SAT Math Practice Questions: Topic Wise For A High Score

The SAT exam is designed by the College Board and is one of the most widely accepted admission tests in the US. Hence, getting a high score on the SAT test is of utmost importance for high school students who want to pursue their education in the USA. The key to getting a good SAT score in the SAT math test is to practice some of the hardest SAT Math Questions. Several books and online guides attempt to provide SAT math sample questions, but unfortunately, many of them are not on par with the difficult standard of the actual SAT Math Question. They may hence not prepare you enough for the test day. In this article, we will look into the different types of SAT maths questions, including SAT geometry practice questions, algebra and trigonometry practice questions, etc., to help you improve your math skills.

Table of Contents

Before we look into the SAT test example math questions, let us have an overview of the SAT math section to help you prepare better for the SAT math exam.

SAT Math Question Papers: Sections of the Test

The SAT exam comprises an evidence-based reading section, a writing section in English, and a math section. In this article, we will look into the SAT test questions math section alone. The SAT exam questions maths section consists of 58 questions in two sections:

No Calculator Section

The No Calculator section has 20 questions in total. The types of questions in this section include the following:

• 15 multiple-choice questions
• 5 grid-ins math questions

Calculator Allowed Section

This section consists of 38 questions, with 30 multiple choice questions and 8 grid-in math problems. Now, let us look into the SAT example math questions in detail for each of the math sections. SAT Maths Syllabus 2022

Sample SAT Math Questions

Both easy SAT Math Question and hard SAT Math Question are given across the different math topics. The following are the major math topics that are part of the SAT Math Question section:

• Heart of algebra
• Problem-solving and data analysis
• Passport to advanced math

Heart of Algebra

Algebra is the topic where the majority of the math questions are from. Various algebra topics are covered under approximately 19 questions in the SAT math section. The heart of algebra includes the following topics:

• Linear equations
• Linear inequalities
• Linear functions
• System of equations
• Systems of linear inequalities
• Relationship among linear equations and their inequalities
• Exponents

Sample SAT Math Question for Heart of Algebra TopicsQ1. Linear Equation Ten added to the product of a number and three is equal to twice the number. Write this statement as an equation.

1. 10(x+3) = 2x
2. 3x +10 = 2x
3. 3(x+10) = 2x
4. 10x + 3 = 2x

Solution X represents the unknown number. Product of a number and three = 3x 10 added to the product of a number and three = 10 + 3x Twice the number = 2x Hence, ten added to the product of a number and three is equal to twice the number can be written as 3x + 10 = 2x Q2. Linear Inequalities  | 4x + 14 | > 30. What is the possible value of x?

1. 1
2. -3
3. 0
4. 7

Solution 4x + 14 > 30    | 4x + 14 < -30 4x > 16            | 4x < -44 x > 4                | x < -11 Anything between -11 and 4 will not work. Hence, 7 is the possible value of x. Q3. Linear Functions Find the point at which these two lines intersect: 2x + 5y = 8; -2x + 2y = −1.

1. (1,3/2)
2. (3/2,1)
3. (−3/2,1)
4. (1,−3/2)

Solution Add both the equations: 2x + (-2x) + 5y + 2y = 8 + (-1) 7y = 7 y = 1 Using y = 1 in the first equation gives, 2x + 5(1) = 8 2x + 5 = 8 2x = 3 x = 3/2 So, the point of intersection is at (3/2, 1) Q4. System of Equations 7x + 3y = 20 and –4x – 6y = 11. Find the value of 3x – 3y.

1. 27
2. 6
3. 16
4. 31

Solution Adding both the equations gives, 7x + (-4x) + 3y + (-6y) = 20 + 11 3x – 3y = 31 Hence, the answer is 31. Q5. Systems of Linear Inequalities  If 3x – y > 6 and y – 2x > 9, which of the following must be true?

1. x > 15
2. x > y
3. y < 10
4. x < 3

Solution Adding both the equations gives, 3x + (-2x) + (-y) + y > 6 + 9 x > 15 Hence, the answer is x > 15. Q6. Exponents If (300)(400) = (12)10n, n =

1. 3
2. 2
3. 4
4. 7
5. 12

Solution (300)(400) = (12)10n 120000 = (12)10n 10000 = 10n 104 = 10n n = 4

Problem Solving & Data Analysis

This section tests your ability to solve real-world problems and includes topics such as:

• Ratio
• Proportion
• Percentage
• Data interpretation using scatterplots, graphs, tables, and equations
• Probability
• Statistics – mean, median and mode

Sample Questions for  Problem Solving & Data Analysis TopicsQ1. Ratio, Proportion A cafeteria with 40 tables can seat 600 people. Some tables can seat 10 people, and some can sit 20 people. What is the ratio of the number of 10-person tables to the number of 20-person tables?

1. 2:1
2. 4:1
3. 1:1
4. 1:4
5. 1:2

Solution No. of 10-person tables = x No. of 20-person tables = y Total tables, x + y = 40 ——- equation (1) No. of people in 10-person tables = 10x No. of people in 20-person tables = 20y Total people, 10x + 20y = 600  ———- equation (2) Equation (1) x 10 gives, 10x + 10y = 400 Subtracting this equation with equation (2) gives, 10x – 10x + 20y – 10y = 600 – 400 10y = 200 y = 20 Substituting y = 20 in equation (1) gives, x + 20 = 40 x = 20. Both x and y are equal to 20. Hence, they are in the ratio of 1:1. Q2. Percentage  Write as a fraction: 22%

1. ⅔
2. 11/100
3. 4/7
4. 4/9
5. 11/50

Solution 22% = 22/100 = 11/50 Q3. Statistics The average (arithmetic mean) of m, n and p is 8. If m + n = 15 then p equals:

1. 9
2. 7.5
3. 8
4. 24
5. 15

Solution (m + n + p) / 3 = 8 m + n + p = 24 15 + p = 24 p = 9 Hence, the solution is 9.

Passport to Advanced Math

This section covers topics that students learn before going on to advanced maths. The following are the topics covered in this section:

• Operations with polynomial
• Rewriting expressions
• Quadratic function
• Quadratic equation
• Exponential functions, equations, expressions, and radicals
• Exponential growth
• Dividing polynomials by a linear equation
• Solving rational equations
• Systems of equations
• Relationships between algebraic and graphical representations of functions

Sample Passport to Advanced Maths Practice QuestionsQ1. Operations With Polynomial  Which of the following is a prime factor of n4−32n2+256?

1. n2−4n+16
2. n2+4n+16
3. None of the other responses gives a correct answer.
4. n2−4n−16
5. n2+4n−16

Solution n4 – 32n2 + 256 = (n2)2 – 2(16)(n2) + 162 It is in the format a2 – 2ab + b2 = (a-b)2 Hence, it can be rewritten as (n2 – 16)2 n2 – 16 is in the format a2 – b2 which is equal to (a + b)(a – b). n2 – 16 = (n + 4)(n – 4) (n2 – 16)2 =  (n + 4)2(n – 4)2 These are the prime factors. As they are not present in the options, option c is the correct answer. Q2. Rewriting Expressions If Jill walks 100ft in 20 secs, how long will it take Jill to walk 1500ft?

1. 100 secs
2. 200 secs
3. 30 secs
4. 300 secs
5. 400 secs

Solution 100 ft = 20 secs 1500 ft = x secs x = (20)(1500) / 100 = 30,000 / 100 = 300 secs Q3. Quadratic Function If x2   + 2x – 1 = 7, which answers for x are correct?

1. x = -4, x = -2
2. x = 8, x = 0
3. x = -3, x = 4
4. x = -4, x = 2
5. x = -5, x = 1

Solution x2 + 2x – 1 = 7 x2 + 2x – 8 = 0 x2 + 4x – 2x – 8 = 0 (x + 4)(x – 2) = 0 The digits, x = -4, x = 2 are the solution for this expression Q4. Dividing Polynomials by a Linear Equation By what expression can 3x + 7 be multiplied to yield the product 6×3+20×2+5x−21?

1. 2×2 – x − 3
2. 2×2 + x – 3
3. 2×2 + 2x – 3
4. 2×2 – 3

Solution Divide  6×3+20×2+5x−21 by 3x + 7 using the long division method. The answer will be 2×2 + 2x – 3.

Additional Topics in Maths

The SAT math section has additional topics, such as SAT geometry questions, in addition to the above-mentioned major topics. Some of the topics could be:

• Integer and complex numbers
• Geometry
• Working with a right triangle, length of the hypotenuse, and sides area and perimeter of the triangle
• Circle radius, area, and circumference
• Trigonometric functions with sine, cosine, tangent, etc.
• Fractions – Numerator and Denominator

Q1. SAT Geometry Practice Question for Triangle In the right triangle ABC, angle ABC = 2x and angle BCA = x/2. What is the value of x?

1. 36
2. 24
3. 30
4. 32
5. 48

Solution The interior angles in a triangle add up to 180 degrees. As it is a right triangle, one angle is 90 degrees. Hence, the remaining two angles add up to 90 degrees. 2x + x/2 = 90 (4x + x) / 2 = 90 5x = 180 x = 36 Hence, the value of x is 36.

Conclusion

Preparing yourself for the SAT math exam may seem like a tough task, but with the right study materials, practising with samples of previous year papers like SAT geometry practice questions, and the right study strategy, you can ace the SAT math section with really good scores. Contact LeapScholar to aid you in your SAT preparation.

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