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    20 Hardest SAT Math Questions Ever

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    The SAT Math section is known for its tricky problems that can challenge even the most prepared students. Whether you’re aiming for a perfect score or just want to improve, tackling the hardest SAT Math questions is a key to success. In this blog, we’ll walk through 20 of the hardest SAT Math questions, break them down, and share helpful tips for mastering them.

    Understanding the SAT Math Section

    About jumping into the hardest questions, it is first helpful to understand what to expect for the SAT Math test. There are two parts: one which includes a calculator and one that does not. The complexity of questions increases significantly, especially in algebra, geometry, and other data analysis areas. Knowing how the test will be structured will help you in tackling each question properly.

    Top 20 Hardest SAT Math Questions

    Now, let’s dive into some of the toughest SAT Math questions ever. These problems are scattered across all the categories-from algebra to geometry to word problems-and we chose them based on how difficult and relevant they would be to the kind of stuff you might encounter on the test.

    1. The measure of angle R is 2π/3 radians. The measure of angle T is 5π/12 radians greater than the measure of angle R. What is the measure of angle T, in degrees? 

    A) 75 

    B) 120 

    C) 195 

    D) 390

    2. In the xy-plane, the point (a, b) lies on the line with equation y = x + c, where c is a constant. The point with coordinates (3a, 7b) lies on the line with equation y = 2x + c. If a ≠ 0, what is the value of a/b?

    3. For line h, the table shows three values of x and their corresponding values of y. Line k is the result of translating line h down 5 units in the xy-plane. What is the x-intercept of line k? 

    x y
    18 130
    23 160
    26 178

    A) (− 26/3 , 0)

    B) (− 9/2 , 0)

    C) (− 11/3 , 0)

    D) (− 17/6 , 0) 

    4. A model estimates that at the end of each year from 2015 to 2020, the number of squirrels in a population was 150% more than the number of squirrels in the population at the end of the previous year. The model estimates that at the end of 2016, there were 180 squirrels in the population. Which of the following equations represents this model, where n is the estimated number of squirrels in the population t years after the end of 2015 and t ≤ 5 ? 

    A) n = 72(1.5)t 

    B) n = 72(2.5)t 

    C) n = 180(1.5)t 

    D) n = 180(2.5)t 

    5. A rectangular prism has dimensions 60 inches by 40 inches by 30 inches. A solid cylinder with a radius of 20 inches and height of 30 inches is inside the prism, such that the cylinder touches the bottom of the prism and is centered along the longer dimension of the base. To the nearest cubic inch, what is the volume of the space in the prism not taken up by the cylinder?

    A) 28,500

    B) 32,000

    C) 34,300

    D) 36,000

    6.     q = (1/2) nv²

    The dynamic pressure q generated by a fluid moving with velocity v can be found using the formula above, where n is the constant density of the fluid. An aeronautical engineer uses the formula to find the dynamic pressure of a fluid moving with velocity v and the same fluid moving with velocity 1.5v. What is the ratio of the dynamic pressure of the faster fluid to the dynamic pressure of the slower fluid?

    7.        5x + 7y = 1 , ax + by = 1 

    In the given pair of equations, a and b are constants. The graph of this pair of equations in the xy-plane is a pair of perpendicular lines. Which of the following pairs of equations also represents a pair of perpendicular lines? 

    A) 10x+ 7y = 1 

         ax − 2by = 1 

    B) 10x + 7y = 1 

         ax + 2by = 1 

    C) 10x + 7y = 1 

         2ax+ by=  1 

    D) 5x − 7y  = 1

         ax +by = 1 

    8. Circle A has a radius of 3n and circle B has a radius of 129n, where n is a positive constant. The area of circle B is how many times the area of circle A? 

    A) 43 

    B) 86 

    C) 129 

    D) 1,849

    9. Which of the following expressions is equivalent to a^(11/12), where a > 0?

    A) (a^132)^(1/12)

    B) (a^132)^(1/144)

    C) (a^132)^(1/121)

    D) (a^132)^(1/11)

    10. Little’s law can be applied to any part of the store, such as a specific section or the customer service counters. The store manager determines that, during business hours, approximately 84 customers per hour make a purchase, and each of these customers spends an average of 5 minutes in the customer service line. At any given moment during business hours, about how many customers, on average, are waiting in the customer service line to make a purchase at the Bargain Mart?

    Want to know the Answers? Find it here

    11. The recommended daily calcium intake for a 20-year-old person is 1,000 milligrams (mg). One cup of milk contains 299 mg of calcium, and one cup of juice contains 261 mg of calcium. Which of the following inequalities represents the possible number of cups of milk, m, and cups of juice, j, a 20-year-old person could drink in a day to meet or exceed the recommended daily calcium intake from these drinks alone? 

    A) 299m + 261j  1,000

     B) 299m + 261j > 1,000

    C) 299m + 261j ≥ 1,000

    D) 299m + 261j < 1,000

    12. A cube has an edge length of 68 inches. A solid sphere with a radius of 34 inches is inside the cube, such that the sphere touches the center of each face of the cube. To the nearest cubic inch, what is the volume of the space in the cube not taken up by the sphere? 

    A) 149,794

    B) 164,500 

    C) 190,955 

    D) 310,800 

    13. In a right triangle, one angle measures y°, where sin y° = . What is cos(90° − y°)?

    14. The equation C = 59 (F – 32) shows how temperature f, measured in degrees Fahrenheit, relates to temperature c, measured in degrees Celsius. Based on the equation, which of the following must be true?

    1. A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 59 degree Celsius.
    2. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
    3. A temperature increase of 59 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.

    A)1 only

    B) 2 only

    C) 3 only

    D) None of them

    15. Mr. Parker is driving from his home to his office. The total distance is 90 miles, divided into three segments:

    Segment 1: 30 miles

    Segment 2: 40 miles

    Segment 3: 20 miles

    If Mr. Parker starts his drive at 7:30 a.m., he can maintain an average speed of 60 miles per hour (mph) for all three segments of the drive. However, if Mr. Parker starts his drive at 8:00 a.m., the travel time for Segment 3 increases by 25% due to heavier traffic. The travel times for Segment 1 and Segment 2 remain unchanged. How many more minutes does Mr. Parker take to complete his drive if he starts at 8:00 a.m. compared to if he starts at 7:30 a.m.?

    A) 5 minutes
    B) 15 minutes
    C) 12 minutes
    D) 20 minutes

    16.        (6 – 2i) / (4 – 3i)

    If the expression above is rewritten in the form a + bi, where a and b are real numbers, what is the value of a? (Note: i = √-1)

    17. For a polynomial q(x), the value of q(4) is 5. Which of the following must be true about q(x)?

    A) x−6 is a factor of q(x). 

    B) x−3 is a factor of q(x). 

    C) x+3 is a factor of q(x). 

    D) The remainder when q(x) is divided by x−4 is 5.

    18. A grain silo is built from two right circular cones and a right circular cylinder with internal measurements represented by the figure above. Of the following, which is closest to the volume of the grain silo, in cubic feet?

    Body Grainsilo

    A) 261.8

    B) 785.4

    C) 1047.2

    D) 916.3

    19. What expression will we get after simplifying this: (y+12)/(x-8) + [y(x-8)/x square y-8xy)?

    20. The incomplete table below summarizes the number of left-handed students and right-handed students by gender for the eighth grade students at Keisel Middle School. There are 5 times as many right-handed female students as there are left-handed female students, and there are 9 times as many right-handed male students as there are left-handed male students. If there are a total of 18 left-handed students and 122 right-handed students in the school, which of the following is closest to the probability that a right-handed student selected at random is female? (Note: Assume that none of the eighth-grade students are both right-handed and left-handed.)

    Body Handedness Chart

    A) 0.410

    B) 0.357

    C) 0.333

    D) 0.250

    Answers
    1. (C)
    2. 6/5
    3. (D)
    4. (B)
    5. (C)
    6. 2.25
    7. (B)
    8. (D)
    9. (B)
    10. 7 Customers
    11. (C)
    12. (A)
    13. 2/3
    14. (D)
    15. (A)
    16. 6/5
    17. (D)
    18. (C)
    19. (y+13x)x-8/x(x-8)
    20. (A)

    Tips and Strategies for Solving the Hardest SAT Math Questions

    Tackling these tough problems requires more than just knowing formulas. Here are some tips to help you succeed:

    • Understand the question thoroughly: Read carefully, and identify what is being asked before diving into the math.
    • Eliminate obvious wrong answers: Use the process of elimination to make educated guesses, especially when time is limited.
    • Practice, practice, practice: The more problems you solve, the more familiar you will become with the patterns in SAT Math questions.

    How to Practice and Improve Your SAT Math Skills

    To prepare for these challenging questions, you need to practice consistently. Here are some ways to improve your skills:

    • Take full-length practice tests to get used to the pacing and pressure of the exam.
    • Focus on weaknesses: Review mistakes, and focus on concepts that are commonly tested.
    • Use online platforms that offer SAT Math practice questions, as they provide real-time feedback and guidance. You can even consider the Moonpreneur website.

    Want to ace the Geometry section? Here are the SAT Geometry Questions You Must Practice Today

    Conclusion

    The hardest SAT Math questions are tough, but with the right approach, you can tackle them with confidence. Practice is key, so don’t get discouraged by difficult problems. The more you practice, the better prepared you will be. Just stay consistent, and you will be ready for whatever the SAT throws your way.

    Want to excite your child about math and sharpen their math skills? Moonpreneur’s online math curriculum is unique as it helps children understand math skills through hands-on lessons, assists them in building real-life applications, and excites them to learn math. You can opt for our Advanced Math or Vedic Math+Mental Math courses. Our Math Quiz for grades 3rd, 4th, 5th, and 6th helps in further exciting and engaging in mathematics with hands-on lessons.

    Moonpreneur

    Moonpreneur

    Moonpreneur is an ed-tech company that imparts tech entrepreneurship to children aged 6 to 15. Its flagship offering, the Innovator Program, offers students a holistic learning experience that blends Technical Skills, Power Skills, and Entrepreneurial Skills with streams such as Robotics, Game Development, App Development, Advanced Math, Scratch Coding, and Book Writing & Publishing.
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