Groton, MA)**

- SSAT score submission deadline:
**January 15**(January test scores will be accepted, but November and December tests are preferred) - Application deadline:
**January 15** - Rolling Admissions: No
- Interviews: Yes (recommended)
- Application Portal: found here
- Additional application requirements: Graded writing sample, candidate statement, parent statement, transcript report, principal/counselor recommendation, current English teacher recommendation, current Mathematics teacher recommendation, personal recommendation, special interest recommendation (optional)

**Noble & Greenough School (Dedham, MA)**

- SSAT score submission deadline:
**January 15** - Application deadline:
**January 15** - Rolling Admissions: No
- Interviews: Yes (required)
- Application Portal: Apply through Ravenna (more info)
- Additional application requirements: Student statement, extracurricular activities form, parent statement, transcript report, principal/counselor recommendations, current English teacher recommendation, current Mathematics teacher recommendation, character skills snapshot (required)

**The Hotchkiss School (Lakeville, CT)**

- SSAT score submission deadline:
**January 15**(January test scores will be accepted, but November and December tests are preferred) - Application deadline:
**January 15** - Rolling Admissions: No
- Interviews: Yes (recommended)
- Application Portal: found here
- Additional application requirements: Graded writing sample, candidate project, parent statement, transcript report, principal/counselor recommendations, current English teacher recommendation, current Mathematics teacher recommendation, personal recommendation, special interest recommendation (optional)

**Middlesex School (Concord, MA)**

- SSAT score submission deadline: Tests
**through February**accepted - Application deadline:
**January 31** - Rolling Admissions: No
- Interviews: Yes (recommended)
- Application Portal: found here
- Additional application requirements: Student essay questions, parent statement, transcript report, principal/counselor recommendations, current English teacher recommendation, current Mathematics teacher recommendation, personal recommendation (optional), special interest recommendation (optional), SSAT character skills snapshot (strongly encouraged)

**The Loomis Chaffee School (Windsor, CT)**

- SSAT score submission deadline:
**January 15** - Application deadline:
**January 15** - Rolling Admissions: All late applicants will be considered on a rolling basis as space becomes available
- Interviews: Yes (required)
- Application Portal: found here
- Additional application requirements: Essay questions, transcript report, principal/counselor recommendations, current English teacher recommendation, current Mathematics teacher recommendation, SSAT character skills snapshot (optional)

**Milton Academy (Milton, MA)**

- SSAT score submission deadline:
**January 15** - Application deadline:
**January 15** - Rolling Admissions: No
- Interviews: Yes (required)
- Application Portal: Apply using the Gateway to Prep Schools common application or the SSAT Standard Application Online (more info)
- Additional application requirements: Short answers and essay questions, parent statement, graded writing sample, transcript report, principal/counselor recommendations, current English teacher recommendation, current Mathematics teacher recommendation, personal recommendation (optional), special interest recommendation (optional)

**St. Andrew’s School (Middletown, DE)**

- SSAT score submission deadline:
**January 15** - Application deadline:
**January 15** - Rolling Admissions: No
- Interviews: Yes
- Application Portal: Common applications not accepted. Apply through the Andrew’s Online Application Portal.
- Additional application requirements: Transcript report, principal/counselor recommendations, current English teacher recommendation, current Mathematics teacher recommendation, special interest in athletics or art form (optional)

**St. Albans School (Washington, DC)**

- SSAT score submission deadline:
**January 15** - Application deadline:
**January 8** - Rolling Admissions: No
- Interviews: Yes
- Application Portal: Apply through Ravenna (more info)
- Additional application requirements: Two personal statements, transcript report, principal/counselor recommendations, current English teacher recommendation, current Mathematics teacher recommendation

**Concord Academy (Concord, MA)**

- SSAT score submission deadline:
**January 15** - Application deadline:
**January 15** - Rolling Admissions: No
- Interviews: Yes (suggested)
- Application Portal: Apply through Ravenna (more info)
- Additional application requirements: Personal statement, parent statement, transcript report, principal/counselor recommendations, current English teacher recommendation, current Mathematics teacher recommendation, visual and performing arts portfolio (if applicable)

**Peddie School (Hightstown, NJ)**

- SSAT score submission deadline:
**January 15** - Application deadline:
**January 15** - Rolling Admissions: Applications received after January 15 will be considered on a rolling basis
- Interviews: Yes (required)
- Application Portal: Apply with the SSAT Standard Application Online (more info)
- Additional application requirements: Student essays, parent statement, transcript report, principal/counselor recommendations, current English teacher recommendation, current Mathematics teacher recommendation, personal recommendation, Peddie School supplemental form

**Hill School (Pottstown, PA)**

- SSAT score submission deadline:
**January 31** - Application deadline:
**January 31** - Rolling Admissions: Applications received after January 31 will be considered on a rolling basis
- Interviews: Yes (required)
- Application Portal: found here
- Additional application requirements: Short answer and essay questions, transcript report, principal/counselor recommendations, current English teacher recommendation, current Mathematics teacher recommendation, personal recommendation (optional), graded writing sample (optional)

**Taft School (Watertown, CT)**

- SSAT score submission deadline:
**January 15** - Application deadline:
**January 15** - Rolling Admissions: No
- Interviews: Yes (required)
- Application Portal: Apply with the SSAT Standard Application Online (more info)
- Additional application requirements: Short answers and essay questions, parent statement, graded writing sample, transcript report, principal/counselor recommendations, current English teacher recommendation, current Mathematics teacher recommendation, character skills snapshot (recommended)

**Blair Academy (Blairstown, NJ)**

- SSAT score submission deadline:
**January 15** - Application deadline:
**January 15** - Rolling Admissions: Applications received after January 15 will be considered on a rolling basis
- Interviews: Yes
- Application Portal: found here
- Additional application requirements: Student questionnaire, parent statement, transcript report, principal/counselor recommendations, current English teacher recommendation, current Mathematics teacher recommendation, personal recommendation (optional)

**Westminster School (Simsbury, CT)**

- SSAT score submission deadline:
**January 15** - Application deadline:
**January 15** - Rolling Admissions: No
- Interviews: Yes (required)
- Application Portal: found here
- Additional application requirements: Graded writing sample, candidate statement, parent statement, transcript report, principal/counselor recommendations, current English teacher recommendation, current Mathematics teacher recommendation, character skills snapshot, personal recommendation (optional)

**Applying to Private High Schools: Next Steps**

When it comes to applying to private high schools in the U.S., the key to success is preparation! Know what to expect when applying and create a schedule to ensure you have the capacity to submit all components on time.

A strong application also starts with strong SSAT scores and an early, effective study plan. The SSAT covers a wide breadth of material, some of which may feel unfamiliar to students, such as the SSAT Verbal section. The best way to be prepared is to practice as much as possible in order to familiarize yourself with different question types and figure out which strategies work best for which questions.

How can you make sure that you’re getting the best SSAT practice possible?

We strongly recommend signing up for one of our state-of-the-art SSAT programs. Working with professionals who utilize real SSAT materials is the surest way to guarantee excellent results as you study for your private school exams.

Good luck!

### Annie

Annie is a graduate of Harvard University (B.A. in English). Originally from Connecticut, Annie now lives in Los Angeles and continues to mentor children across the country via online tutoring and college counseling. Over the last eight years, Annie has worked with hundreds of students to prepare them for all-things college, including SAT prep, ACT prep, application essays, subject tutoring, and general counseling. She is a Master tutor at Princeton Tutoring.

### SAT Math No-Calculator Tips

# SAT Math No-Calculator Tips

The SAT has two math sections: SAT Math without a calculator, and SAT Math with a calculator.

This first math section, SAT Math No-Calculator, can present a real challenge to test-takers. It can feel downright intimidating to plunge into 20 standardized math questions without a trusty calculator at your side!

However, the No-Calculator section tends to contain more straightforward questions than the Calculator section. It also requires simpler calculations, and every question is designed to be answered without the aid of a device.

That being said, students should feel comfortable working with complicated values *without* a calculator on hand, such as simplifying expressions involving radicals and pi, reducing long fractions, and completing basic mental math.

We've discussed SAT Math more generally in previous posts. In this post, we provide our favorite SAT Math No-Calculator tips and strategies for experiencing success on this section.

Here's what we'll cover:

- The SAT Math No-Calculator Section in a Nutshell
- SAT Math No-Calculator Tips & General Strategies
- Guided Examples
- Next Steps

## The SAT Math No-Calculator Section in a Nutshell

On the No-Calculator section of the SAT, students can expect the following:

**20 questions***15 multiple-choice questions**5 student-response questions*

- A time limit of
**25 minutes**

All of these questions are designed to be answered in about one minute or less and *can* be completed without a calculator.

The No-Calculator section focuses on the following four math content areas:

- Algebra (8-10 questions)
- Trigonometry (0-2 questions)
- Geometry (2-4 questions)
- Advanced math (6-10 questions)

We discuss these content areas in greater detail in our SAT Math post.

Students should be aware that **questions get more difficult as the section progresses,** with the exception of the 5 student-response questions, or "grid-ins," which appear at the end of the section and follow their own order of difficulty.

Here's what that might generally look like on a typical No-Calc. section:

- Questions 1-5: EASY
- Questions 6-10: MEDIUM
- Questions 11-15: HARD
- Questions 16-17 (grid-in): EASY
- Question 18 (grid-in): MEDIUM
- Questions 19-20: HARD

Keep in mind that all SAT Math No-Calculator questions are worth the same number of individual section points.

What does this mean?

Students should prioritize taking their time on those first, easy questions to avoid making careless errors! Harder questions do *not *grant a student more points if answered correctly. In fact, we've seen many students hurt their scores by rushing to complete more challenging questions.

## SAT Math No-Calculator Tips & General Strategies

Even though students won’t have a calculator for this test, they should still have all of the tools that they need to answer the questions! These "tools" include content knowledge and section strategies.

Remember: everything on the No-Calculator section is specifically designed to be answered with a pencil, piece of paper, and your own brain. Yet success on any section of the SAT, a standardized test, also involves strategy.

Here are our top* *SAT Math No-Calculator tips.

**1. Prioritize easy questions first**

Within 25 minutes, students must complete 20 No-Calculator questions. Every question thus should be able to be answered in 60 seconds or less.

As we discussed in the last section, the questions on the SAT Math No-Calculator section are arranged generally in order of increasing difficulty. This does not mean that students should speed through those easier questions to get to higher-difficulty problems!

Take your time on those first, easy questions to avoid careless errors and maximize your point potential. Save challenging questions for the end of the section.

In fact, some students prefer to take the section in waves, following a strategy like this:

- Answer the questions you can solve in under a minute
- Go back and solve the questions you know how to solve (but are more time-consuming)
- Save questions you're unsure about for last

If you find yourself spending more than 60 seconds on one problem, stop and re-evaluate. If you think you can solve it in 30 more seconds, keep going. Otherwise, skip it and come back.

**2. Never leave a question blank**

You don’t lose points for wrong answers on SAT Math, so always fill something in, even if it’s a total guess!

To maximize this guessing strategy, use the process of elimination to rule out incorrect answer choices. You significantly increase your chances of guessing correctly with every wrong answer eliminated.

You can even use "guesstimating" to get rid of answers, crossing off choices that are obviously too big or too small.

In the event that no answer choices can be ruled out, choose a “Letter of the Day” (i.e. A, B, C, or D) and use that same letter for every guess on the section. Statistically, you are more likely to get questions right this way than by bubbling in random choices.

**3. Save time by coming prepared**

Memorize the section's instructions and essential formulas ahead of time. While the test will give you a few key formulas at the start of the section (pictured below), the students who are most successful have committed these formulas to memory to save time flipping back-and-forth between reference information and problems.

Be sure to know the rules associated with student-response or "grid-in" questions, too, especially when it comes to bubbling in fractions or decimals.

You don't want to lose valuable points simply by bubbling in the correct answer *incorrectly *here!

It's also important to know which strategies are the quickest for you on the No-Calc. section. Many problems can be solved in multiple ways. It doesn’t matter which one you use, so pick whichever one is going to get you to the solution the quickest! This method is likely to be different for every student.

**4. Check your answers**

Once you think you’ve found the correct answer, try plugging it back into the question to make sure it is the right one. If you don’t get the desired value, this is a good indicator that you've done something wrong.

If you’re left with extra time on the SAT Math No-Calculator section, try going back and checking your work on select problems. You might also want to attempt a problem that you were unsure of in a different way.

### 5. Use the "no-calculator" rule to your advantage

If you find yourself needing to make intense calculations on a No-Calculator section question, this is a good sign it's time to back up and take a simpler approach.

Ask yourself: how can I approach this question more simply? There *must *be a way to solve it without a device, so what can I do to minimize calculations?

This is exactly the type of critical thinking that rewards test-takers on SAT Math, especially with No-Calculator problems.

**6. Apply problem-solving techniques**

If you’re ever stuck on a problem – or if you’re afraid that the straightforward approach might take too long – see if you can use a different method.

In fact, the No-Calculator Math section is designed to encourage students to efficiently work through problems, even if that means using methods they don't use in high school classrooms. According to the College Board, SAT Math tests students' ability to

solve problems quickly by identifying and using the most efficient solution approaches. This might involve solving a problem by inspection, finding a shortcut, or reorganizing the information you’ve been given.

Here are some of our favorite SAT math problem-solving techniques, which can give you those shortcuts the CollegeBoard is referencing:

**Back-solving:**With this method, students plug the answers themselves into the problem to see which fits. This is particularly helpful when there are variables in the question and numbers in the answer choices.**Plugging in your own numbers:**Using the plugging in technique, students choose their own values to represent variables. This method is particularly helpful when there are a lot of variables in the question*and*answer choices.**Structure in expressions:**With this method, students simplify complicated expressions by looking for patterns. If you see a certain expression repeating in an equation, you can replace it with a single variable, for example.

We will apply some of these problem-solving techniques to guided examples in the next section.

## SAT Math No-Calculator Tips: Guided Examples

We'll apply some of these unconventional problem-solving methods to select problems from an SAT Math No-Calculator section.

### Method #1: Back-solving

Usually, if you see numbers in the answer choices and variables in a question, you can work backward to find the right solution. This means using the answer choices to solve the problem!

Let’s look at an example.

Working with radicals can be tricky, especially because you have to remember to check for *extraneous solutions* (solutions to the squared equation that arise when solving, but which don’t actually fit the original equation).

The simplest way to solve these problems (not to mention the quickest *and* most fool-proof way to avoid making an error) is to simply plug in the answer choices.

When plugging in the answer choices, start with B or C. These are usually "middle" values that can help guide your search if they don’t work by cluing you in to whether you need a greater value (allowing you to rule out A without plugging it in) or a smaller value (allowing you to rule out D). The only exception to this is if the question is asking you to find the “least possible value” or “greatest possible value” – in those instances, start with A or D, respectively.

Since that condition doesn’t apply to this problem, let’s start by subbing in C, which is 4.

When K=4, the value under the radical becomes 2(4)^2 + 17, which equals 49. The square root of 49 is 7. If x also equals 7, then the equation becomes 7-7=0, which is a true statement. **C must be the answer.**

### Method #2: Plugging in Your Own Numbers

When there are a lot of variables in both the question and answer choices, a good strategy is to plug in your own numbers for the variables so that you’re working with real values instead of abstract ones.

Let’s look at an example of plugging in.

This equation might be tricky to simplify, but it becomes a lot easier if you turn the variable into a number. Just pick a value for x and sub that value into the expression in the question *and *the answer choices and see which answer choice gives you an equivalent value.

Here are a few important qualifications to note with this method:

- When picking your own values, avoid choosing 0 or 1, as these can result in trick answers. Any other value should work, though, so pick numbers that are easy to work with, such as 2, 5, or 10.
- For problems involving percentages, the number 100 usually works best.
- If there’s more than one variable in the question, choose different values for the different variables.
- Check all of the answer choices! Unlike back-solving, this strategy may result in more than one answer that seems to work. If this happens, rule out all of the answer choices that didn’t initially work out, then choose a different value for the variable and plug that back into the remaining choices. Keep doing this until you’re left with only one answer.

For the above problem, let’s say that x=2. When we plug 2 in for x in the original equation, we end up with 8/5.

Choice A simplifies to 1, which does not equal 8/5. Rule out A.

Choice B simplifies to 13/3, which does not equal 8/5. Rule out B.

When we plug in 2 for x in choice C, we get 23/5, which does not equal 8/5. Rule out C.

By process of elimination, the answer must be D, and when we plug in 2 for x in choice D, sure enough, we get 8/5. **Our answer is D.**

### Method #3: Structure in Expressions

When you notice a certain expression repeating within an equation, a great way to simplify the problem is to substitute a single variable for the repeating expression. This will make it much easier to solve.

Let's apply this to the example below.

This problem looks super complicated, but it becomes much more straightforward if you simplify the expressions by subbing in x for r/1200, which we can see pops up repeatedly throughout the problem.

The original equation is now [(x)(1 + x)^N]/ [1 + x)^N] – 1, all multiplied by P. In order to isolate for P, just multiply m by the reciprocal, which gives us **choice B, our correct answer.**

## SAT Math No-Calculator Tips: Next Steps

More so than anything else, the secret to mastering the SAT Math No-Calculator section is practice.

While the majority of the section's material will be familiar to most high school students, the test oftentimes presents that material in challenging and unusual ways. In many cases, critical thinking is just as essential as content knowledge when it comes to arriving at the correct answer.

The best way to be prepared is to practice as much as possible in order to familiarize yourself with different question types, as well as to figure out which strategies work best for which questions.

How can you make sure that you’re getting the best practice possible, now that you're armed with these SAT Math No-Calculator tips and strategies?

We strongly recommend signing up for one of our state-of-the-art SAT programs. Working with professionals who utilize real College Board materials is the surest way to guarantee excellent results as you study for the SAT. Learn more about PrepMaven's SAT prep offerings now!

### Annie

Annie is a graduate of Harvard University (B.A. in English). Originally from Connecticut, Annie now lives in Los Angeles and continues to mentor children across the country via online tutoring and college counseling. Over the last eight years, Annie has worked with hundreds of students to prepare them for all-things college, including SAT prep, ACT prep, application essays, subject tutoring, and general counseling. She is a Master tutor at Princeton Tutoring.

### SAT Math: Charts and Graphs Questions

**SAT Math: Charts and Graphs Questions**

One of the SAT's biggest goals is to measure students’ abilities for future success.

For this reason, the SAT doesn’t *just* test content you've learned in high school. It also tests what you need to succeed in college, such as critical thinking skills and logical reasoning.

The SAT, for example, incorporates many charts and graphs questions that challenge students to interpret data on their own. In fact, charts and graphs appear on all required sections of the test!

Unsurprisingly, these figures are especially prevalent on both SAT math sections, which are very interested in students' data analysis skills.

Such graphs might look overwhelming at first, particularly for students who haven't done much data analysis in high school. But these questions are much easier if you know exactly what the SAT is looking for.

Here's what we cover in this post:

## Reading SAT Graphs Successfully

Both SAT Math sections (No-Calculator and Calculator) include a significant number of charts and graphs questions. These questions often include a figure and require students to perform basic data analysis.

Fortunately, these questions usually don’t require too much calculation beyond simple arithmetic. For this reason, they should actually be some of the easiest on the test, as long as you understand what you're looking at.

We discuss strategies for approaching Charts and Graphs questions in a recent post.

When it comes to SAT Math data analysis questions, it's always vital to identify some key information about a chart or graph before plunging into the question.

For example, we encourage students to ask the following questions when looking at an SAT graph:

- What is the
**title**of the chart or graph? - If it’s a graph, is there a key? What are the labels on the axes? What are the units?
- Make sure to pay extra attention to the
**units**on the axes, as many incorrect answers will be off by a factor of 10

- Make sure to pay extra attention to the
- What is the general trend/shape of the graph?
- Is the relationship linear? Is it exponential?

- Are there any
**outliers**? How do they affect the overall data set? - Note how data is
**clustered**.- Is it very spread out? Centered around the mean?

- If the graph is a line, ask yourself what the
**slope**is.- Slope is always rise over run (change in y vs. change in x), and the unit of the slope will also correspond to the unit on the y-axis divided by the unit on the x-axis

- If there are a
**pair of lines**in a chart, notice where the greatest points of similarity/difference between the lines are

You won't necessarily have to ask *all *of these questions when engaging with an SAT chart or graph. However, these questions encourage students to consider the graph in context before identifying the task itself.

## Types of SAT Math Charts and Graphs Questions

It’s worth noting that students shouldn’t expect to see an even distribution of graphs/charts throughout the math sections.

The Calculator Section (Section 4) tends to be much heavier on Data Analysis & Problem Solving, and so you can expect to see most graphics in the latter portion of the test.

What kinds of charts and graphs appear on SAT Math?

Students can expect to see problems involving:

- Scatterplots
- Bar Graphs/Histograms
- Line Charts
- Two-Way Tables

We do want to note that students can expect to encounter many Cartesian graph questions testing algebraic principles like slope, slope-intercept form, midpoints, and distance formula. As these require extensive outside content knowledge to answer, we will not address these in this post.

Let’s look at some of these common graph types in more detail below.

## Scatterplots on SAT Math

Scatterplots are an important tool in statistics. An important function of statistics is its ability to predict values based on a limited amount of data, and scatterplots help us to do just that.

In a scatterplot, each individual point on the graph represents a **real point of data. **

A **line of best fit **is then drawn through those points to represent the approximate trend of those values. We can then use that line to predict values outside of the tested range.

For SAT Math, you should understand the following about scatterplots:

- The further a point is from the line of best fit, the more likely it is to be an
**outlier** - You can extend the line of best fit to
**predict future values** - The line of best fit is an
**estimate**, which means we cannot determine definitive values off of the line - The
**slope**of the line of best fit represents the predicted increase (or decrease) in y for each unit increase of x - The
**y-intercept**is the value of*y*when the x-value is 0

Let’s look at an example of a question involving a scatterplot:

**How to solve:**

In the scatterplot, each individual point represents a recorded heart rate at a given swim time. The line of best fit provides the predicted heart rate for the set of times. The question asks us to determine the difference between the predicted heart rate at 34 minutes and the actual heart rate at 34 minutes.

We can see that at 34 minutes, Michael’s actual recorded heart rate was 148 BPM, and the line of best fit predicts a heart rate of 150 BPM. The difference, therefore, is 2, oranswer choice B.

## Bar Graphs / Histograms

Another common type of SAT Math graph is the bar graph or histogram. Bar graphs are used to show the frequency with which different variables occur within a data set.

Bars of differing heights reflect the relative frequencies of each variable.

For example, a *taller *bar indicates a higher frequency of that piece of data. A *shorter *bar indicates a lower frequency of that piece of data.

When approaching a bar graph, be sure to pay attention to the following:

- The
**title**of the graph, which will identify the type of data set - The
**variable(s)**listed along the**x-axis** - The
**frequencies**measured along the**y-axis**

Let’s look at an example:

**How to solve:**

As mentioned, the x-axis on a histogram will list the different items measured, while the y-axis will list the frequency with which each item occurs.

In this histogram, the x-axis lists the different number of seeds in each of 12 apples.

Based on the graph, we can conclude that2 apples had 3 seeds, 4 apples had 5 seeds, 1 apple had 6 seeds, 2 apples had 7 seeds, and 3 apples had 9 seeds.

To find the average number of seeds per apple, we simply need to add up the total number of seeds and divide by the total number of apples. To find the total number of seeds, we multiply the different number of seeds along the x-axis by their respective frequencies, and then add those values together. In other words:

Total seeds = (2 apples x 3 seeds) + (4 apples x 5 seeds) + (1 apple x 6 seeds) + (2 apples x 7 seeds) + (3 apples x 9 seeds) = 73 seeds

We then divide that value by the total number of apples, which is 12.

73 seeds/12 apples = 6.08, which is closest toChoice C.

## Line Graphs on SAT Math

Line graphs are used to show how the relationship between two variables changes over time. Like a bar graph, the title of a line graph on SAT Math usually describes this relationship.

For example, a line graph may be titled "Number of SAT prep companies in the U.S. from 2000 to 2020" or "Percentage of students who graduated high school in New Jersey between 1992 and 1997."

In the case of line graphs:

- The
**x-axis**will list the**independent variable** - The
**y-axis**will list the**dependent variable**

Often, the x-axis will designate a given time frame, such as years or hours. Pay careful attention to units when analyzing a line graph, as it can be easy to gloss over these (and lose precious points)!

Let’s look at an example of an SAT line graph question:

**How to solve:**

In this line graph, the y-axis marks the number of millions of portable media players sold worldwide. The x-axis lists each year sales were measured (between 2006 and 2011).

First, we need to determine how many portable media players were sold in 2008. If we go over to 2008 on the x-axis, we can see that there is a point hitting 100 (million) on the y-axis. That means that100 million portable media players were sold in 2008.

Using this same method, we can see that160 million portable media players were sold in 2011. That means that the fraction of portable media players sold in 2008 versus 2011 is 100,000,000 / 160,000,000, which simplifies to5/8.

## Two-Way Tables

Two-way tables efficiently display the distribution of a set of data, organized by the data's defining characteristics.

These tables often appear throughout both SAT math sections. They are often combined with other concepts like probability, rates, and proportions.

While specific questions might vary, their purpose is the same: the SAT wants to make sure that students know how to read tables correctly!

When analyzing a two-way table on the SAT, pay attention to the following:

- The
**titles of the column(s)** - The
**titles of the row(s)** - Rows or columns that specify
**total values**

Let’s look at an example of an SAT two-way table now.

**How to solve:**

In this problem, the columns reflect the ages of contestants and the rows reflect the genders. To find a specific age/gender combination, simply look at where the two desired variables intersect.

Remember that probability is calculated by dividing the total number of desired outcomes by the total number of possible outcomes.

Here, the desired outcome is either a female under age 40, or a male older than age 40. If we start by looking in the row labeled “female” and then move over to the column labeled “under 40,” we see that 8 people fall into this category.

Using the same process, we can also see that there are 2 males age 40 or older. That means that the total number of subjects in our “desired outcomes” bucket is 8 + 2, or 10.

To find the probability that one of these outcomes will occur, we need to divide by the total number of subjects. To determine the total number of subjects, look in the bottom right corner of the table to find the total number of all gender and age groups. We can see that it’s 25. Therefore, the probability is 10/25, orChoice B.

## Next Steps

The SAT Math sections are very interested in students' ability to analyze data.

With charts and graphs questions on the math sections, it's always vital to spend time with the figure or chart *first*. This will minimize the possibility of falling for a trap answer!

Remember that these questions often don't require intense calculations or knowledge of specific formulas. In fact, they contain all the information you need to find the right answer.

Seeking ways to boost your fluency in data analysis on the SAT? We've got you covered. Our expert tutors are here to help you experience confidence on the SAT Math sections and beyond.

Learn more about private SAT tutoring at PrepMaven here!

### Annie

### SAT Math: What You Need to Know

**SAT Math: What You Need to Know**

The SAT has two math sections: No-Calculator (20 questions) and Calculator (38 questions).

Students’ performance on these two sections contributes to 50% of their SAT composite score (400-800).

What math do you need to know for the SAT?

First things first: SAT math is very different than high school math!

SAT math tends to cover the same basic concepts that students have probably seen before. However, it tests those concepts in unfamiliar ways.

The best way to prepare for SAT math is to know what to expect going in so that there are no surprises. It’s also essential to have some strategies on hand for approaching a variety of math question types.

In this post, we cover the following:

- SAT Math: The Basics
- General Tips for Approaching SAT Math
- Problem-Solving Strategies
- The No-Calculator Section
- The Calculator Section
- Next Steps

**SAT Math: The Basics**

There are two math sections on the SAT:

- No-Calculator Permitted: 20 questions, 25 minutes
- Calculator Permitted: 38 questions, 55 minutes

These two sections come **after** the Reading and Writing & Language sections. (We discuss SAT format at greater length in our post about the 5 SAT Sections.)

In general, the no-calculator math section tends to contain more straightforward questions. The calculator section often requires more critical thinking, translating words into math, and data analysis.

In both sections, the questions are arranged in **order of increasing difficulty**.

That may sound intimidating, but smart test-takers can use that structure to their advantage by knowing to prioritize the earlier, easy questions first!

**General Tips for Approaching SAT Math**

As with all SAT sections, one of the biggest keys to success is using time efficiently. What can you do to maximize your time on SAT Math?

We have a few tips.

**Question Order**

All questions on the SAT are worth the **same number of points **(within each individual section).

It just doesn’t make sense to waste five minutes struggling through a difficult problem (that a student might get wrong anyway!) at the expense of spending that time on easy/intermediate questions a student can definitely get right.

Similarly, it doesn’t make sense to rush through the initial easy questions to get to the hard problems if it means making careless errors! Focus attention on where you’ll have the most success.

For that reason, don’t feel like you have to answer every question on SAT Math *in order*. In fact, this is what we recommend:

- Skip around, prioritizing quick, easy questions first
- Then work questions you feel comfortable answering but know will be time-consuming
- Finally, attempt any difficult questions (if there is time left)

How do you recognize hard questions on SAT Math?

As a rule-of-thumb, hard questions require more than **1 minute** to complete.

If you’ve spent a full minute on an SAT Math question, pause and re-evaluate. If you can solve the problem in another 30 seconds, go for it. Otherwise, skip it and come back to it later.

**Guessing**

While you might not have time to attempt every SAT Math question, never leave a question blank.

There are no penalties for wrong answers on the SAT, so make sure to grid in an answer for every question, even if it’s a total guess!

That being said, try to use **process of elimination** as much as possible to weed out unlikely answers and increase the probability of guessing correctly. Every answer choice ruled out *significantly* increases your odds of getting a correct answer.

In the event that no answer choices can be ruled out, choose a “Letter of the Day” (i.e. A, B, C, or D) and use that same letter for every guess.

**Be Prepared**

Finally, while this may sound obvious, students should come into the test prepared.

Save yourself time by memorizing the SAT Math instructions and reference information that appear on every test at the start of each section. For example, here are the directions and reference information for the no-calculator section:

Both SAT Math sections involve grid-in questions, where students must supply their own answers. Familiarize yourself with how to grid-in answers correctly ahead of time to avoid careless errors and wasted time.

Lastly, understand the how-and-when of using calculators. While many students rely on a calculator for computation, it’s not always the quickest way to solve a problem (especially on the SAT!).

Practice problems with and without a calculator in advance of the test to understand which is fastest for you!

**Problem-Solving Strategies for SAT Math**** **

The most important strategy for SAT math is solving problems in the fastest way possible.

This does not mean rushing through problems. Rather, it means being a savvy test taker and adapting your strategy for each problem!

Unlike high school math, the SAT doesn’t care how students solve the problem. You don’t get credit for showing your work (although showing your work can help you avoid careless errors).

Choose whichever method is quickest for solving an SAT math problem.

There are 5 main approaches to SAT math problems.

**1. The Straightforward Approach**

With this approach, simply solve the problem in the “traditional” way.

However, know that there are multiple ways to solve the same problem. As you practice, try to get into the habit of identifying which approaches are quickest for different question types.

**2. Plugging in an Answer Choice**

This SAT Math strategy is great if you’re not sure how to answer the question, or if you think the traditional approach will take longer. This strategy works best when there are variables in the question and numbers as the answer choices.

Pick an answer choice, plug it back into the question, and see if it works.

If it doesn’t, try again with another answer choice.

Start by checking answer B or C, as these answers will tend to be values in the middle of the range. This can help you rule out answer choices more quickly.

For example, if you start by checking B and the value is too low, you know that you need a bigger number--you don’t need to waste time checking answer A.

The only exception to this rule is if a question asks about the least or greatest possible value. In this case, start by testing A (for least possible value) or D (for greatest possible value) and move on from there.

Here's a great question for plugging in the answers:

**3. Plugging in Your Own Numbers**

This is an effective strategy if there are a lot of variables and it’s hard to keep track of them all.

Replace variables with your own numbers and see which answer choice fits the stipulations of the question.

Make sure to check all answer choices when using this method – it’s possible that more than one answer will come out to the same correct value. If that happens, rule out all answer choices with incorrect values, then choose new numbers and test the remaining answers again.

Choose different numbers for different variables (i.e. x and y). Choose numbers that are friendly to work with, but avoid choosing 1 or 0, which may result in trick answers.

This is a great method for percentage word problems (choose 100 as your number!).

Here's a question that can easily be solved by plugging in your own numbers:

**4. Graphing**

Graphing on your calculator can be useful if you’re ever in a jam finding points of intersection, x- or y-intercepts, minimums/maximums, etc.

This method is usually more time-consuming, so only use it if you’re totally lost!

**5. Guessing**

If all else fails, use process of elimination and Letter of the Day to make an educated guess. This is a great approach for high-difficulty SAT Math questions.

In general, high-difficulty SAT Math questions occur at the end of each section:

- No Calculator: questions 14-15, 19-20
- Calculator: questions 20-29, 35-38

## SAT Math **Section 1: The No-Calculator Section**

The first SAT Math section is the no-calculator section. Students have 25 minutes to answer 20 questions.

The first 15 questions are multiple-choice, while the final 5 questions are grid-in questions that require students to fill in their own answers.

In general, this section encompasses the following four content areas:

- Algebra (8-10 questions)
- Trigonometry (0-2 questions)
- Geometry (2-4 questions)
- Advanced math (6-10 questions)

All of the questions in this section are designed to be answered in about one minute or less and can be completed without a calculator.

Common algebra topics include:

- Fractions
- Single Equations
- Simplification
- Substitution
- Percentages
- Inequalities

Common geometry questions include:

- Triangles
- Circles
- Volume/Area

The SAT tests geometry in limited and predictable ways, so students don’t need to be well-versed in the entirety of geometry in order to be successful.

Rather, they should be comfortable solving problems involving circles (especially finding circle area, circumference, arc length, and sector area), triangles (especially Pythagorean theorem, special right triangles, and similar triangles), and volume/area problems for all regular shapes.

That’s pretty much it!

A typical no-calculator geometry problem might look something like this:

###### Source: The College Board Official Practice Test 1

Trigonometry questions will test a pretty basic understanding of trigonometry (if it appears on the test at all!), so don’t worry about being an expert.

The SAT wants to see that students have a working knowledge of trigonometric concepts, but the test usually doesn’t require students to apply trigonometry in overly complicated ways.

A typical trigonometry question might look something like this:

###### Source: The College Board Official Practice Test 1

With this sample problem, once students recognize the trigonometric identity that states that sin *x°*=cos(90*°*-*x°*), the problem becomes a no-brainer.

Common trigonometry questions involve:

- Sine, cosine, and tangent
- Trigonometric identities
- Evaluating trigonometric expressions

Similarly, “Advanced Math” is not as scary as it sounds. For the sake of the SAT, “Advanced Math” simply means testing a basic understanding of more advanced algebra topics, but not necessarily more difficult problems.

A typical “Advanced Math” problem might look something like this:

###### Source: The College Board Official Practice Test 1

Topics covered in Advanced Math include:

- Factoring
- Polynomials
- Systems of Equations
- Translating Words into Math
- Fractions
- Ratios
- Functions
- Substitution
- Imaginary Numbers
- Square Roots

## SAT Math **Section 2: The Calculator Section**

The second SAT math section is longer and a bit more challenging. It is composed of 38 questions to be completed in 55 minutes.

The first 30 questions are multiple-choice, while the final 8 questions are grid-in questions.

In general, the calculator section of the SAT tends to cover similar concepts to the no-calculator section, but with a few key differences.

The calculator section places a lot more emphasis on data analysis and problem-solving than the no-calculator section. Students should expect to encounter some wordy problems that require more critical thinking than straight computation.

This will mean translating English into math and analyzing a lot more charts and figures that emphasize “real-world” math!

A typical “Data & Analysis” question from the calculator section might look something like this:

###### Source: The College Board Official Practice Test 1

The flip-side is that students won’t come across as many geometry or trigonometry problems on this SAT Math section. In fact, the frequency with which each concept is tested in this section is quite different. In general, students should expect to see:

- Geometry (3-6 questions)
- Data Analysis & Problem Solving (16-18 questions)
- Algebra (10-13 questions)
- Advanced Math (5-8 questions)

Note that there is still quite a bit of algebra on the calculator section. However, it might look different than it does on the no-calculator section.

There will likely be more word problems that require students to interpret real-world situations and figure out how to turn them into mathematical expressions.

A typical algebra problem from the calculator section might look something like this:

###### Source: The College Board Official Practice Test 1

**Next Steps**

More so than anything else, the secret to mastering the SAT math section is practice.

While the majority of the material will be familiar to most high school students, the test oftentimes presents that material in challenging and unusual ways.

The best way to be prepared is to practice as much as possible in order to familiarize yourself with different question types, as well as to figure out which strategies work best for which questions.

How can you make sure that you’re getting the best practice in possible?

We strongly recommend signing up for one of our state-of-the-art SAT programs. Working with professionals who utilize real College Board materials is the surest way to guarantee excellent results as you study for the SAT.

Check out our course offerings here!

### SAT Geometry: What You Need to Know

**SAT Geometry: What You Need to Know**

**Bonus Material: PrepMaven's SAT Geometry Guide**

The SAT has two math sections: a no-calculator section (20 questions) and a calculator section (38 questions).

Test-takers are likely to encounter geometry questions on both of these.

This can be intimidating to a lot of students!

For many SAT test-takers, geometry can be a somewhat "dusty" concept, especially for juniors and seniors who haven't studied triangles and circles for years. For others, geometry might simply be that one area of math that simply never made sense!

Fortunately, SAT geometry is very different than geometry students learn in traditional classroom settings. There aren't any proofs on the SAT, for one thing.

Plus, SAT geometry accounts for only a *very small portion* of the test. While these questions do cover a fairly broad scope, the topics are finite and should feel familiar after review.

You can apply everything you learn in this post to the practice problems available in our SAT Geometry Guide. Grab it below.

Here's what we cover in this post:

- SAT Geometry: The Basics
- General Approach to SAT Geometry Questions
- SAT Geometry: The Content
**Bonus**: PrepMaven's SAT Geometry Guide

**SAT Geometry: The Basics**

The SAT contains two math sections:

- No-Calculator: 20 questions, 25 minutes
- Calculator: 38 questions, 55 minutes

SAT geometry is likely to appear in *both *of these sections. Yet there's some good news to this:** these questions are only likely to make up about 10% of SAT math questions.**

Here's what we tend to see:

- 2-4 Geometry questions on the No-Calculator section
- 3-6 Geometry questions on the Calculator section

Plus, these questions test a *finite *amount of geometry content. SAT geometry questions frequently concern the following topics:

- Angles & Polygons
- Volume & Surface Area
- Triangles
- Circles

What does this mean for SAT test-takers?

Two things: **know the content, and know how it is tested**. We'll discuss this more in the next section of this post!

**General Approach to SAT Geometry**** **

There are a few core strategies students should keep in mind when it comes to SAT Geometry.

### 1) Understand what is expected of you

If you have a solid understanding of which concepts will be tested, then you’ll know which tools to pull from your arsenal. You'll also be able to more efficiently attack the problems themselves.

### 2) Know the formulas

Second, you should take the time to make sure that you know all of the required formulas inside-and-out. This includes the formulas that are given in the reference box at the beginning of each math section:

You will save yourself valuable time and mental energy if you’re not scrambling to find the right equation for a problem!

### 3) Draw pictures when possible

If a geometry question does not include an image, **make sure to draw pictures**. Sometimes something that sounds difficult in words becomes immediately apparent when you see it sketched out in front of you.

If you are given a picture with certain side lengths and angles marked and others left as variables, make sure to physically write in new measurements as you solve for them. You don’t want to try to keep everything straight in your head!

Keep in mind that figures are not often drawn to scale. Don't assume an angle measure or side length based off of *how *a picture looks. You must prove a value based off of what you know to be true.

### 4) Take these questions out of order

Geometry problems tend to be some of the more time-consuming problems on the test, so it might make sense to save these for last.

Remember that all questions on the SAT are worth the same number of points, and so it doesn’t make sense to waste minutes on difficult problems. If you are short on time and/or having trouble with the earlier sections, focus on those first before moving on to this section.

**SAT Geometry: The Content**

The main geometry topics that students can expect to see covered include:

**Angles & Polygons****Volume & Surface Area****Triangles****Circles**

We take a deep dive into each of these content areas below. You can also download all of these tips *and *apply them to practice problems now, with our **free SAT Geometry Guide**.

## Topic 1: Angles & Polygons

This might sound like a large topic. That's because it is! However, as we've said a few times in this post, the way the SAT tests this topic is predictable.

In general, these SAT geometry questions cover:

- Points in the XY-Coordinate plane
- Parallel lines
- Polygons

*Points in the XY-Coordinate Plane*

Some SAT geometry questions might ask you to find the distance between two points, or the halfway point between two sets of coordinates.

In order to solve these questions, students should be familiar with the following equations:

**Midpoint formula:**

** **

**Distance formula:**

*Parallel Lines*

*Parallel Lines*

Other questions might show a set of parallel lines intersected by another line called a **transversal line.**

These questions often ask students to solve for one or more of the angles created by the intersection. In order to solve these questions, students should be aware of the following angle relationships:

- Vertical angles are equal
- Corresponding angles are equal
- Alternate interior angles are equal
- Same side interior angles are supplementary (sum to 180°)
- The angles that make up a straight line are supplementary (sum to 180°)

**Shortcut: Remember that when a set of parallel lines are cut by a third line, all small angles are equal to one another and all large angles are equal to one another. Any big angle + a small angle will equal 180°.**

In this graphic, angles 1, 4, 5, and 8 are equal, and angles 2, 3, 6, and 7 are equal. Any of these first angles (i.e. 1, 4, 5, and 8) plus any of these second angles (i.e. 2, 3, 6, and 7) will sum to 180°.

Now let’s look at an example of an SAT geometry question involving parallel lines:

**How to solve:**

This is an easy one!You know that any large angle will be supplementary to any small angle. Since angle 1 is 35°, angle 2 is simply180° - 35°, which equals 145°, or choiceD.

*Polygons*

*Polygons*

Students might also see questions involving polygons. A **regular polygon **is any shape in which all side lengths and angles are equal to one another.

Students should be familiar with the following rules about polygons:

**The sum of all the interior angles in a polygon with***n*sides = 180°(*n-*2).- Accordingly, each interior angle in a regular polygon with
*n*sides = 180°(*n-*2)/n.

- Accordingly, each interior angle in a regular polygon with
**Exterior Angle Theorem**- An exterior angle is formed when any side of a polygon is extended. The exterior angle will always be equal to the supplement of the adjacent angle (i.e. the exterior angle + the adjacent angle will equal 180°).
- If the polygon is a triangle, the exterior angle equals the sum of the non-adjacent angles in the triangle.

Let’s look at an example of a problem involving polygons:

**How to solve:**

This polygon has 4 sides, and so the sum of the interior angles will be equal to 180° x ([4]-2), which comes out to 360°. That means that 45° + x° + x° + x° = 360°. Solving for x, we get 105°, or choiceD.

**Topic 2: Volume and Surface Area **

These SAT geometry questions are likely to test any (or all) of the following:

- The volume of regular solids
- The surface area of regular solids

In general, there’s not too much to memorize with volume and surface area for the SAT.

The reference information at the beginning of each section of SAT math will provide most of the necessary formulas, and any uncommon formulas will most likely be given in the problem.

But remember: you can save valuable time by memorizing the formulas provided in the reference information!

*Volume*

*Volume*

It's helpful to remember that the volume of all regular solids can be found using the following formula:

**Volume = Area of base x Height**

Most volume questions on the SAT involve right cylinders. Since the base of a cylinder is a circle, these questions will also incorporate concepts involving circles (see the final section of this post for more detail).

Below are the volume formulas that you should know for the test:

- Volume of a Cylinder

- Volume of a Rectangular Prism

- Volume of a Cube

- Volume of a Cone

- Volume of a Sphere

Let’s look at an example of a question involving volume:

**How to solve:**

If the volume of the cylinder is equal to 72 π and the height is 8 yards, then plugging into the formula for the volume of a right cylinder, we get 72π=8πr^2. Solving for r, that gets us 3 yards.

However, the question is asking about diameter, not radius. Since diameter=2r,the answer is 6 yards.

Some volume problems might be more involved, combining multiple shapes into a single question. Let’s look at one of those:

**How to solve:**

While this question might look overwhelming at first glance, it’s really no more difficult than the previous problem. All we need to do is find the volume of the central cylinder and the volume of each of the cones and add those values together.

We know the volume of a cone is (1/3)πr^2(h). Here, the radius for each cone is 5 feet, and the height is likewise 5 feet. That means the volume of each cone is (25/3) π, or ~130.90 cubic feet. Similarly, the volume of a cylinder = πr^2(h). Here, the radius of the cylinder is 5 feet, and the height is 10 feet. That means the volume of the cylinder is 250π, or ~785.40 cubic feet. The total volume of the silo, then, equals 130.90 cubic feet + 130.90 cubic feet + 785.40 cubic feet, or 1,047.2 cubic feet, choiceD.

*Surface Area*

Surface area is just the sum of the area of each of the faces of a polygon.

For most prisms, this is pretty straightforward.

For a cylinder, it’s a bit less intuitive: a cylinder is basically a rectangle wrapped around a circular base (giving that rectangle a length equal to the circumference of that circle).

That means that the equation for the surface area of a cylinder is as follows:

- Surface Area of a Cylinder

**Topic 3: Triangles**

The SAT loves to test triangles and incorporate them into other geometry questions. The major types of triangles that the SAT tests are:

- Isosceles Triangles
- Two sides are equal, and the corresponding angles across from those sides are also congruent.

- Equilateral Triangles
- All sides and all interior angles are equal. Each interior angle is 60°.

- Right Triangles
- One angle is 90°.

Students should also be familiar with a few other rules of triangles:

- All of the interior angles add to 180°
- For any triangle, the sum of any two sides must be greater than the third side. This is called the
**Triangle Inequality Theorem** - Area of a Triangle = (1/2)base(height)
- Side lengths are proportionate to the angles they’re across from. So, the longer the length of a side, the larger the angle across from it

Let’s look at a basic triangle problem:

**How to solve:**

We know that all of the interior angles in a triangle add up to 180°. If a=34, then 34° + b° + c° = 180°. That means that b + c = 180° - 34°, orb + c = 146°.

*Right Triangles*

Right Triangles are made up of two legs and a hypotenuse (the side opposite the right angle). Every right triangle obeys the **Pythagorean theorem, **which states:

Here, a and b are the legs of the triangle and c is the hypotenuse.

You will see certain right triangles come up repeatedly on the SAT.

These are **Pythagorean triples **or sets of three whole numbers that satisfy the Pythagorean theorem and are therefore used frequently to represent the side lengths of right triangles on the SAT.

**Recognizing Pythagorean Triples can save you a lot of time because if you know two sides, you can easily identify the third without having to use the Pythagorean theorem.**

Common Pythagorean triples include:

- 3, 4, 5 (this is the most common triple)
- Any multiple – i.e. [6, 8, 10], [9, 12, 15], [12, 16, 20]

- 5, 12, 13
- Any multiple – 10, 24, 25

- 7, 24, 25

*Special Right Triangles*

You will have to memorize two special right triangle relationships.

**1) 30° – 60° – 90° Triangles**

- The ratio of sides is: x, x√3, 2x
- This is the most common type of special right triangle on the SAT
- The shortest side, x, is opposite the smallest angle, and the largest side, 2x, is opposite the largest angle
- If you cut an equilateral triangle down the middle from its vertex, you will get two 30°-60°-90° triangles

**2) 45° – 45° – 90° Triangles**

- The ratio of sides is: x, x, x√2
- A 45°-45°-90° triangle is also an isosceles triangle, which might help you remember that both legs must be equal

Any time that you see an angle marked as 45°, 30°, or 60°, you should be looking to utilize the rules of special right triangles, even if it’s not immediately obvious!

Let’s look at an example of a question involving special right triangles:

**How to solve:**

Since Angle ABD is equal to 30° and angle ADB is equal to 90°, angle BAD must equal 60°. That means that triangle ABC is an equilateral triangle, and triangles ABD and DBC are congruent 30° – 60° – 90° triangles.

The hypotenuse of triangle DBC is 12. We know from the rules of special right triangles that the hypotenuse of a 30° – 60° – 90° triangle is equal to 2x, where x is the length of the side opposite the 30° angle (in this case, line DC). That means that DC is 6.

Since triangles ABD and DBC are congruent, as proven above, DC=AD. Therefore, line AD is also 6, and the answer is choiceB.

** Similar Triangles**When two triangles have the same angle measures, their sides are proportional.

- If you can prove 2 angles in 2 separate triangles are identical, then the 3rd angle will also be identical
- To solve similar triangle problems, match up the corresponding sides of the triangle and create a proportion to solve for the missing side

Let’s look at an example of an SAT geometry problem that tests students' knowledge of similar triangles:

**How to solve:**

Because the three shelves are parallel, the three triangles in the figure are similar. Since the shelves break up the largest triangle in the ratio 2:3:1, the ratio of the middle shelf to the largest triangle is 3:6 (the largest value is found by adding all of the partial values together, i.e. 2 + 3 + 1).

Since the height of the largest triangle is 18, the height of the middle shelf can be found by creating a proportion that relates the side lengths of the middle and largest triangles to their respective heights. In other words, (side length of middle shelf)/(side length of largest triangle) = (height of middle shelf)/(height of largest triangle). Subbing in the above values, that gives us 3/6 = x/18. Solving for x, we get9 as our answer.

**Topic 4: Circles **

Circle properties do not appear as frequently as triangle properties on the SAT Math sections. However, students can expect to encounter 1-3 of these questions, so it's wise to know this content when preparing for SAT Geometry problems.

In general, these geometry questions cover:

- Basic properties of a circle, including area and circumference
- Advanced circle vocabulary, including
*sector*,*chord*,*arc*, and*tangent* - Arc measure/length
- Sector area
- Central angles

*Basic Properties of Circles*

Students should be familiar with the following key formulas and properties of circles:

- Diameter of a Circle =
- Area of a Circle:
- Circumference of a Circle =

- A
*chord*is a line segment that connects two points on a circle - A
*tangent*is a line that touches a circle at exactly one point. A tangent is always perpendicular to the radius it intersects.

*Arc Length and Sector Area*

Sometimes, instead of being asked to calculate the entire circumference or area of a circle, students will be asked to calculate the length of just a piece of the circumference – known as the *arc length – *or the area of one slice of the pie – known as the *sector. *

Sectors and arcs will always be bound by two radii. The angle formed by the two radii is known as the *central angle. *

In the figure to the left, the length along the edge from A to B would be the *arc length*, the wedge-shaped area bound by angle AOB would be the *sector*, and angle AOB would be the *central angle* (i.e. 45°).

The ratio between the central angle and the total number of degrees in the circle (i.e. 360°) will always be the same as the ratio between the area of the sector and the total area of the circle.

Similarly, the ratio between the central angle and the total number of degrees in the circle (i.e. 360°) will always be the same as the ratio between the arc length and the total circumference of the circle.

For this reason, the formulas for arc length and sector area are actually quite simple to remember.

You just take the formula for circumference and area, respectively, and multiply them by the proportion taken up by the central angle. Here’s what that looks like:

- Arc Length = (2πr)(central angle/360°)
- Sector Area = (πr^2 )(central angle/360°)

Let’s look at an example of a question involving arc length:

**How to solve:**

Because angle AOB is marked as a right angle, we know that the central angle is 90°. The question also tells us that the total circumference is 36. Plugging into the equation for arc length, we get Arc Length = (36)( 90°/360°), which simplifies to 9, or choiceA.

*Arc Measure*

Many students confuse arc length and arc measure.

*Arc length* is the actual distance between points A and B on the circle. *Arc measure* is the number of degrees that one must turn to get from A to B.

You can think of it as a partial rotation along the circumference of the circle – a full rotation is 360°.

Central angles have the same measure as the arcs they “carve out.” Inscribed angles are half the measure of the arcs they “carve out.”

In the figure to the left, angle AOB would be the central angle, angle ACB would be the inscribed angle, and the arc measure of minor arc AB would be 70° (which is equivalent to the central angle and twice that of the inscribed angle).

Let’s look at an example question involving arc measure:

**How to solve:**

The measure of an angle inscribed in a circle is half the measure of the central angle that intercepts the same arc. That means that angle A is equal to (x°/2). We also know that angle P is equal to (360° - x°).

The sum of the interior angles of any quadrilateral equals 360°. That means the interior angles of ABPC must sum to 360°, or (x°/2) + (360° - x°) + 20° + 20° = 360°. Solving for x, that gets us80° as our answer.

*The Equation of a Circle*

Students should also be familiar with the standard form for the equation of a circle in the XY-coordinate plane:

- Where (h, k) are the coordinates for the center of the circle
- Where r is the radius of the circle

How is this equation usually tested? Given the equation, you must be able to identify the center and the radius of the circle.

Let’s look at an example of a question involving the standard equation of a circle:

**How to solve:**

Using what we know from the standard form for the equation of a circle, we can conclude that this circle has a center at (6, -5) and a radius of 4. If P is located at (10, -5), then the end of the diameter lies 4 units directly to the right of the center. That means the other end of the diameter will lie 4 units directly to the left of the center, which would put Q at (2, -5), or choiceA.

## Download PrepMaven's SAT Geometry Guide

There you have it--all of the geometry principles you need to succeed on the SAT Math sections! With our free SAT Geometry Guide, you'll get all of these principles in one place.

With this worksheet, you'll get:

- A recap of the content areas, skills, and strategies discussed in this post
- FREE practice questions
- Detailed explanations of SAT geometry questions
- Information about where to find additional practice questions

### SAT Charts & Graphs Questions: What You Need to Know

**SAT Charts & Graphs Questions: What You Need to Know**

The SAT absolutely loves to test students’ ability to interpret data.

You’re probably used to reading tables in math class. Yet you might be less prepared to see these charts and graphs incorporated into Evidence-Based Reading and Writing & Language passages on the SAT.

While such graphics might appear overwhelming at first, they shouldn’t be any cause for alarm.

In fact, these tend to be some of the most straightforward questions on the test!

The SAT does not expect you to bring any expert knowledge with you. Any time that you encounter a graph or chart, you can rest assured that the answer is right in front of you if you can interpret the data correctly.

Here's what we cover in this post:

- SAT Charts and Graphs Questions: General Approach
- SAT Charts and Graphs: Writing & Language
- SAT Charts and Graphs: Evidence-Based Reading
- SAT Charts and Graphs: Math
- Next Steps

**SAT Charts and Graphs Questions: General Approach**

Charts and graphs questions appear on four sections of the SAT:

- Evidence-Based Reading
- Writing & Language
- Math (No Calculator)
- Math (Calculator)

Most students aren't surprised to see these questions appear on the SAT's two math sections. But what are charts and graphs doing on two verbal sections?

The truth is that the SAT is deeply interested in students' abilities to analyze both quantitative and verbal information, and often at the same time. This is why the Math sections have a lot of word problems, and it's why figures appear on Evidence-Based Reading and Writing & Language.

This is a skill that most students will need in college, regardless of what major they pursue.

Of course, that doesn't mean these questions won't seem intimidating to a lot of students the first time around! Yet following this general approach for SAT Charts and Graphs questions can help you take advantage of these additional points.

**1) Take Them Out of Order**

Charts and Graphs questions can appear at any time on the SAT, but that doesn't mean you have to take them in order. Build these questions into your personal order of difficulty.

What does that mean?

Well, if you excel at Math but find the Evidence-Based Reading section to be challenging, these may be great questions to prioritize on the two Verbal sections, especially the Charts and Graphs questions that don't require knowledge of the passage.

If you dread data analysis, save these questions for the end of a section.

### 2) Identify the Task

Charts and Graphs questions can feel tedious.

For this reason, always identify what the task is. Underline and annotate the question to make this even clearer. Pay attention to the differences between the answers, too, to further support your understanding of what you need to find.

When it comes to charts and graphs questions on Writing & Language or Evidence-Based reading, assess whether you can answer the question just by looking at the graph *or *if you'll also need to research the text.

### 3) Pay Attention to Titles, Axes, and Labels

This may sound obvious, but it's actually an important step with most any charts and graphs question. When analyzing the data, prioritize the title of the graph (similar to its main idea), what any x- and y- axes designate, and/or any keys or other labels.

Sometimes you can eliminate answer choices based on this type of primary analysis alone.

### 4) Identify Trends and Patterns

It's also important to take the time to assess the patterns and trends of a general graphic *before *diving into the associated question.

Feel free to annotate or make any markings as you do this. Doing so can help you move through those trap answer choices a lot more easily!

**SAT Charts and Graphs: Writing and Language **** **

On the SAT Writing and Language section, **1-2 passages will be accompanied by an informational graph or chart. **

The passage will have an underlined statement, and students will have to determine whether or not that statement is supported by the chart.

Students can expect two general types of graph questions in this section:

**Detail-based questions**, which ask about a specific aspect of the graph**Big-picture questions**, which ask students to identify a major trend

The most important thing to remember with either type of question is that **the answer will be right in front of you! **

These questions don’t require any sort of outside knowledge, so just fact-check the answer choices against the information in the graph. Below are some tips to help minimize the possibility of error.

*Reading the Graph*

Before you jump to the answer choices, try to identify some key information upfront.

For example:

- What’s the general trend/shape of the graph?
- As one variable increases, does the other likewise increase? Decrease? Is it a bell curve?
- Are there any “outliers”? Any big spikes or jumps?
- Is there a key? What are the labels on the axes? What are the units?
- Most importantly, what is the
**title**of the graph?

Identifying the title of a figure is essential in determining the scope of the chart. We cannot extrapolate information beyond the stated scope (i.e., the title!).

Let’s look at an example to clarify:

The title of this chart tells us that it represents recorded temperatures in Greenland from 1961-1990. That means any answer that we choose must be specific to Greenland during those years.

We cannot use this chart to predict anything about current temperatures, nor can we extend the bell-curve trend to temperatures in Europe generally.

This is important because most wrong answers will play on this concept. The incorrect answers will likely be too broad, or potentially too narrow.

Other common traps to look out for:

- Answers with extreme language (words like every, all, must, never, etc.)
- Choices that might be true, but aren’t explicitly supported by the graph
- Information that is supported by the graph, but doesn’t answer the question

*Unfamiliar Graphics*

As mentioned, the graphics on the Writing and Language section don’t require any outside knowledge and will be pretty straightforward.

However, the College Board tries to make things trickier by occasionally throwing in an infographic that isn’t in the traditional bar graph form.

Here’s what that might look like:

Because the format of these graphics may vary, there’s no real way to study for them, but don’t let that overwhelm you! Trust yourself to correctly read labels and titles, and remember the same strategies that you applied elsewhere.

For example, the above question might appear daunting at first. You’ve probably never seen a graph like this, but you can break it down logically.

The smallest circle is entirely contained within the middle circle, which is entirely contained within the biggest circle.

That is probably meant to suggest that within the framework of Professional Development, Professional Networks are the largest umbrella of Professional Development, followed by Coaching and Consultation, and then Foundation and Skill-Building Workshops, as stated by answer choice** C. **

## SAT Charts and Graphs: Evidence-Based Reading

Much like the Writing and Language section, **1-2 of the 5 Evidence-Reading Passages will also contain graphs and/or charts. **

Thankfully, many of the same strategies from the Writing and Language section can be applied, and the graphics in the Reading section tend to be even more straightforward.

In fact, most of the graphic questions on the SAT Reading section can be answered on the basis of the graphic alone without looking at the text at all!

Even questions that seem to be about both the text and the graphic really only require an understanding of the graph to be answered.

Let’s look at an example:

This is a very common question type. Mention of the passage might send test-takers back to the text, frantically skimming for details, but in questions such as these, all of the statements are supported by the passage.

Your only job is to determine which statement is *also* supported by the graph.

Just like in the Writing and Language section, orient yourself for one of these questions by asking the following questions ahead of time:

- What’s the general trend/shape of the graph?
- As one variable increases, does the other likewise increase? Decrease? Is it a bell curve?
- Are there any “outliers”? Any big spikes or jumps?
- Is there a key? What are the labels on the axes? What are the units?
- What’s the title of the graph?
- Are there multiple lines? Where do they meet? Are there any points where values don’t change?

*Common Errors*

Incorrect answer choices in the Reading section might contain similar errors to those in the Writing and Language section.

Specifically, be on the lookout for answers that

- Offer conclusions that are too broad or too narrow to be considered reasonable based on the specific study presented in the graph
- Are out of the question's scope
- Contain extreme language (words like every, all, must, never, etc.)
- Might be true, but aren’t explicitly supported by the graph
- Correctly interpret the information in the graph, but do not answer the question at hand
- Contain units that don't exactly match the units on the graph

## SAT Charts & Graphs: Math

The SAT Math sections, of course, are where students can expect to see the most graphs and charts on the SAT.

Fortunately, these questions usually don’t require too much calculation beyond simple arithmetic, so they should actually be some of the easiest on the test, as long as students understand what they’re looking at.

Here are the types of charts and graphs you can expect to find on SAT Math:

- Scatterplots (discussed below)
- Generic bar graphs and histograms
- Cartesian graphs
- Line graphs
- Simple tables

In a lot of ways, the same basic strategies that we discussed for reading graphs and charts in the Verbal sections still apply to these questions, regardless of the type of figure.

When analyzing a graph on SAT Math (No-Calculator or Calculator), it is particularly important to:

- Identify the units on the axes
- Note the title of the graph
- Identify the general trend/shape of the graph
- Note any outliers
- Observe how data is clustered
- Identify slope, if the graph contains a linear equation
*Clearly identify what the question is asking!*

It’s worth noting that students shouldn’t expect to see an even distribution of graphs and charts throughout the SAT Math sections.

The Calculator Section (Section 4) tends to be much heavier on Data Analysis & Problem Solving questions, and so you can expect to see most graphics in the latter portion of the test.

*Scatterplots*

One particular type of chart worth mentioning is the scatterplot. Scatterplots are an important tool in statistics! The point of statistics is to be able to predict values based on a limited amount of data, and scatterplots help us to do just that.

The scatterplot appears the *most frequently *of all charts and graphs on SAT Math.

In a scatterplot, each individual point on the graph represents a real point of data**. **

A **line of best fit **is then drawn through those points to represent the approximate trend of those values. We can use this line to predict values outside of a tested range of data.

For the SAT, you should understand the following about scatterplots:

- The further a point is from the line of best fit, the more likely it is to be an outlier
- You can extend the line of best fit to predict future values
- We cannot determine definitive values off of the line of best fit, but we can make estimates
- The slope of the line of best fit represents the predicted increase (or decrease) in
*y*for each*x* - The y-intercept is the value of
*y*when the x-value is 0

Let’s look at an example of a question involving a scatterplot:

In the above graphic, each individual point represents a recorded heart rate at a given swim time, and the line of best fit provides the predicted heart rate for the set of times.

The question asks us to determine the difference between the predicted heart rate at 34 minutes and the actual heart rate.

We can see that at 34 minutes, Michael’s actual recorded heart rate was 148 BPM, and the line of best fit predicts a heart rate of 150 BPM. The difference, therefore, is 2, or answer choice** B.**

**Next Steps**** **

Remember: SAT Charts and Graphs questions appear on four sections of the test. The key to navigating these successfully is to be strategic in how you approach your data *and *question analysis.

Make sure to do a little work up front to minimize the possibility of falling for a trap answer. Identify the overall trend of a figure, for example, and what all of the units and labels represent.

The most important thing is not to let yourself become overwhelmed by all of the information in front of you. In fact, that information should be a blessing!

The answer is right under your nose--you don’t need to bring any sort of advanced knowledge with you, nor do you need to perform any sort of convoluted calculations. As long as you feel confident in your skills of interpretation, the rest should be a piece of cake.

Looking for world-class assistance in your SAT prep? We've got scores of professional tutors just waiting to help you succeed on SAT Charts and Graphs questions and more. Learn more about our SAT prep offerings here!

### The SAT Writing & Language Test: The Basics

**The SAT Writing & Language Test: The Basics**

Writing & Language is the second verbal section of the SAT.

In this section, students have 35 minutes to complete 44 questions.

About half of those questions concern standard English conventions, or straight-up grammar, and punctuation. The other half tests rhetorical skills, or “expression of ideas.”

Your performance on this section is calculated on a scale of 200 and 400, and your Writing and Language score contributes to 50% of your SAT verbal score.

This section has fewer questions than Evidence-Based Reading, which has 52 questions. This means that each question on Writing & Language is technically worth *more *individually.

In this introductory post to SAT Writing and Language, we discuss the following:

- SAT Writing & Language: Introduction
- SAT Writing & Language: What You Actually Need to Know
- SAT Writing & Language: General Tips
- Next Steps

**SAT Writing & Language: Introduction**

SAT Writing and Language consists of four passages. These cover the following topics:

- Science
- Humanities
- History
- Social science
- Career fields

Each passage is accompanied by 11 questions.

Unlike the Reading section, Writing & Language questions occur *throughout* the passage instead of at the end.

Here’s what that looks like:

No passage on SAT Writing & Language is necessarily “harder” than another. In fact, each passage is likely to contain a healthy mix of grammar, punctuation, and expression of ideas questions.

That being said, a punctuation question may be easier for most students than an expression of ideas question! But we’ll get to that in a minute.

**Question Categories**

The College Board breaks the Writing & Language section down into two sub-scores:

**Standard English Conventions**and**Expression of Ideas**

These sub-scores reflect the two general question categories in this section.

**Standard English Conventions**questions test mastery of the fundamental rules of grammar/punctuation.**Expression of Ideas**questions measure proficiency in writing strategy, such as rhetoric, diction, and the organization of ideas.

This might sound like a lot, but it becomes a lot easier once you know what kind of questions to expect!

By definition, the SAT is standardized, which means that **every test repeats the same set of concepts**. What’s more, SAT Writing & Language only tests a *finite *amount of concepts, grammatical and rhetorical.

This means that you don’t have to go out and memorize pages and pages of grammar rules. Nor do you have to be a rhetorical genius to get a 400 here.

The key to success on SAT Writing and Language? Knowing what it tests and getting absolutely comfortable with those concepts ahead of time!

**SAT Writing & Language: What You Actually Need to Know**

In order to master the SAT Writing & Language section, students need to be comfortable with the following concepts:

College Board Sub-score |
Concept |

Standard English Conventions |
Apostrophes: Plural vs. Possessive |

Colons and Dashes | |

Combining and Separating Sentences | |

Comma Uses and Misuses | |

Dangling and Misplaced Modifiers | |

Essential & Non-Essential Clauses | |

Parallel Structure | |

Pronoun and Noun Agreement | |

Question Marks | |

Relative Pronouns | |

Verbs: Agreement and Tense | |

Word Pairs and Comparisons | |

Expression of Ideas |
Add, Delete, Revise |

Diction, Idioms, and Register | |

Infographics | |

Sentence and Paragraph Order | |

Sentence vs. Fragments | |

Shorter is Better | |

Transitions |

As you can see from this chart,** Standard English Conventions (i.e., grammar) **questions will test your knowledge of standard written English grammar, punctuation, and other rules.

A typical Standard English Conventions question might look something like this:

**How to solve:**

At first glance, this question might appear difficult, but comparing the answer choices to one another can give us clues on how to crack it.

The primary difference between choices A-D is the type of punctuation used, which tells us that this question is probably testing our ability to join incomplete and complete ideas with the proper punctuation.

A comma (choice B) can only be used to separate an incomplete thought (or dependent clause) with a complete thought (or independent clause). A comma plus a coordinating conjunction (choice C) can be used just like a period to separate two independent clauses. A colon (choice D) is used to introduce a list or explanation, and everything that comes before the colon must be a complete thought.

In context, the punctuation is separating an independent and dependent clause, and so the answer must beB.

**Expression of Ideas **questions will ask you to improve the effectiveness of communication in a piece of writing.

A typical Expression of Ideas question might look something like this:

**How to solve:**

Notice how the question asks students to accomplish a very specific purpose: it asks for the answer that describes a self-reinforcing cycle. Many students solve these questions by subbing the answer choices back into the passage, but doing so can actually result in error.

It's vital to read the context first, which says that "as the ice melts, the land and water under the ice become exposed, and since land and water are darker than snow, the surface absorbs even more heat, which _____."

The context is discussing the melting of ice, as reinforced by heat absorption. Logically, heat absorption is only likely to increase ice's capacity to melt. OnlyDsuits this assessment, and reiterates the fact that this is a cumulative melting process (i.e., a self-reinforcing cycle).

As you can see from these examples, most **Expression of Ideas questions will have a question in front of them**, whereas the **Standard English Convention questions will not**.

In general, this often means that Expression of Ideas questions *take more time to complete *than Standard English Conventions questions. They often require a firm understanding of context, rather than rote grammar rules.

In some cases, they may even feel more challenging! But they are still worth the same amount of points on Test Day.

**Question Breakdown**

As discussed earlier, students can expect to work through 20-22 English Convention questions and 20-22 Expression of Ideas questions.

Here’s a general breakdown:

Question Type | Number of Questions |
---|---|

Punctuation | 6-12 questions |

Writing Strategy | 20-26 questions |

Verbs | 3-8 questions |

Misc. Grammar Topics | 0-5 questions |

Charts and Graphs | 1-4 questions |

As you can see, the Writing and Language section is slightly more interested in Writing Strategy than it is in straight-up grammar!

Some students notice those “Charts and Graphs” questions here and panic a bit. Isn’t this the grammar section after all?

Charts and Graphs questions actually appear on all four sections of the SAT (including Evidence-Based Reading).

Don’t be alarmed by these. They do involve a bit of data analysis, but mostly, they test a student’s ability to synthesize quantitative and verbal information.

Here’s a sample question:

### How to solve:

While this question might look technical, it actually only involves a little bit of data analysis and interpretation of context.

The context specifies that "average daily low temperatures can drop _______." The graph reveals that the average daily low temperatures recorded at Nuuk weather station in Greenland sank as low as 12 degrees F in March.

Thus, our answer isB.

**SAT Writing & Language: General Tips **

What strategies do you need to succeed on SAT Writing and Language? Here are some great general tips.

**1) Read the full text.**

Unlike the SAT Reading section, students do not need to have an in-depth understanding of the passages in order to be successful on the Writing & Language section.

That being said, there will usually be 1-2 questions per passage that require students to tie a detail, title, or transition to the main idea of the passage as a whole.

For this reason, it’s a good idea to give the passage a quick skim before jumping to the questions. Failing to do so might lead students to miss out on the big picture. After skimming the passage, students should dive into the questions.

**2) Identify which concept the question is actually testing**.

Compare the answer choices to one another for clues – how do they differ? Do some answer choices include a plural subject, while others make the subject possessive?

If so, this is probably a question focusing on apostrophes. Once students have identified the guiding principle, it becomes much easier to identify the error and correct it.

### 3) Prove answer choices wrong.

Remember that for every Standard English Convention question, there will only be one answer that is grammatically correct. In addition to finding the right answer, it’s important to check every other answer and identify why that answer choice is grammatically incorrect.

If students ever feel that there are two or more grammatically correct answers, they need to look closer because they are probably missing something. The SAT loves to include “nearly correct” choices that appear solid at first glance, which is why it’s important to check every answer carefully.

Students should be able to definitively rule out all but one choice.

The Expression of Idea questions can be a little trickier because more than one answer may be grammatically correct, but only one will communicate the author’s intention most clearly.

**4) Shorter is often better.**

In general, if more than one answer is grammatically correct, the shortest answer will be the right one. The SAT loves to test on wordiness and how to avoid it – in general, shorter is always better.

By extension, if there’s ever an answer choice that says “DELETE the underlined portion,” students should check it first because it’s usually correct.

Remember that process of elimination is your best friend. If you’re ever stuck on the rhetoric questions, compare the answer choices to one another to see how they differ. If every piece of information included in an answer choice isn’t absolutely necessary, then you’re probably better off cutting it out.

### 5) Plug it in.

Finally, before students choose an answer, they should plug it back into the passage to make sure it fits. An answer that makes perfect sense on its own might create an error in the context of the passage.

**A Word About “No Change”**

**A Word About “No Change”**

As you’ve probably noticed, almost every question includes an answer choice that reads “No Change.”

Students are oftentimes wary of choosing this option, but in reality, it should be treated like every other answer choice.

The layout of the Writing and Language section necessitates a “No Change” option so that the passages can be read in their entirety without gaping holes. Yet the underlined information is no more or less likely to be correct than any other answer choice.

When you’re selecting your answer, read the full underlined portion included in the text and treat it just like any other answer choice! How does it differ from the other answers? What rule is the question testing on, and how does the original phrase match up to that rule?

Remembering to check the original text is especially important for the rhetoric questions: what was originally in the passage may very well have been the shortest answer, and so don’t disregard it when you’re trying to play the “shorter is always better” card!

**Next Steps**

More so than anything else, the secret to mastering the SAT Writing & Language section is practice.

Many students rely on their ears to solve problems, but the majority of the questions are testing hard-and-fast rules that can be studied and mastered.

None of these concepts are particularly difficult, but they require some time and attention to get down.

How can you make sure that you’re getting the best practice possible?

We strongly recommend signing up for one of our state-of-the-art SAT programs. Working with professionals who utilize real College Board materials is the surest way to guarantee excellent results as you study for the SAT.

Check out our course offerings here!

Annie is a graduate of Harvard University (B.A. in English). Originally from Connecticut, Annie now lives in Los Angeles and continues to mentor children across the country via online tutoring and college counseling. Over the last eight years, Annie has worked with hundreds of students to prepare them for all-things college, including SAT prep, ACT prep, application essays, subject tutoring, and general counseling.