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:
In the system 5x+y=−13 and y=2x+2, what is the value of x?A. −4
B. −15/7
C.15/7
D. 4/21Correct answer: B. −15/7
Why B is correct:
Substitute y=2x+2 into 5x+y=−135x+(2x+2)=−13
Combine like terms:
7x+2= -13
Subtract 2 from both sides:
7x=−15/7x
Divide by 7:
x=−15/7x
Why the others are incorrect:
A. −4 gives y=−6y = -6, and 5(−4)+(−6)=−26≠−13C. 15/7
If x = 15/7, then y = 2(15/7) + 2 = 44/7. Substituting into 5x + y gives 5(15/7) + 44/7 = 17, not -13.D. 4/21
If x = 4/21, then y = 2(4/21) + 2 = 50/21. Substituting into 5x + y gives 5(4/21) + 50/21 = 10/3, not -13.2. Question:
A theater has 22 rows. Each row has either 16 or 20 seats. If there are 388 seats in all, how many rows have 20 seats?A. 7
B. 8
C. 9
D. 10Correct answer: C. 9
Why C is correct:
If all 22 rows had 16 seats, there would be 22 × 16 = 352 seats.
There are 388 – 352 = 36 extra seats.
Each 20-seat row adds 4 more seats than a 16-seat row, so 36 ÷ 4 = 9.Why the others are incorrect:
A. Too few 20-seat rows.
B. Too few 20-seat rows.
D. Too many 20-seat rows.3. Question:
Which equation represents the line that passes through the points (0, -11) and (5, -1)?A. y = -2x + 11
B. y = 2x – 11
C. y = 2x + 11
D. y = -2x – 11Correct answer: B. y = 2x – 11
Why B is correct:
Slope = (-1 – (-11)) / (5 – 0) = 10 / 5 = 2.
Since the line passes through (0, -11), the y-intercept is -11.
So the equation is y = 2x – 11.Why the others are incorrect:
A. Wrong slope and wrong intercept sign.
C. Correct slope but wrong y-intercept.
D. Wrong slope.4. Question:
A line passes through (4, 17/4) and is perpendicular to the line y = 4x – 2. Which equation could represent the line?A. y = (1/4)x + 3
B. y = -4x + 3
C. y = 4x – 3
D. y = -(1/4)x + 21/4Correct answer: D. y = -(1/4)x + 21/4
Why D is correct:
The given line has slope 4, so a perpendicular line has slope -1/4.
Use the point (4, 17/4):
17/4 = -(1/4)(4) + b
17/4 = -1 + b
17/4 = -4/4 + b
b = 21/4
So the equation is y = -(1/4)x + 21/4.Why the others are incorrect:
A. Wrong slope.
B. Wrong slope.
C. Wrong slope.5. Question:
A music subscription charges a 15 dollar monthly fee plus 4 dollars per bonus pack. If the total bill was 39 dollars, how many bonus packs were purchased?A. 4
B. 5
C. 6
D. 7Correct answer: C. 6
Why C is correct:
Set up the equation: 15 + 4b = 39.
Then 4b = 24, so b = 6.Why the others are incorrect:
A. 15 + 4(4) = 31
B. 15 + 4(5) = 35
D. 15 + 4(7) = 436. Question:
If 3x + 4y = 10 and y = 4, what is the value of x?A. x = 5
B. x = 2
C. x = -2
D. x = -5Correct answer: C. x = -2
Why C is correct:
Substitute y = 4:
3x + 4(4) = 10
3x + 16 = 10
3x = -6
x = -2Why the others are incorrect:
A. Positive instead of negative.
B. Positive instead of negative.
D. Too small.7. Question:
For positive x, if x + 9/x = 10, what is the value of x² + 81/x²?
Correct answer: B. 82
Why 82 is correct:
Square both sides:(x + 9/x)² = 10²
x² + 2(x)(9/x) + 81/x² = 100
x² + 18 + 81/x² = 100
x² + 81/x² = 82
8. Question:
What is the slope of the line through the points (-2, 1) and (2, 21)?A. 4
B. 5
C. 6
D. 7Correct answer: B. 5
Why B is correct:
Slope = (21 – 1) / (2 – (-2)) = 20 / 4 = 5.Why the others are incorrect:
A. Too small.
C. Too large.
D. Too large.9. Question:
In the system 4x + y = -6 and y = x + 2, what is the value of x?
A. -8/5
B. 8/5
C. 8/6
D. -8/6Correct answer: A. -8/5
Why A is correct:
Substitute y = x + 2 into 4x + y = -6:4x + (x + 2) = -6
5x + 2 = -6
5x = -8
x = -8/5Why the others are incorrect:
B. 8/5 has the wrong sign.
C. 8/6 is not equal to -8/5.
D. -8/6 simplifies to -4/3, which is not equal to -8/5.10. Question:
A theater has 21 rows. Each row has either 18 or 22 seats. If there are 414 seats in all, how many rows have 22 seats?A. 8
B. 9
C. 10
D. 11Correct answer: B. 9
Why B is correct:
If all 21 rows had 18 seats, there would be 21 × 18 = 378 seats.
There are 414 – 378 = 36 extra seats.
Each 22-seat row adds 4 more seats, so 36 ÷ 4 = 9.Why the others are incorrect:
A. Too few 22-seat rows.
C. Too many.
D. Too many.11. Question:
At noon, a car begins a 235-mile trip. For the first 2 hours, it travels at 35 miles per hour. It completes the trip at 5:00 p.m. on the same day. What was the car’s average speed, in miles per hour, from 2:00 p.m. to 5:00 p.m.?A. 45
B. 50
C. 55
D. 60Correct answer: C. 55
Why C is correct:
In the first 2 hours, the car travels 2 × 35 = 70 miles.
That leaves 235 – 70 = 165 miles.
From 2:00 p.m. to 5:00 p.m. is 3 hours.
165 ÷ 3 = 55 miles per hour.Why the others are incorrect:
A. Too low.
B. Too low.
D. Too high.12. Question:
A 2,400-gallon pond is being filled by a pump that adds water at 75 gallons per hour, while a drain removes water at 35 gallons per hour. If the pond starts empty, how many hours will it take to fill completely?A. 42
B. 50
C. 60
D. 70Correct answer: C. 60
Why C is correct:
Net fill rate = 75 – 35 = 40 gallons per hour.
Time = 2,400 ÷ 40 = 60 hours.Why the others are incorrect:
A. Too short.
B. Too short.
D. Too long.13. Question:
The price of one share of a company’s stock on June 1 was 80 dollars. On July 1, the price was 10 dollars more than it was on June 1 and 85 percent of the price on August 1. To the nearest dollar, what was the price of one share on August 1?A. 94
B. 106
C. 112
D. 118Correct answer: B. 106
Why B is correct:
On July 1, the price was 80 + 10 = 90 dollars.
This was 85% of the August 1 price.
So August price = 90 ÷ 0.85 ≈ 105.88, which rounds to 106.Why the others are incorrect:
A. Too low.
C. Too high.
D. Too high.14. Question:
From 2018 to 2019, a company’s profit increased by 25 percent. From 2019 to 2020, the profit rose from 360 million dollars to 450 million dollars. By what percent did the company’s profit increase from 2018 to 2020?A. 44%
B. 52%
C. 56.25%
D. 68%Correct answer: C. 56.25%
Why C is correct:
From 2019 to 2020, the increase was 360 to 450, which is 90 ÷ 360 = 25%.
So the company increased by 25% twice.
Multiply growth factors: 1.25 × 1.25 = 1.5625
That is a total increase of 56.25%.Why the others are incorrect:
A. Too low.
B. Too low.
D. Too high.15. Question:
Which of the following is equivalent to 5 fourth root of (ab¹⁶)?A. 5a¹⁄⁴b⁴
B. 5a⁴b¹⁄⁴
C. 5a¹⁄³b⁴
D. 5a⁴b¹⁄³Correct answer: A. 5a¹⁄⁴b⁴
Why A is correct:
Fourth root of ab¹⁶ = a¹⁄⁴ × b¹⁶⁄⁴ = a¹⁄⁴b⁴.
Then multiply by 5 to get 5a¹⁄⁴b⁴.Why the others are incorrect:
B. The exponents are reversed.
C. Uses 1/3 instead of 1/4 for a.
D. Both exponents are wrong.16. Question:
Which of the following equations is true for some value of x?A. |x + 5| + 2 = 0
B. |x – 5| + 2 = 0
C. |x + 5| – 2 = 0
D. |x – 5| + 5 = 0Correct answer: C. |x + 5| – 2 = 0
Why C is correct:
This becomes |x + 5| = 2, which has solutions: x = -3 or x = -7.Why the others are incorrect:
A. |x + 5| cannot be -2.
B. |x – 5| cannot be -2.
D. |x – 5| cannot be -5.17. Question:
If the polynomial f(x) is evenly divisible by x – 4 and the polynomial g(x) = f(x) + 4, what is the value of g(4)?A. -3
B. 0
C. 4
D. 9Correct answer: C. 4
Why C is correct:
If f(x) is divisible by x – 4, then f(4) = 0.
So g(4) = f(4) + 4 = 0 + 4 = 4.Why the others are incorrect:
A. Too low.
B. Ignores the +4.
D. No basis for 9.18. Question:
The product of all the solutions to the equation 3u² + 2u – 4 = 0 is M. What is the value of M?A. -5⁄3
B. -4⁄3
C. 4⁄3
D. 5⁄3Correct answer: B. -4⁄3
Why B is correct:
For ax² + bx + c = 0, the product of the solutions is c/a.
Here, c = -4 and a = 3, so the product is -4/3.Why the others are incorrect:
A. Wrong numerator.
C. Wrong sign.
D. Wrong numerator and sign.19. Question:
A train travels 420 miles. For the first 2 hours, it travels at 45 miles per hour. It completes the trip in 5 hours total. What was the train’s average speed, in miles per hour, for the last 3 hours of the trip?A. 90
B. 100
C. 110
D. 120Correct answer: C. 110
Why C is correct:
In the first 2 hours, the train travels 2 × 45 = 90 miles.
That leaves 420 – 90 = 330 miles.
330 ÷ 3 = 110 miles per hour for the last 3 hours.Why the others are incorrect:
A. Too low.
B. Too low.
D. Too high.20. Question:
From 2020 to 2021, a company’s revenue increased by 25 percent. From 2021 to 2022, the revenue rose from 250 million dollars to 280 million dollars. By what percent did the company’s revenue increase from 2020 to 2022?A. 32%
B. 40%
C. 44%
D. 48%Correct answer: B. 40%
Why B is correct:
From 2021 to 2022, the increase was 250 to 280, which is 30 ÷ 250 = 12%.
If 2021 revenue was 250, then 2020 revenue was 250 ÷ 1.25 = 200.
From 200 to 280 is an increase of 80.
80 ÷ 200 = 40%.Why the others are incorrect:
A. Too low.
C. Too high.
D. Too high.21. Question:
In the xy-plane, the line y = x intersects the circle x² + y² = 36 at two points. What is the distance between those two points?
A. 6
B. 6√2
C. 12
D. 12√2Correct answer: C. 12
Why C is correct:
Substitute y = x into the circle equation:x² + x² = 36
2x² = 36
x² = 18
x = ±3√2
So the two intersection points are:
(3√2, 3√2) and (-3√2, -3√2)
Use the distance formula:
√[(6√2)² + (6√2)²]
= √(72 + 72)
= √144
= 12Why the others are incorrect:
A. Too small
B. Too small
D. This overestimates the distance22. Question:
The product of all the solutions to the equation 2t² + 5t – 7 = 0 is K. What is the value of K?A. -7⁄2
B. -5⁄2
C. 5⁄2
D. 7⁄2Correct answer: A. -7⁄2
Why A is correct:
For ax² + bx + c = 0, the product of the solutions is c/a.
Here, c = -7 and a = 2, so the product is -7/2.Why the others are incorrect:
B. Wrong numerator.
C. Wrong sign.
D. Wrong sign.Next Step:
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