# 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.

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