CALIFORNIA – SAT MATH – COMPREHENSIVE PRACTICE TESTS, QUESTIONS & DETAILED SOLUTIONS –
2026/2027 – QUESTIONS AND ANSWERS | VERIFIED AND WELL DETAILED ANSWERS | PLUS
RATIONALES | GUARANTEED PASS | LATEST EXAM UPDATE
CORE DOMAINS
Heart of Algebra
Problem Solving and Data Analysis
Passport to Advanced Math
Geometry and Trigonometry
Functions and Linear Models
Ratios, Proportions, and Percentages
Statistics and Probability
Mathematical Reasoning and Critical Thinking
INTRODUCTION
This comprehensive practice assessment is designed to prepare students for the SAT Math
examination by assessing essential mathematical knowledge, reasoning ability, and applied problem-
solving skills. It evaluates understanding across algebra, advanced mathematics, data analysis,
geometry, and trigonometry. Questions include multiple-choice and scenario-based formats that
emphasize real-world application, interpretation, and professional decision-making. The assessment
supports critical thinking, analytical reasoning, and precise mathematical communication. It provides a
rigorous and balanced review to help students build confidence and achieve success on the SAT Math
section.
SECTION ONE – QUESTIONS 1–100
Question 1
If 3x + 5 = 20, what is the value of 6x + 10?
A. 20
B. 30
C. 40
D. 50
🟢 Correct answer: B
🔴 Explanation: Since 6x + 10 is exactly twice 3x + 5, and 3x + 5 = 20, the value is 2 × 20 = 40. Wait,
let me recalculate: 6x + 10 = 2(3x + 5) = 2(20) = 40. So the correct answer is C, not B. Let me correct:
6x + 10 = 40. The correct option is C.
Question 1 (corrected)
If 3x + 5 = 20, what is the value of 6x + 10?
A. 20
,B. 30
C. 40
D. 50
🟢 Correct answer: C
🔴 Explanation: Since 6x + 10 = 2(3x + 5), and 3x + 5 = 20, the value is 2 × 20 = 40.
Question 2
A line passes through (2, 3) and (6, 11). What is its slope?
A. 1
B. 2
C. 3
D. 4
🟢 Correct answer: B
🔴 Explanation: Slope = (11 − 3)/(6 − 2) = 8/4 = 2.
Question 3
If f(x) = 2x² − 3x + 1, what is f(2)?
A. 1
B. 2
C. 3
D. 4
🟢 Correct answer: C
🔴 Explanation: f(2) = 2(4) − 3(2) + 1 = 8 − 6 + 1 = 3.
Question 4
A rectangle has length 3x and width 2x. If its area is 54, what is x?
A. 2
B. 3
C. 4
D. 5
🟢 Correct answer: B
🔴 Explanation: Area = 3x · 2x = 6x² = 54, so x² = 9, x = 3.
Question 5
If 2x − 3y = 12 and x = 3, what is y?
A. −2
B. −1
C. 1
D. 2
🟢 Correct answer: A
🔴 Explanation: 2(3) − 3y = 12 → 6 − 3y = 12 → −3y = 6 → y = −2.
Question 6
The average of five numbers is 12. If four of the numbers are 8, 10, 14, and 16, what is the fifth
number?
A. 10
B. 12
,C. 14
D. 16
🟢 Correct answer: B
🔴 Explanation: Sum = 5 × 12 = 60. Known sum = 8 + 10 + 14 + 16 = 48. Fifth = 60 − 48 = 12.
Question 7
If x² − 5x + 6 = 0, what are the possible values of x?
A. 1 and 6
B. 2 and 3
C. −2 and −3
D. 0 and 5
🟢 Correct answer: B
🔴 Explanation: Factor: (x − 2)(x − 3) = 0, so x = 2 or x = 3.
Question 8
A car travels 150 miles in 3 hours. At the same rate, how far will it travel in 5 hours?
A. 200 miles
B. 225 miles
C. 250 miles
D. 275 miles
🟢 Correct answer: C
🔴 Explanation: Rate = 150/3 = 50 mph. Distance = 50 × 5 = 250 miles.
Question 9
If 4x + 2y = 18 and 2x − 2y = 6, what is x?
A. 2
B. 3
C. 4
D. 5
🟢 Correct answer: C
🔴 Explanation: Add equations: 6x = 24 → x = 4.
Question 10
What is the value of √144 + √81?
A. 15
B. 18
C. 21
D. 24
🟢 Correct answer: C
🔴 Explanation: √144 = 12, √81 = 9, sum = 21.
Question 11
A triangle has angles 2x, 3x, and 4x. What is x?
A. 15
B. 20
C. 25
D. 30
, 🟢 Correct answer: B
🔴 Explanation: 2x + 3x + 4x = 180 → 9x = 180 → x = 20.
Question 12
If y = 3x + 2 and x = 4, what is y?
A. 10
B. 12
C. 14
D. 16
🟢 Correct answer: C
🔴 Explanation: y = 3(4) + 2 = 12 + 2 = 14.
Question 13
The ratio of boys to girls in a class is 3:5. If there are 40 students, how many girls are there?
A. 15
B. 20
C. 25
D. 30
🟢 Correct answer: C
🔴 Explanation: Total parts = 8. Girls = 5/8 × 40 = 25.
Question 14
If 5x − 7 = 3x + 9, what is x?
A. 6
B. 7
C. 8
D. 9
🟢 Correct answer: C
🔴 Explanation: 2x = 16 → x = 8.
Question 15
What is the slope of a line perpendicular to y = 2x + 5?
A. −2
B. −1/2
C. 1/2
D. 2
🟢 Correct answer: B
🔴 Explanation: Perpendicular slope is negative reciprocal: −1/2.
Question 16
If a circle has radius 7, what is its area?
A. 14π
B. 21π
C. 49π
D. 77π
🟢 Correct answer: C
🔴 Explanation: Area = πr² = π(7)² = 49π.
2026/2027 – QUESTIONS AND ANSWERS | VERIFIED AND WELL DETAILED ANSWERS | PLUS
RATIONALES | GUARANTEED PASS | LATEST EXAM UPDATE
CORE DOMAINS
Heart of Algebra
Problem Solving and Data Analysis
Passport to Advanced Math
Geometry and Trigonometry
Functions and Linear Models
Ratios, Proportions, and Percentages
Statistics and Probability
Mathematical Reasoning and Critical Thinking
INTRODUCTION
This comprehensive practice assessment is designed to prepare students for the SAT Math
examination by assessing essential mathematical knowledge, reasoning ability, and applied problem-
solving skills. It evaluates understanding across algebra, advanced mathematics, data analysis,
geometry, and trigonometry. Questions include multiple-choice and scenario-based formats that
emphasize real-world application, interpretation, and professional decision-making. The assessment
supports critical thinking, analytical reasoning, and precise mathematical communication. It provides a
rigorous and balanced review to help students build confidence and achieve success on the SAT Math
section.
SECTION ONE – QUESTIONS 1–100
Question 1
If 3x + 5 = 20, what is the value of 6x + 10?
A. 20
B. 30
C. 40
D. 50
🟢 Correct answer: B
🔴 Explanation: Since 6x + 10 is exactly twice 3x + 5, and 3x + 5 = 20, the value is 2 × 20 = 40. Wait,
let me recalculate: 6x + 10 = 2(3x + 5) = 2(20) = 40. So the correct answer is C, not B. Let me correct:
6x + 10 = 40. The correct option is C.
Question 1 (corrected)
If 3x + 5 = 20, what is the value of 6x + 10?
A. 20
,B. 30
C. 40
D. 50
🟢 Correct answer: C
🔴 Explanation: Since 6x + 10 = 2(3x + 5), and 3x + 5 = 20, the value is 2 × 20 = 40.
Question 2
A line passes through (2, 3) and (6, 11). What is its slope?
A. 1
B. 2
C. 3
D. 4
🟢 Correct answer: B
🔴 Explanation: Slope = (11 − 3)/(6 − 2) = 8/4 = 2.
Question 3
If f(x) = 2x² − 3x + 1, what is f(2)?
A. 1
B. 2
C. 3
D. 4
🟢 Correct answer: C
🔴 Explanation: f(2) = 2(4) − 3(2) + 1 = 8 − 6 + 1 = 3.
Question 4
A rectangle has length 3x and width 2x. If its area is 54, what is x?
A. 2
B. 3
C. 4
D. 5
🟢 Correct answer: B
🔴 Explanation: Area = 3x · 2x = 6x² = 54, so x² = 9, x = 3.
Question 5
If 2x − 3y = 12 and x = 3, what is y?
A. −2
B. −1
C. 1
D. 2
🟢 Correct answer: A
🔴 Explanation: 2(3) − 3y = 12 → 6 − 3y = 12 → −3y = 6 → y = −2.
Question 6
The average of five numbers is 12. If four of the numbers are 8, 10, 14, and 16, what is the fifth
number?
A. 10
B. 12
,C. 14
D. 16
🟢 Correct answer: B
🔴 Explanation: Sum = 5 × 12 = 60. Known sum = 8 + 10 + 14 + 16 = 48. Fifth = 60 − 48 = 12.
Question 7
If x² − 5x + 6 = 0, what are the possible values of x?
A. 1 and 6
B. 2 and 3
C. −2 and −3
D. 0 and 5
🟢 Correct answer: B
🔴 Explanation: Factor: (x − 2)(x − 3) = 0, so x = 2 or x = 3.
Question 8
A car travels 150 miles in 3 hours. At the same rate, how far will it travel in 5 hours?
A. 200 miles
B. 225 miles
C. 250 miles
D. 275 miles
🟢 Correct answer: C
🔴 Explanation: Rate = 150/3 = 50 mph. Distance = 50 × 5 = 250 miles.
Question 9
If 4x + 2y = 18 and 2x − 2y = 6, what is x?
A. 2
B. 3
C. 4
D. 5
🟢 Correct answer: C
🔴 Explanation: Add equations: 6x = 24 → x = 4.
Question 10
What is the value of √144 + √81?
A. 15
B. 18
C. 21
D. 24
🟢 Correct answer: C
🔴 Explanation: √144 = 12, √81 = 9, sum = 21.
Question 11
A triangle has angles 2x, 3x, and 4x. What is x?
A. 15
B. 20
C. 25
D. 30
, 🟢 Correct answer: B
🔴 Explanation: 2x + 3x + 4x = 180 → 9x = 180 → x = 20.
Question 12
If y = 3x + 2 and x = 4, what is y?
A. 10
B. 12
C. 14
D. 16
🟢 Correct answer: C
🔴 Explanation: y = 3(4) + 2 = 12 + 2 = 14.
Question 13
The ratio of boys to girls in a class is 3:5. If there are 40 students, how many girls are there?
A. 15
B. 20
C. 25
D. 30
🟢 Correct answer: C
🔴 Explanation: Total parts = 8. Girls = 5/8 × 40 = 25.
Question 14
If 5x − 7 = 3x + 9, what is x?
A. 6
B. 7
C. 8
D. 9
🟢 Correct answer: C
🔴 Explanation: 2x = 16 → x = 8.
Question 15
What is the slope of a line perpendicular to y = 2x + 5?
A. −2
B. −1/2
C. 1/2
D. 2
🟢 Correct answer: B
🔴 Explanation: Perpendicular slope is negative reciprocal: −1/2.
Question 16
If a circle has radius 7, what is its area?
A. 14π
B. 21π
C. 49π
D. 77π
🟢 Correct answer: C
🔴 Explanation: Area = πr² = π(7)² = 49π.
