Hard Math Sat Problems: Top 10 Hardest Questions

September 22, 2022
Hard Math Sat Problems
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Hard Math Sat Problems: Do you find yourself dreading the SAT Math section. You are not the only one. This is a common problem. That’s okay. Knowing what to expect is half the battle.

This article will help you prepare for the exam and provide examples of some of the most difficult SAT math questions that you might face. Follow centralfallout to get updated.

What does the SAT Math Section include?

Hard Math Sat Problems

Hard Math Sat Problems: The math section of the SAT has 58 questions and you have only 80 minutes to complete them. The first section is “no calculator”, which lasts 25 minutes and has 15 multiple-choice and 5 grid-ins. The second section allows you to use a calculator and lasts 55 minutes. It has 30 multiple choices and 8 grid-ins. You can access certain formulas in both sections, so you don’t need to remember them.

Math questions cover these topics:

  • Heart of Algebra. This section allows you to ask questions about graphs, linear relationships and functions.
  • Data Analysis and Problem Solving. This includes scatterplots, ratios and proportions as well as data inferences, precents and data collections.
  • Passport to Advanced Math. This section addresses questions regarding nonlinear expressions and polynomial factors.
  • Additional Topics. The majority of questions will be answered in one of these sections, but others will cover geometry, complex numbers and trigonometry.

This exam will include questions about geometry, trigonometry and radians.

Do You Need to Focus on the Most Complex Math Question Right Now?

You can take a practice test to see if your score is in line if you are just starting your study prep or if you have skipped this crucial step. Take a look at our guide to the free SAT practice exams online, and then go ahead and take a test.

It is best to take the SAT practice test and assess your current level. Keep the timing straight and use only the permitted breaks. Once you have a clear idea of your current level, percentile ranking and your goals, you can set milestones for your ultimate SAT Math score.

If your score is in the 200-400 range or 400-600 range, you should first read our guide to improving math scores. Then tackle the hardest test questions.

You can read the rest of this guide if you score above 600 in the Math section. If perfection is your goal, or close to it, then you will need to be able to identify the most difficult SAT mathematics questions and how to solve them. We’re able to do that, thankfully.

Tips for taking the SAT Math Section: 

Hard Math Sat Problems: These are some tips to help you pass the SAT Math section.

1. Practice Exams

Practice exams are one of the best ways to prepare for the SAT. You will be able to get as close as possible to the “real deal” before you take your official test. You must also take them in the same conditions. This means that there are no distractions, no time limits, no turning back to previous sections, or taking breaks at the right times.

Once you’ve taken a practice exam, review your work. Do you have any areas of the Math section that you failed to do well on? Before you take another practice exam, make sure to pay attention to those sections. If you are really struggling with math, you might want to speak to your teacher or work with a tutor.

2. Take a look at the questions. They range from easy to difficult.

The easiest SAT Math questions come first, then the hardest. You’ll need to pace yourself as you want to be able answer the difficult questions.

If time is running out and you don’t have the answers to those difficult questions, you can finish what you can and guess the rest. If you are serious about the section, there is no penalty for guessing!

3. If it’s not in the Calculator Section, you don’t need a calculator to answer it!

Many students fail to answer questions in the no calculator section of the SAT exam. They believe there was a mistake. It’s also impossible to answer the question without a calculator. This section will not require your calculator. If you can’t find your calculator, it is likely that you don’t know what you need.

Hardest Questions

Hard Math Sat Problems: The “hardest” math questions can vary from person-to-person, just as beauty is in the eyes of the beholder. A practice exam can help you identify the areas that are most difficult.

This College Board study guide has examples of difficult questions and information about each section.

  • Questions about Heart of Algebra
  • Sample questions on Problem Solving and Data Analysis
  • Questions from Passport to Advanced Math
  • Additional Topics sample questions
  • Multiple choice sample questions

Preparation is the best thing you can do for your SAT Math section score improvement and to tackle difficult questions. Knowing what to expect and practicing will help you succeed, even when the official test date comes around.

Even if the school does not require SAT/ACT scores, they can have an impact on your admission prospects. Use our College Match tool to find out what schools want in a student, and which SAT score should you aim for.

Top Hardest SAT Math Questions

Question 1

Hard Math Sat Problems

People see this question quickly and assume it’s asking for the laptop’s price with the tax discount, says SAT Blog Love The SAT. Pay attention, it is asking for the original cost of the computer.

Alma pays 8% sales tax. This can be expressed as 108% of price. A 20% discount is also available, which means that Alma pays 80% of the price or 0.8.

If p is Alma’s total payment to the cashier, and x the original price for the laptop, then the equation will read as follows:

p = (1.08)(0.8)(x).

Divide both sides by (1.08)(0.8) to solve for x.

x = p/(1.08)(0.8).

The correct answer to this question is “D.”

Question 2

Hard Math Sat Problems

The price per pound for beef (b), when it is equal to the chicken price (c) is what you are trying to find. Or, if b = c, then 2.35 + 0.25x = 1.75+ 0.40x. Dora Seigel, PrepScholar writes that you must find x to put it back in the “b” equation .

Add 1.75 to each side:

2.35(-1.75) + 0.25x = 1.75(-1.75) + 0.40x

This leaves you with 0.06 + 0.25x = 0.40x. Add 0.25x to each side.

0.6 + 0.25x(-0.25x) = 0.40x(-0.25x)

0.60 = 0.15x

Last step:

0.60/0.15 =x

4 = x

Once you have the value of x, it is possible to use it in the equation to calculate the beef price:

b = 2.35 + 0.25x

– 2.35 + 0.25(4)

– 2.35 + 1.

= 3.35

The correct answer to is “D”, $3.35

Question 3: Hard Math Sat Problems

Hard Math Sat Problems

Mark the most important information and determine the question before starting work.

In this instance, you are looking for sinF’s value.

You should start with the basics: triangle ABC is a right triangular, and angle B an angle. This means that AC is the hypotenuse, and BC is one side.

To find the length of the side remaining, you can use the Pythagorean Theorum:

A+ B= C2

A+ 16= 202

A= 20– 162

A = (400)-(1)256

A = 144 = 12.

According to the problem, triangle DEF is very similar to triangle ABC. This means that C and F are the corresponding vertices of sinF = sinC.

You’ll be able to recognize the acronym SOHCAHTOA and know that sin is opposite/hypotenuse.

sin F = sinC = 12/20 = 3/5 = 0.6

The answer to this question is 3/5 or 0.

Question 4

Hard Math Sat Problems

Caroline C. of Chegg wrote that there were a few correct answers. But be careful. This question asks for the absolute value of x. It is not asking for the actual value.

The absolute value of x-3 should be between six to seven. Multiple values of x can work, such as -3.1,-3.2, and so on. You would then write the absolute value of these numbers, such as 3.1,3.2, etc., because that’s what they want.

Question 5

Hard Math Sat Problems

PrepScholar says eight is the power of two. This means you can simplify things before you start:

8x/2y = (23)x/2y = 23x/2y

You can now rewrite the equation 2 (3x-3y) because the numerator AND denominator are the same. It’s so convenient! It was clear that the problem indicated that 3x – 12 = 12.

2(3x-y) = 2(12)

The answer to this question is “A”, 2 (12),.

Question 6

Hard Math Sat Problems

PrepScholar shows a cylindrical grain silo with two cones. Both have formulas to calculate their volume.

Volume of a cone = 1/3 pr 2h

Volume  of a Cylinder = pr 2h

Volume of silo = pr 2h + (1/3 pr 2h).

Simply use the image to determine the radius and height.

p(52)(10) + (2)(1/3) p(52)(5) = (4/3)(250)p = 1047.2

The answer to this question is “D”, 1047.2 cubic feet.

Question 7

Hard Math Sat Problems

First, the graph shows that the yintercept for the graph is 2. This automatically removes “C” from areas where the yintercept is 2.

The graph’s vertex is located at x = 0. This means that the “b”, in the quadratic equation 2 + Bx + C, must be 0. The graph would shift to the right or left if it were not. You can use the FOIL method to rule out “B”, and “D”. PrepScholar provides a detailed explanation of the FOIL method and how it can be applied to this question.

The answer to this question is “A”, y = x 2 + 2.

Question 8

Hard Math Sat Problems

If you know the length of one radius of a circle, you know them all.

Here, the problem tells you that sides AB and AO of a triangle are equal. BO and AO are circle radii. AO and BO are equal because circle radii are always equal. That means that triangle ABO is an equilateral triangle, and all of its angles measure 60 degrees.

The answer is “D,” 60 degrees.

Question 9

Hard Math Sat Problems

Prepscholar says speed is important for the SAT. Imagine that RS is the circumference of a complete circle. This is possible because the image shows two radii, and two half-circles. Add them together and you get one circle.

Circumference = Pd, so “C” is 12p.

Question 10: Hard Math Sat Problems

Hard Math Sat Problems

PrepScholar recommends plugging in real numbers to a theoretical math question to figure out the correct answer.

Let’s say a = 3 and b = 2. Which of the options results in an odd number?

A: 3 x 2 = 6

B: 3 + 3 = 6

C: 2(2+3) = 10

D: 3 + 2(2) = 7

E: 2(3) + 2 = 8

The answer is “D,” a + 2b.

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