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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1. Question:
Solve for x: 4x – 5 = 39.A. 9
B. 11
C. 13
D. 15Correct answer: B. 11
Why B is correct:
Add 5 to both sides: 4x = 44. Then divide by 4: x = 11.Why the others are incorrect:
A. 4(9) – 5 = 31
C. 4(13) – 5 = 47
D. 4(15) – 5 = 552. Question:
Consider right triangle ABC with ∠C = 90°.
AB = 26, AC = 10
Find sin B.
sin B = _____
Answer: 5/13
Explanation:
Since AB is the hypotenuse, use the Pythagorean Theorem to find BC.BC² = 26² − 10²
BC² = 676 − 100
BC² = 576
BC = 24For angle B, the opposite side is AC and the hypotenuse is AB.
sin B = AC / AB
sin B = 10 / 26
sin B = 5 / 133. Question:
Solve for x: (x / 2) – 2 = 3.A. 6
B. 8
C. 10
D. 12Correct answer: C. 10
Why C is correct:
Add 2 to both sides: x / 2 = 5. Then multiply by 2: x = 10.Why the others are incorrect:
A. 6 / 2 – 2 = 1
B. 8 / 2 – 2 = 2
D. 12 / 2 – 2 = 44. Question:
A cone has height 15 inches and volume 320π cubic inches.
Find the radius of the base.
r = _____
Answer: 8
Explanation:
Use the cone volume formula.V = (1/3)πr²h
320π = (1/3)πr²(15)
320π = 5πr²
320 = 5r²
64 = r²
r = 85. Question:
Solve for x: |x – 1| = 5, where x > 1.A. 2
B. 4
C. 6
D. 8Correct answer: C. 6
Why C is correct:
|x – 1| = 5 gives x – 1 = 5 or x – 1 = -5, so x = 6 or x = -4. Since x > 1, the only valid answer is 6.Why the others are incorrect:
A. |2 – 1| = 1
B. |4 – 1| = 3
D. |8 – 1| = 76. Question:
A gym charges a 12 dollar sign-up fee plus 4 dollars per class. If the total cost is 32 dollars, how many classes were taken?A. 3
B. 4
C. 5
D. 6Correct answer: C. 5
Why C is correct:
Set up the equation: 12 + 4c = 32. Then 4c = 20, so c = 5.Why the others are incorrect:
A. 12 + 4(3) = 24
B. 12 + 4(4) = 28
D. 12 + 4(6) = 367. Question:
In a circle, a sector has central angle 225° and radius 4.
Find the exact area of the sector.
sector area = _____
Answer: 10π
Explanation:
Use the sector area formula.sector area = (θ / 360)πr²
sector area = (225 / 360)π(4²)
sector area = (5 / 8)π(16)
sector area = 10π8. Question:
A taxi charges 3 dollars to start a ride and 2 dollars per mile. What is the total cost, in dollars, of a 2.5-mile ride?A. 6
B. 7
C. 8
D. 9Correct answer: C. 8
Why C is correct:
Cost = 3 + 2(2.5) = 3 + 5 = 8.Why the others are incorrect:
A. Too low
B. Too low
D. Too high9. Question:
Consider the diagram below.
∠F = 47°
∠D = 79°Find ∠ABC.
∠ABC = _____°
Answer: 54°
Explanation:
We are told that ∠ABC is congruent to ∠IHJ. That means the two horizontal lines are parallel.
Now look at the left transversal DCF.
∠DCE and ∠CFG are corresponding angles, so they are equal.
4x + 7 = (11/2)x − 23
Solve for x:
8x + 14 = 11x − 46
60 = 3x
x = 20Now find ∠DCE:
∠DCE = 4x + 7
∠DCE = 4(20) + 7
∠DCE = 87°At point C, ∠DCE and ∠ECF form a linear pair, so they add to 180°.
∠ECF = 180° − 87°
∠ECF = 93°∠ABC and ∠ECF are corresponding angles, so they are congruent.
Therefore:
∠ABC = 93°
10. Question:
Correct answer: B) 15/17
Explanation:
Since ∠C is 90°, AB is the hypotenuse.AB = √(8² + 15²) = √(64 + 225) = √289 = 17
For angle B:
cos B = adjacent / hypotenuse = BC / AB = 15 / 1711. Question:
Correct answer: 7/13
Explanation:
For angle C:
tan C = opposite / adjacent = AB / AC = 3.5 / 6.53.5 / 6.5 = 35 / 65 = 7 / 13
12. Question:
Correct answer: 7/√58
Explanation:
Since ∠A is 90°, AB and AC are the legs, so BC is the hypotenuse.BC = √(3² + 7²) = √(9 + 49) = √58
For angle B:
sin B = opposite / hypotenuse = AC / BC = 7 / √5813. Question:
A membership charges a 15 dollar sign-up fee plus 4 dollars per visit. If the total cost is 43 dollars, how many visits were made?A. 4
B. 5
C. 6
D. 7Correct answer: D. 7
Why D is correct:
15 + 4v = 43, so 4v = 28 and v = 7.Why the others are incorrect:
A. 15 + 4(4) = 31
B. 15 + 4(5) = 35
C. 15 + 4(6) = 3914. Question:
What is the slope of the line through the points (1, 4) and (3, 12)?A. 3
B. 4
C. 5
D. 6Correct answer: B. 4
Why B is correct:
Slope = (12 – 4) / (3 – 1) = 8 / 2 = 4.Why the others are incorrect:
A. Too small
C. Too large
D. Too large15. Question:
What is the value of sin 60°?A. 1/2
B. √3/2
C. 1
D. 0Correct answer: B. √3/2
Why B is correct:
sin 60° is a standard special-angle value: √3/2.Why the others are incorrect:
A. 1/2 is sin 30°
C. 1 is sin 90°
D. 0 is sin 0° or sin 180°16. Question:
Solve for x: 3x + 2 = 17.A. 4
B. 5
C. 6
D. 7Correct answer: B. 5
Why B is correct:
Subtract 2 from both sides: 3x = 15. Then divide by 3: x = 5.Why the others are incorrect:
A. 3(4) + 2 = 14
C. 3(6) + 2 = 20
D. 3(7) + 2 = 2317. Question:
What is the value of cos 90°?A. √3/2
B. 1/2
C. 0
D. 1Correct answer: C. 0
Why C is correct:
cos 90° = 0.Why the others are incorrect:
A. √3/2 is cos 30°
B. 1/2 is cos 60°
D. 1 is cos 0°18. Question:
Correct answer: B. 4/3
Explanation:
Let:
AD = 9k
DB = 16kThen:
AB = 25k
Use the right-triangle altitude relationship:
AC² = AD · AB
Substitute:
18² = (9k)(25k)
324 = 225k²
k² = 324 / 225
k² = 36 / 25
k = 6 / 5Now find BC using the other altitude relationship:
BC² = DB · AB
BC² = (16k)(25k)
BC² = 400k²Since k = 6/5:
BC² = 400(36/25)
BC² = 576
BC = 24Now find tan A:
tan A = opposite / adjacent
tan A = BC / AC
tan A = 24 / 18
tan A = 4 / 3So the correct answer is 4/3.
19. Question:
Correct answer: B. √21/5
Explanation:
First find the hypotenuse:
AB = AD + DB
AB = 4 + 21
AB = 25In a right triangle with an altitude drawn to the hypotenuse,
BC² = DB · AB
So:
BC² = 21 · 25
BC² = 525
BC = √525
BC = 5√21Now find cos B:
cos B = adjacent / hypotenuse
cos B = BC / AB
cos B = 5√21 / 25
cos B = √21 / 5So the correct answer is √21/5.
20. Question:
What is the value of cos 180°?A. 1
B. 0
C. -1
D. 1/2Correct answer: C. -1
Why C is correct:
cos 180° = -1.Why the others are incorrect:
A. 1 is cos 0°
B. 0 is cos 90°
D. 1/2 is cos 60°21. Question:
A music service charges a 4 dollar sign-up fee plus 3 dollars per month. If the total cost is 19 dollars, how many months were paid for?A. 5
B. 6
C. 7
D. 8Correct answer: A. 5
Why A is correct:
4 + 3m = 19, so 3m = 15 and m = 5.Why the others are incorrect:
B. 4 + 3(6) = 22
C. 4 + 3(7) = 25
D. 4 + 3(8) = 2822. Question:
Correct answer: C. 48
Explanation:
Since ∠A = 30° and ∠C = 90°, triangle ABC is a 30-60-90 triangle.
Let the short leg BC = x.
Then:AC = x√3
AB = 2xFor a right triangle with altitude to the hypotenuse,
DB = BC² / AB
Substitute the 30-60-90 expressions:
DB = x² / 2x
DB = x / 2We are told DB = 12, so:
x / 2 = 12
x = 24Now find AB:
AB = 2x
AB = 48So the correct answer is 48.
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