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Top 10 Hardest SAT Math Questions

Boosting your SAT score can change your life. When I raised my SAT score from average to perfect, I saw countless doors open for me: scholarship money, acceptance into prestigious schools, and opportunities that I never would have received without a high score.

When many test-takers attempt to improve their SAT score, the area they are most concerned about is the math section. With all of its fairly recent changes, the Math section of the SAT may seem more daunting than ever, but it can be conquered easily if you know what problems to prepare for when you take the test.

You will want to be ready to handle every type of math question that will come your way during the test if you want to raise your SAT score (or even get a perfect score!)

Here are the top 10 hardest SAT Math questions you should look out for if you want to improve your score on the SAT Math section:

1. Combining ace exponents and ace expressions

Before you take the SAT, you will want to brush up on your exponents. You are going to encounter questions that ask you to add, multiply, or divide exponents so that they are equal to one another and then factor them into an appropriate expression.

For example:

If f(x) = (2 – x)(x/3), and 4n = f(10), then what is the value of n?

This question requires you to create and evaluate an expression using the properties of exponents, which can prove to be quite tricky during an exam.

Oh, and n=5 by the way.

2. Rationalizing denominators with complex numbers

On the SAT Math section, you will also have to rationalize denominators that have complex numbers, represented by a+bi.

For example, 7+3i is a complex number.

You might be asked to find the value of a when presented with a fraction and the value of i on your test, requiring you to rationalize the denominator to solve the problem.

Working with radical expressions like these can be complicated, so it is important that you understand how to work with complex numbers.

3. Exponential decay

When you take the SAT Math section, you will see “story” problems asking you to solve exponential decay problems usually surrounding population density or radioactive substance decay.

To successfully solve these math problems, you will need to be able to substitute the abstract figures with tangibles from the problem (ie: replacing t in the equation with the appropriate value of years; using people or grams to represent the population or the remaining amount of a substance), and use exponential decay models.

4. Equivalent expressions

Another common type of difficult question you will face on the SAT Math exam is one asking you to find an equivalent expression.

Essentially, these questions ask you to look at an expression and see which multiple-choice solution is equivalent to the original expression.

5. Splitting tasks

Splitting tasks questions are ones where you have two variables and you have to determine how many or how much of each variable is present within a given story problem or situation.

The following math problem would be an example of this type of question:

A farmer has chickens and goats. When he went to feed his animals this morning, he counted a total of 12 heads and 32 feet. How many of the animals were goats?

This type of question will require you to craft an equation to solve for the variable presented in the problem (which would end up being four goats in the example above).

6. Use coefficients only to solve

There will be questions on the SAT Math section that require you to use coefficients to solve an equation instead of simplifying the equation. You will need to know when and how to set coefficients equal to one another in order to answer these questions.

7. SAP on tables

Some SAT Math questions will require you to use strategies where you Substitute Answers in the Problem (SAP) using a provided table.

You might have a table with a column listing values of x and another column listing values for f(x). Your job will be to substitute answers in the problem to figure out which multiple-choice solution correctly defines f.

8. Higher function graphs

When you take the SAT, you may be faced with some math questions that provide a graph of a particular function and rely on you to find the points where a specific value intersect with the graphed function. Other problems may ask that you use the graph to solve for the specific value.

It is important that you know what to do when you see these common but difficult math questions.

9. Adding proportions or ratios

On the SAT, you will typically see math questions that involve proportions or ratios.

For example:

135 boys and girls went to their school carnival. The ratio of girls to boys was 3 to 2. How many boys were at the carnival?

In order to find the correct answer, 34, you will need to know how to add the ratio together, divide the total number of people in the scenario by the number you received when you added the ratio, and multiply that number by the part of the ratio for the variable you are trying to solve (boys in this scenario).

If you do not know all of these steps, these problems will be hard to answer correctly.

10. Consecutive numbers

The final type of the top 10 hardest SAT Math questions will ask you to add or subtract consecutive integers.

For example:

The sum of two consecutive odd integers is 40. Find the value of the smaller integer.

You will need to be able to solve this type of problem when you take the SAT. (Just in case you were working on this problem on your own, the answer is 19.)

While these common SAT Math problems are difficult, you can learn to master even the hardest SAT Math questions with Prep Expert. When you sign up for a Prep Expert SAT Class, you will learn strategies that will help you tackle these top 10 hardest SAT Math questions with ease.

Learn more about how Prep Expert can help you score higher on the SAT when you visit our website or sign up for one of our free classes.

Dr. Shaan Patel MD MBA

Written by Dr. Shaan Patel MD MBA

Prep Expert Founder & CEO

Shark Tank Winner, Perfect SAT Scorer, Dermatologist, & #1 Bestselling Author
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