240 SAT MATH QUESTIONS & ANSWERS FROM 800
SCORER QUESTIONS AND CORRECT ANSWERS WITH
DETAILED RATIONALES
Questions 1–50: Heart of Algebra (Linear Equations, Inequalities, and
Systems)
Question 1
If 3x + 7 = 22, what is the value of x?
A) 3
B) 5
C) 7
D) 9
Correct Answer: B
Rationale: Subtract 7 from both sides: 3x = 15. Divide by 3: x = 5.
Question 2
What is the slope of the line passing through the points (2, 5) and (6, 13)?
A) 1
B) 2
C) 3
,D) 4
Correct Answer: B
Rationale: Slope = (13 − 5)/ (6 − 2) = 8/4 = 2.
Question 3
Solve for x: 2(x − 4) = 3x + 6
A) −14
B) −10
C) 10
D) 14
Correct Answer: A
Rationale: 2x − 8 = 3x + 6 → −8 − 6 = 3x − 2x → −14 = x.
Question 4
If 5y + 3 = 2y − 9, what is the value of y?
A) −4
B) −2
C) 2
D) 4
,Correct Answer: A
Rationale: 5y − 2y = −9 − 3 → 3y = −12 → y = −4.
Question 5
A line has a slope of −3 and passes through the point (1, 2). What is its
equation in slopeintercept form?
A) y = −3x + 5
B) y = −3x − 1
C) y = 3x + 5
D) y = 3x − 1
Correct Answer: A
Rationale: y − 2 = −3(x − 1) → y = −3x + 3 + 2 = −3x + 5.
Question 6
What is the xintercept of the line y = 4x − 12?
A) −12
B) −3
C) 3
D) 12
, Correct Answer: C
Rationale: Set y = 0: 0 = 4x − 12 → 4x = 12 → x = 3.
Question 7
Solve the inequality: 3x − 7 > 11
A) x > 6
B) x > 4
C) x < 6
D) x < 4
Correct Answer: A
Rationale: 3x > 18 → x > 6.
Question 8
If 2a + 3b = 17 and a = 4, what is the value of b?
A) 2
B) 3
C) 4
D) 5
SCORER QUESTIONS AND CORRECT ANSWERS WITH
DETAILED RATIONALES
Questions 1–50: Heart of Algebra (Linear Equations, Inequalities, and
Systems)
Question 1
If 3x + 7 = 22, what is the value of x?
A) 3
B) 5
C) 7
D) 9
Correct Answer: B
Rationale: Subtract 7 from both sides: 3x = 15. Divide by 3: x = 5.
Question 2
What is the slope of the line passing through the points (2, 5) and (6, 13)?
A) 1
B) 2
C) 3
,D) 4
Correct Answer: B
Rationale: Slope = (13 − 5)/ (6 − 2) = 8/4 = 2.
Question 3
Solve for x: 2(x − 4) = 3x + 6
A) −14
B) −10
C) 10
D) 14
Correct Answer: A
Rationale: 2x − 8 = 3x + 6 → −8 − 6 = 3x − 2x → −14 = x.
Question 4
If 5y + 3 = 2y − 9, what is the value of y?
A) −4
B) −2
C) 2
D) 4
,Correct Answer: A
Rationale: 5y − 2y = −9 − 3 → 3y = −12 → y = −4.
Question 5
A line has a slope of −3 and passes through the point (1, 2). What is its
equation in slopeintercept form?
A) y = −3x + 5
B) y = −3x − 1
C) y = 3x + 5
D) y = 3x − 1
Correct Answer: A
Rationale: y − 2 = −3(x − 1) → y = −3x + 3 + 2 = −3x + 5.
Question 6
What is the xintercept of the line y = 4x − 12?
A) −12
B) −3
C) 3
D) 12
, Correct Answer: C
Rationale: Set y = 0: 0 = 4x − 12 → 4x = 12 → x = 3.
Question 7
Solve the inequality: 3x − 7 > 11
A) x > 6
B) x > 4
C) x < 6
D) x < 4
Correct Answer: A
Rationale: 3x > 18 → x > 6.
Question 8
If 2a + 3b = 17 and a = 4, what is the value of b?
A) 2
B) 3
C) 4
D) 5
