Complete this realistic SAT Math exam, featuring Module 2, and strengthen the algebra, functions, percentages, quadratics, and problem-solving skills needed to choose the best answer under timed pressure. These modules are designed to mirror the feel of the real exam, helping you build accuracy, confidence, and control as you work through each problem with speed and precision. Each module includes 22 questions and is timed for 35 minutes.
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Question 1:
Solve for x: 3x – 5 = 16.A. 5
B. 6
C. 7
D. 8Correct answer: C
Why C is correct:
Add 5 to both sides: 3x = 21. Then divide by 3: x = 7.Why the others are incorrect:
A. 3(5) – 5 = 10
B. 3(6) – 5 = 13
D. 3(8) – 5 = 19Question 2:
Consider a 30-60-90 triangle with hypotenuse 20.
Find the exact length of the longer leg.
longer leg = _____
Answer: 10√3
Explanation:
In a 30-60-90 triangle, the short leg is half the hypotenuse.
Short leg = 20/2 = 10
The longer leg = 10√3Question 3:
Solve for x: (x / 2) + 4 = 9.A. 8
B. 10
C. 12
D. 14Correct answer: B
Why B is correct:
Subtract 4 from both sides: x / 2 = 5. Then multiply by 2: x = 10.Why the others are incorrect:
A. 8 / 2 + 4 = 8
C. 12 / 2 + 4 = 10
D. 14 / 2 + 4 = 11Question 4:
If 2x + y = 11 and y = 5, what is the value of x?A. 3
B. 4
C. 5
D. 6Correct answer: A
Why A is correct:
Substitute y = 5: 2x + 5 = 11. Then 2x = 6, so x = 3.Why the others are incorrect:
B. 2(4) + 5 = 13
C. 2(5) + 5 = 15
D. 2(6) + 5 = 17Question 5:
Solve for x: 2(x + 3) + 2 = 18.A. 5
B. 6
C. 8
D. 9Correct answer: A
Why A is correct:
Distribute first: 2x + 6 + 2 = 18. So 2x + 8 = 18, then 2x = 10, so x = 5.Why the others are incorrect:
B. 2(6 + 3) + 2 = 20
C. 2(8 + 3) + 2 = 24
D. 2(9 + 3) + 2 = 26Question 6:
Solve for x: |x – 2| = 2, where x > 2.A. 2
B. 3
C. 4
D. 5Correct answer: C
Why C is correct:
The equation gives x – 2 = 2 or x – 2 = -2, so x = 4 or x = 0. Since x > 2, only x = 4 works.Why the others are incorrect:
A. 2 does not satisfy x > 2
B. |3 – 2| = 1
D. |5 – 2| = 3Question 7:
If 3x – 4 = 14, what is the value of x?A. 4
B. 5
C. 6
D. 7Correct answer: C
Why C is correct:
Add 4 to both sides: 3x = 18. Then divide by 3: x = 6.Why the others are incorrect:
A. 3(4) – 4 = 8
B. 3(5) – 4 = 11
D. 3(7) – 4 = 17Question 8:
A cone has height 12 inches and volume 100π cubic inches.
Find the radius of the base.
r = _____
Answer: 5
Explanation:
Use the cone volume formula:
V = (1/3)πr²h100π = (1/3)πr²(12)
100π = 4πr²
100 = 4r²
25 = r²
r = 5Question 9:
What is the slope of the line through the points (2, 1) and (4, 9)?A. 2
B. 3
C. 4
D. 5Correct answer: C
Why C is correct:
Use the slope formula: (9 – 1) / (4 – 2) = 8 / 2 = 4.Why the others are incorrect:
A. The slope is not 2
B. The slope is not 3
D. The slope is not 5Question 10:
A taxi charges 2 dollars to start a ride and 2 dollars per mile. What is the total cost, in dollars, of a 1.5-mile ride?A. 5
B. 6
C. 7
D. 8Correct answer: A
Why A is correct:
Cost = 2 + 2(1.5) = 2 + 3 = 5.Why the others are incorrect:
B. 6 is too high
C. 7 is too high
D. 8 is too highQuestion 11:
Solve for x: 5x – 8 = 27.A. 6
B. 7
C. 8
D. 9Correct answer: B
Why B is correct:
Add 8 to both sides: 5x = 35. Then divide by 5: x = 7.Why the others are incorrect:
A. 5(6) – 8 = 22
C. 5(8) – 8 = 32
D. 5(9) – 8 = 37Question 12:
Solve for x: 2(x + 1) = 12.A. 3
B. 4
C. 5
D. 6Correct answer: C
Why C is correct:
Divide both sides by 2: x + 1 = 6. Then subtract 1: x = 5.Why the others are incorrect:
A. 2(3 + 1) = 8
B. 2(4 + 1) = 10
D. 2(6 + 1) = 14Question 13:
Solve for x: (x / 2) – 1 = 3.A. 6
B. 8
C. 10
D. 12Correct answer: B
Why B is correct:
Add 1 to both sides: x / 2 = 4. Then multiply by 2: x = 8.Why the others are incorrect:
A. 6 / 2 – 1 = 2
C. 10 / 2 – 1 = 4
D. 12 / 2 – 1 = 5Question 14:
If 4x + y = 15 and y = 3, what is the value of x?A. 2
B. 3
C. 4
D. 5Correct answer: B
Why B is correct:
Substitute y = 3: 4x + 3 = 15. Then 4x = 12, so x = 3.Why the others are incorrect:
A. 4(2) + 3 = 11
C. 4(4) + 3 = 19
D. 4(5) + 3 = 23Question 15:
Solve for x: 3(x + 2) – 3 = 24.A. 7
B. 8
C. 9
D. 10Correct answer: A
Why A is correct:
Distribute: 3x + 6 – 3 = 24. So 3x + 3 = 24, then 3x = 21, so x = 7.Why the others are incorrect:
B. 3(8 + 2) – 3 = 27
C. 3(9 + 2) – 3 = 30
D. 3(10 + 2) – 3 = 33Question 16:
Solve for x: |x – 1| = 4, where x > 1.A. 2
B. 3
C. 4
D. 5Correct answer: D
Why D is correct:
The equation gives x – 1 = 4 or x – 1 = -4, so x = 5 or x = -3. Since x > 1, only x = 5 works.Why the others are incorrect:
A. |2 – 1| = 1
B. |3 – 1| = 2
C. |4 – 1| = 3Question 17:
A sector of a circle has radius 12 and arc length 8π.
Find the measure of the central angle, in degrees.
central angle = _____°
Answer: 120
Explanation:
Use the arc length formula in radians:s = rθ
Substitute:
8π = 12θ
θ = 8π / 12
θ = 2π / 3Now convert radians to degrees:
(2π / 3) · (180 / π) = 120
So the central angle is 120°.
Question 18:
A studio charges a 9 dollar sign-up fee plus 4 dollars per class. If the total cost is 37 dollars, how many classes were taken?A. 4
B. 5
C. 6
D. 7Correct answer: D
Why D is correct:
Set up the equation: 9 + 4c = 37. Subtract 9 to get 4c = 28. Divide by 4: c = 7.Why the others are incorrect:
A. 9 + 4(4) = 25
B. 9 + 4(5) = 29
C. 9 + 4(6) = 33Question 19:
What is the slope of the line through the points (1, 3) and (3, 11)?A. 3
B. 4
C. 5
D. 6Correct answer: B
Why B is correct:
Use the slope formula: (11 – 3) / (3 – 1) = 8 / 2 = 4.Why the others are incorrect:
A. The slope is not 3
C. The slope is not 5
D. The slope is not 6Question 20:
A taxi charges 3 dollars to start a ride and 2 dollars per mile. What is the total cost, in dollars, of a 2-mile ride?A. 5
B. 6
C. 7
D. 8Correct answer: C
Why C is correct:
Cost = 3 + 2(2) = 3 + 4 = 7.Why the others are incorrect:
A. Too low
B. Too low
D. Too highQuestion 21:
Solve for x: 4x – 9 = 19.A. 6
B. 7
C. 8
D. 9Correct answer: B
Why B is correct:
Add 9 to both sides: 4x = 28. Then divide by 4: x = 7.Why the others are incorrect:
A. 4(6) – 9 = 15
C. 4(8) – 9 = 23
D. 4(9) – 9 = 27Question 22:
Consider right triangle ABC with angle C = 90°.
AC = 9, BC = 12Find tan A.
tan A = _____
Answer: 4/3
Explanation:
tan A = opposite / adjacent
For angle A, the opposite side is BC and the adjacent side is AC.
tan A = 12/9 = 4/3Next Step:
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