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:
A function is defined by f(x) = 2x² – 3. What is the value of f(-2)?A. 5
B. -11
C. 13
D. 19Correct answer: A. 5
Why A is correct:
Substitute x = -2 into the function:
f(-2) = 2(-2)² – 3
= 2(4) – 3
= 8 – 3
= 5Why the others are incorrect:
B. -11 is not the result of the substitution.
C. 13 is too large.
D. 19 is far too large.2. Question:
In a right triangle, the lengths of the two shorter sides are 14 inches and 48 inches. What is the length of the third side?A. 50
B. 52
C. 54
D. 56Correct answer: A. 50
Why A is correct:
Use the Pythagorean theorem:
14² + 48² = c²
196 + 2304 = 2500
c = √2500 = 50Why the others are incorrect:
B. 52 does not satisfy the theorem.
C. 54 does not satisfy the theorem.
D. 56 does not satisfy the theorem.3. Question:
If x is measured in degrees and cos x = sin g, which expression gives a value of g that makes the equation true for acute angles?A. g = π/2 – x
B. g = 90 – x
C. g = π – x
D. g = 270 – xCorrect answer: B. g = 90 – x
Why B is correct:
For acute angles, the cofunction identity is:
cos x = sin(90 – x)So g = 90 – x.
Why the others are incorrect:
A. π/2 – x mixes radians with degrees.
C. π – x also mixes radians with degrees and is not the correct identity.
D. 270 – x does not match the acute-angle relationship.4. Question:
Which of the following is equivalent to sin(7π/6)?A. sin(19π/6)
B. sin(13π/6)
C. sin(8π/3)
D. sin(5π/3)Correct answer: A. sin(19π/6)
Why A is correct:
Sine has period 2π. Since
19π/6 = 7π/6 + 2π,
sin(19π/6) = sin(7π/6).Why the others are incorrect:
B. 13π/6 has a different sine value.
C. 8π/3 has a different sine value.
D. 5π/3 has a different sine value.5. Question:
Consider triangle ABC where AB = 9 and ∠C = 27°. If triangle ABC is increased by a scale factor of 2 to create triangle A′B′C′, find A′B′ and the measure of angle C′.A. A′B′ = 18, ∠C′ = 27°
B. A′B′ = 18, ∠C′ = 54°
C. A′B′ = 9, ∠C′ = 27°
D. A′B′ = 9, ∠C′ = 54°Correct answer: A. A′B′ = 18, ∠C′ = 27°
Why A is correct:
A scale factor of 2 doubles side lengths, so
A′B′ = 9 × 2 = 18.A dilation does not change angle measures, so
∠C′ = 27°.Why the others are incorrect:
B. The side is right, but the angle should not double.
C. The angle is right, but the side should double.
D. Neither value is correct.6. Question:
For a specific forest area, the function g represents the percentage of the area covered by a certain species of plant g(m) on the mth week of the year 2024. Which of the following is the best interpretation of g(24) = 45?A. On the 24th week of 2024, the plant species covered 45% of the forest area.
B. The plant species covered 45% of the forest area for 24 weeks in 2024.
C. The plant species covered 24% of the forest area for 45 weeks in 2024.
D. On the 45th week of 2024, the plant species covered 24% of the forest area.Correct answer: A
Why A is correct:
g(24) = 45 means that when the input is week 24, the output is 45 percent coverage.Why the others are incorrect:
B. It turns the statement into a duration claim.
C. It swaps the values.
D. It reverses input and output.7. Question:
Which of the following is equivalent to (1 / (x√x))^n ?A. x^(-3n/2)
B. x^(n – 1/2)
C. x^(n/2)
D. x^(3n/2)Correct answer: A. x^(-3n/2)
Why A is correct:
Since √x = x^(1/2),
x√x = x · x^(1/2) = x^(3/2)So
1 / x^(3/2) = x^(-3/2)Raise to the nth power:
(x^(-3/2))^n = x^(-3n/2)Why the others are incorrect:
B. Incorrect exponent pattern.
C. Wrong sign and wrong exponent.
D. Wrong sign.8. Question:
Correct answer: C. 132°
Explanation:
We are told that ∠ABC ≅ ∠IHJ, so their angle measures are equal.
Set the expressions equal and solve for x:
5x + 2 = 7x − 18
20 = 2x
x = 10
Now find m∠CFG:
m∠CFG = 4x + 8
m∠CFG = 4(10) + 8
m∠CFG = 48°Because ∠ABC and ∠IHJ are congruent corresponding angles, the two horizontal lines are parallel.
Now use the left slanted transversal.
∠DCE and ∠CFG are corresponding angles, so they are congruent.Therefore:
m∠DCE = 48°
At point C, ∠DCE and ∠ECF form a linear pair, so they sum to 180°.
m∠ECF = 180° − 48°
m∠ECF = 132°So the correct answer is C. 132°.
9. Question:
In triangle ABC, ∠B = 90° and sin C = 16/65. Find ∠A. Round your answer to the nearest hundredth of a degree.A. 75.75°
B. 14.25°
C. 0.99°
D. 0.25°Correct answer: A. 75.75°
Why A is correct:
Since ∠B = 90°, angles A and C are complementary, so
A = 90° – C.Given sin C = 16/65,
C ≈ sin⁻¹(16/65) ≈ 14.25°So
A ≈ 90° – 14.25° = 75.75°Why the others are incorrect:
B. 14.25° is angle C, not angle A.
C. Too small.
D. Much too small.10. Question:
A fair number cube is numbered from 1 to 6. If the cube is rolled, what is the probability of getting either a 6 or a number less than 4?A. 1/6
B. 1/2
C. 2/3
D. 5/6Correct answer: C. 2/3
Why C is correct:
Numbers less than 4 are 1, 2, and 3. Also include 6.
That gives 4 favorable outcomes: 1, 2, 3, 6.Probability = 4/6 = 2/3.
Why the others are incorrect:
A. 1/6 counts only one outcome.
B. 1/2 = 3/6, but there are 4 favorable outcomes.
D. 5/6 is too large.11. Question:
A parabola has vertex (8.5, 6) and one x-intercept at (5.5, 0). What is the other x-intercept?A. 11.5
B. 9.5
C. 8.5
D. 10.5Correct answer: A. 11.5
Why A is correct:
The axis of symmetry is x = 8.5.
One intercept is at x = 5.5, which is 3 units left of 8.5.
The other intercept must be 3 units right of 8.5:8.5 + 3 = 11.5
Why the others are incorrect:
B. 9.5 is only 1 unit right of the axis.
C. 8.5 is the axis of symmetry, not an x-intercept.
D. 10.5 is only 2 units right of the axis.12. Question:
A population of bacteria doubles every t hours. The population P after h hours is modeled by P = 200(2^(h/t)). If the population doubles every 4 hours, what is the value of t?A. 8
B. 6
C. 4
D. 2Correct answer: C. 4
Why C is correct:
The problem directly says the population doubles every 4 hours, and the model uses t for the doubling time.
So t = 4.Why the others are incorrect:
A. Not the stated doubling time.
B. Not the stated doubling time.
D. Not the stated doubling time.13. Question:
Correct answer: C. 5
Explanation:
For two chords that intersect inside a circle:
(AP)(PD) = (CP)(PB)
Substitute:
6(8) = (x + 1)(x + 3)
48 = x² + 4x + 3
0 = x² + 4x − 45
Factor:
0 = (x + 9)(x − 5)
So:
x = -9 or x = 5
Since a segment length must be positive, x = 5.
14. Question:
Given the system 2x + 6y = 8 and kx + 3ky = 4k, where k ≠ 0, the system has infinitely many solutions. Which of the following could be the value of k?A. 2
B. 7
C. 22
D. 29Correct answer: A. 2
Why A is correct:
For the system to have infinitely many solutions, the two equations must represent the same line.First equation:
2x + 6y = 8Second equation:
kx + 3ky = 8To match the first equation exactly, the coefficients must be the same.
That means:
k = 2If k = 2, then the second equation becomes:
2x + 3(2)y = 8
2x + 6y = 8Now both equations are identical, so the system has infinitely many solutions.
Why the others are incorrect:
B. If k = 7, the equation becomes 7x + 21y = 8, which is not the same as 2x + 6y = 8.
C. If k = 22, the equation becomes 22x + 66y = 8, which is not the same as 2x + 6y = 8.
D. If k = 29, the equation becomes 29x + 87y = 8, which is not the same as 2x + 6y = 8.15. Question:
Which of the following is equivalent to (x² – 1) / (x + 1), assuming x ≠ -1?Correct answer: x – 1
Why this is correct:
Factor the numerator:
x² – 1 = (x – 1)(x + 1)Then cancel x + 1, since x ≠ -1:
(x – 1)(x + 1) / (x + 1) = x – 116. Question:
If f(x) = |3x – 5| and f(x) = 11, what is the smaller possible value of x?A. 2
B. -2
C. 4
D. -4Correct answer: B. -2
Why B is correct:
Solve |3x – 5| = 11.Case 1:
3x – 5 = 11
3x = 16
x = 16/3Case 2:
3x – 5 = -11
3x = -6
x = -2The smaller value is -2.
Why the others are incorrect:
A. 2 gives |6 – 5| = 1.
C. 4 gives |12 – 5| = 7.
D. -4 gives |-12 – 5| = 17.17. Question:
Explanation: C. 16
Because DE is parallel to AC, triangles BDE and BAC are similar.
That means the matching sides are proportional:
BD / BA = DE / AC
We are told that:
BD : AB = 2 : 3
So:
DE / AC = 2 / 3
Since AC = 24:
DE = (2/3)(24)
DE = 16So the correct answer is 16.
18. Question:
A store marks up the price of an item by 20% and then discounts the new price by 20%. The final price is what fraction of the original price?A. 24/25
B. 3/4
C. 2/3
D. 1/2Correct answer: A. 24/25
Why A is correct:
Let the original price be 1.After a 20% markup:
1 × 1.2 = 1.2After a 20% discount:
1.2 × 0.8 = 0.96And 0.96 = 96/100 = 24/25.
Why the others are incorrect:
B. 3/4 = 0.75, too small.
C. 2/3 ≈ 0.667, too small.
D. 1/2 = 0.5, much too small.19. Question:
The total cost c of renting a kayak is modeled by c = 6h + 12, where h is the number of hours. How many hours can a customer rent the kayak for 120 dollars?A. 12
B. 15
C. 18
D. 24Correct answer: C. 18
Why C is correct:
Substitute c = 120:120 = 6h + 12
108 = 6h
h = 18Why the others are incorrect:
A. 6(12) + 12 = 84.
B. 6(15) + 12 = 102.
D. 6(24) + 12 = 156.20. Question:
A bag contains 4 red marbles, 5 blue marbles, and 3 green marbles. If one marble is chosen at random, what is the probability that it is green?A. 1/6
B. 1/3
C. 1/2
D. 1/4Correct answer: D. 1/4
Why D is correct:
Total marbles = 4 + 5 + 3 = 12
Green marbles = 3Probability = 3/12 = 1/4
Why the others are incorrect:
A. 1/6 is too small.
B. 1/3 would be 4/12, not 3/12.
C. 1/2 is too large.21. Question:
If 3x – 2y = 7 and x + y = 4, what is the value of x?A. 3
B. 5
C. 6
D. 7Correct answer: A. 3
Why A is correct:
From x + y = 4, we get y = 4 – x.Substitute into 3x – 2y = 7:
3x – 2(4 – x) = 7
3x – 8 + 2x = 7
5x = 15
x = 3Why the others are incorrect:
B. Too large.
C. Too large.
D. Too large.22. Question:
Correct answer: B) 8
Explanation:
When two chords intersect inside a circle, the products of the segment lengths are equal:AP · PB = CP · PD
Substitute the given values:
x(12) = 8(x + 4)
12x = 8x + 32
4x = 32
x = 8
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