While the prohibition of a calculator on some SAT math questions may leave you worried, rest assured that you don't need a calculator on this section. In fact, having one would probably just slow you down!
This guide will discuss the third section of the SAT, the Math with No Calculator section. Read on to learn about the types of questions you can expect to see, along with some tips for getting a high score. First, let’s go over the format of the SAT Math No Calculator section.
How Is the Math No Calculator Section Formatted?
Let’s start with the basics: how much time you have, and how the Math No Calculator section is structured. This section will always come third, after Reading and Writing and Language. It’s only 25-minutes long, making it the shortest section on the SAT. You’ll get a short break after you take it, during which you can take out your calculator to get ready for the next section, the Math with Calculator section.
In these 25 minutes, you’ll be asked to answer 20 questions. You'll have an average of one minute and fifteen seconds, or 75 seconds, per question. Fifteen of these questions will be multiple choice, each with four answer choices, and five will be grid-ins, also known as student-produced responses. You’ll fill in your answers to these five grid-ins on a special section of your answer sheet.
Here’s how the section breaks down exactly:
|Time||Number of Multiple Choice||Number of Grid-ins|
|25 minutes||15 (#1-15)||5 (#16-20)|
Since the No Calculator section is the shorter of the two math sections, it will only count for one-third of your total math score. Now let’s move beyond logistics and discuss the skills that will be tested on the SAT Math No Calculator section.
You don't need a calculator to answer these questions, just a pencil and paper!
What Skills Are Tested On the No Calculator Section?
According to College Board, the Math No Calculator section tests two major categories, Heart of Algebra and Passport to Advanced Math, along with problems that fall under Additional Topics. These categories focus on concepts such as solving linear equation, linear inequalities, functions, quadratic equations, graphs, geometry, and complex numbers, among others.
Unlike on the longer math section, you won’t find any Problem Solving and Data Analysis questions, the ones that ask you to interpret data from tables and scatterplots or calculate ratios, rates, and proportions. The chart below shows exactly how many questions you can expect to find in each of the three major skills areas:
|Content Categories||Number of questions||Percent of test|
|Heart of Algebra||8||40%|
|Passport to Advanced Math||9||45%|
Some questions may be multi-step and require you to combine two or more concepts to work toward a solution. To gain a sense of how the math section tests the above skills, you can find official SAT sample questions below. Let’s take a look at how this calculator-free section tests the above skill areas.
This amphibian romantic wears his Heart of Algebra on his sleeve.
How Does the No Calculator Section Test Your Skills?
The No Calculator section won’t ask you to do long, complex calculations out by hand. For the most part, this section seeks to test your reasoning and problem-solving. College Board wants to ensure that you understand fundamental math concepts and don’t need to rely on a calculator to reach a solution. There will still be some arithmetic - basic adding, subtracting, multiplying, or dividing by decimals - but the majority of the problems will focus more on reasoning than on figures.
Below are some official sample questions provided by the testmakers. You’ll find two questions that fall into the Heart of Algebra category, two in Passport to Advanced Math, and one in Additional Topics. Notice how, for the most part, a calculator wouldn’t actually be useful at all for reaching your answer.
Examples of No Calculator Section Questions
The questions below are borrowed from College Board’s four official SAT practice tests, a free resource that should definitely be part of your test prep. You should also check out Khan Academy's SAT resources, though it probably won't be a replacement for more thorough test prep.
#1: Heart of Algebra
This Heart of Algebra question asks you to solve for x in an algebraic equation.
To solve, you could go through the following steps:
- Multiply both sides by 3, so you're working with x - 1 = 3k
- Add 1 to both sides, leaving you with x = 3k + 1
- Then solve for x by substituting k with 3. Since x = 3k + 1, x = 3(3) + 1, or x = 10.
This Heart of Algebra example represents an easy level question. If you didn't solve for x, you could also plug the answer choices in and work backwards (ie, which value of x would equal 3). Either way you decide to solve it, this problem definitely doesn't require the use of a calculator.
#2: Heart of Algebra
This is another Heart of Algebra question of medium level difficulty. It tests your reasoning skills and understanding of an algebraic expression. You could plug in numbers to make the scenario more concrete, but the easiest way to solve this problem is by understanding how to represent rates with algebraic variables.
The problem asks about the total number of messages Armand and Tyrone sent.
- The total number of texts Armand sent is his rate (m texts/hour) multiplied by the number of hours (5). Your product for Armand's texts is 5m.
- The total number of texts Tyrone sent is his rate (p texts/hour) multiplied by the number of hours (4). Your product for Tyrone is 4p.
- To get a total, you would add these two products together, leaving you with 5m + 4p.
If you were unsure about your answer, you could plug in sample numbers for m and p to check your reasoning. The easiest way to solve this problem, though, is with a conceptual understanding of the relationship between rates and time and how to represent this relationship with a variable.
#3: Passport to Advanced Math
This sample question tests your ability to manipulate an algebraic equation.
The initial expression gives you m in terms of r, N, and P. The problem asks you to solve for P in terms of m, r, and N. To switch around the equation, you should multiply both sides by the reciprocal of the expression beside P. Basically, you can just flip the current expression, ending up with answer choice B.
#4: Passport to Advanced Math
The question below is the first example that requires arithmetic. While a calculator would be helpful here, the College Board wants to see that you can do addition, subtraction, division, multiplication long hand.
Since the problem asks when the price per pound of beef (b) was equal to the price per pound of chicken (c), you can solve it by setting b as equal to c, or 2.35 + 0.25x = 1.75 + 0.40x. Then you solve for x with these steps:
- To avoid negative numbers, subtract 1.75 from both sides and 0.25x from both sides, leaving you with 0.60 = .15x.
- Divide both sides by .15 to get x = 4.
- The question asks about the price per pound of beef when both meats were equal, so plug in x to solve for b. Your equation should look like this: b = 2.35 + 0.25(4).
- b = 2.35 + 0.25(4) = 2.35 + 1 = 3.35.
- The price per pound of beef when it was equal to the price per pound of chicken was $3.35.
#5: Additional Topics in Math
Finally, the following is an “Additional Topics” question that involves geometry (right triangles) and basic trigonometry. Here you need to demonstrate understanding of sin and cosine and how they relate to one another in a right triangle. Without knowing this relationship, you'd have a tough time answering this question.
The easiest way to solve this problem is to recall the complementary angle relationship of sine and cosine, sin(x°) = cos(90° − x°). Then you can immediately know, without having to do any calculations, that your answer is 4/5.
Answer: 4/5 or .8
As you can see above, the Math No Calculator questions ask you to demonstrate a deep understanding of mathematical concepts. So how can you study to ensure your understanding of these challenging questions? Read on for some study tips as you prepare for SAT Math.
Let's talk strategy.
How Can You Do Well On the Math No Calculator Section?
Any prep you do for the Math No Calculator section will help you on the Math with Calculator section of the SAT, so these study tips will help your overall preparation. The following study tips, though, are especially essential for the No Calculator section.
Tip 1: Study Key Concepts
As you saw in the example questions above, many questions won’t ask you to do any calculations with numbers. Instead, they require that you have a deep understanding of the underlying concepts and can apply operations to work towards a solution. In this way, some of the problems are more abstract and theoretical, rather than based on figures and equations with real numbers.
This shift, by the way, aligns more closely with the Common Core. Both the SAT and Common Core standards now present math with fewer topics presented more in depth. Some SAT critics have pointed out that this shift continues to benefit students who attend better-resourced schools whose teachers are well-versed in the Common Core. If your math classes teach curriculum that aligns with Common Core standards, then they should be teaching you key concepts in a way that will help you on the SAT Math No Calculator section.
Outside of school, you should also make time to study the key topics that will appear on SAT Math. Because of College Board’s recent commitment to transparency, it shares exactly what those concepts will be. Algebra is especially important, and you’ll want to ensure you have a firm grasp of topics like linear and nonlinear equations, quadratic equations, and functions.
Beyond the main topics shared by College Board, you should make sure your study materials break down each broad topic into its component subtopics. By covering each detail, you can fill in any gaps in knowledge. On this section, you can’t rely on a calculator to do any of the thinking for you. You need to show up with a strong understanding of the key concepts.
Tip 2: Practice Close Reading
Just as No Calculator problems emphasize your conceptual understanding over your ability to manipulate figures and carry out calculations, they also test your reading comprehension. You’ll have to be able to read a problem and figure out what steps it’s asking you to take.
Word problems, especially, can be relatively involved, sometimes containing more information than is necessary for you to work towards a solution. That means it’s up to you to figure out which details are relevant and which details are useless. Some of these problems, according to College Board, feature real-world scenarios, such as calculating gas mileage or converting from one country’s currency to another.
Of course, not all these real-world scenarios are part of everybody’s actual everyday experiences. Practice problems will help get you familiar with the types of scenarios that College Board considers to be real world. Critics have suggested that this emphasis on word problems, along with the above mentioned alignment with the Common Core, could disadvantage some test-takers, especially those who speak English as a second language. To prep for this section’s emphasis on reading comprehension, make sure to study with multi-step word problems.
FAQ: Can I use my abacus during the No Calculator section? Sadly, no, you'll have to rely on your own counting skills.
Tip 3: Brush Up On Your Arithmetic Skills
For the most part, I’ve stressed that the No Calculator section prioritizes a conceptual understanding over the ability to carry out calculations. There are still a handful of problems, though, that will require you to do arithmetic. Without a calculator, you’ll have to be able to write out these calculations in long form.
In example problem #4 above, for instance, you would have to subtract and divide using decimal points. While these are basic math skills, many students may have grown used to performing these simple calculations on a calculator. You’ll want to brush up on your ability to write these operations out by hand quickly, efficiently, and with an eye for accidental mistakes.
Tip 4: Write Out Your Work
If you’ve been in any math class, you’re probably familiar with the much repeated math teacher mantra: write out your work. Teachers don’t want you to seemingly pull an answer out of thin air; they want you to show, step by step, how you worked through a problem. Not only does this demonstrate your understanding, but it also helps you catch any mistakes along the way.
Just as you should write out any calculations you do, you should also write out the steps in other problems, whether you’re solving for x or simplifying a multi-variable expression. Many of the problems require multiple steps, so writing out your work will help you keep track of your thinking and avoid errors.
Tip 5: Answer Hundreds of Practice Problems
Answering practice problems should go hand in hand with reviewing key topics. Make sure you’re comfortable with the concepts and know when and how to apply them to realistic SAT problems. Taking timed practice tests will also help you develop your time management skills and ability to answer questions quickly and accurately.
So where can you find all these practice problems? One place, of course, is College Board. You can find automatically graded online practice questions, along with four free official practice tests that you can print out and download. You can also find problems of varying difficulty levels on Khan Academy, along with video explanations of the different concepts.
You might also use SAT Math prep books or try out PrepScholar’s SAT prep program. Finally, you could also use practice tests for the old SAT, as long as you make sure to adjust your focus for the redesigned test. (For instance, you’ll find fewer geometry problems but will need to add some basic trigonometry.)
After you answer questions and take timed tests, take the time to analyze your results. Figure out exactly why you got a question wrong and what you can do to fix your mistake for next time. If you lacked core knowledge, study that concepts. If you made careless errors, work on your strategies for time management. Walk yourself through the answer explanations step by step to figure out how you can improve.
By analyzing your results and using practice tests as valuable feedback for your approach to test prep, you can gear your math toward doing well on the SAT. As we draw to a close, let’s review the key features you need to know about the SAT Math No Calculator section.
FAQ: If I can't use my calculator or my abacus, can I at least count on my fingers and toes? Probably, but it doesn't seem like the most efficient use of time.
Key Facts About the SAT Math No Calculator Section
The Math No Calculator is the third section of the SAT. It’s 25 minutes and consists of 20 questions: 15 multiple choice and 5 grid-ins. These questions cover Heart of Algebra, Passport to Advanced Math, and Additional Topics.
Most questions draw on your conceptual reasoning skills. Calculations with equations and figures will be limited to basic arithmetic skills. As you prep, you should make sure to brush up on those arithmetic skills, along with your word problem comprehension. Most importantly, you should show up to the SAT with an in-depth conceptual understanding of algebra, geometry, and basic trigonometry.
Any prep you do for the Math No Calculator section will also be helpful for the Math with Calculator section. Above all, prioritize a strong grounding in the fundamental concepts that will appear on SAT math. As long as you do this, you won’t even miss your calculator as you work through the first SAT math section.
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Rebecca graduated with her Master's in Adolescent Counseling from the Harvard Graduate School of Education. She has years of teaching and college counseling experience and is passionate about helping students achieve their goals and improve their well-being. She graduated magna cum laude from Tufts University and scored in the 99th percentile on the SAT.