Complete this realistic SAT Math exam, featuring Module 1, 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: 2x + 5 = 17.A. 6
B. 7
C. 8
D. 9Correct answer: A. 6
Why A is correct:
Subtract 5 from both sides: 2x = 12. Then divide by 2: x = 6.Why the others are incorrect:
B. 2(7) + 5 = 19
C. 2(8) + 5 = 21
D. 2(9) + 5 = 232. Question:
In the xy-plane, a circle has center (2, -1) and radius 5. What is the value of the radius squared?
A. 5
B. 10
C. 25
D. 50Correct answer: C. 25
Why C is correct:
The radius is 5.
Radius squared means 5² = 25.Why the others are incorrect:
A. This is the radius, not the radius squared
B. 10 is not 5²
D. 50 is not 5²3. Question:
A population starts at 400 and grows by 5% each year. Which expression represents the population after t years?
A. 400(0.95)ᵗ
B. 400(1.05)ᵗ
C. 405ᵗ
D. 400 + 1.05tCorrect answer: B. 400(1.05)ᵗ
Why B is correct:
A 5% growth rate means multiply by 1.05 each year.
Start with 400, so the expression is 400(1.05)ᵗ.Why the others are incorrect:
A. This shows a 5% decrease
C. This is not the correct exponential model
D. This is linear, not exponential4. Question:
If x + y = 9 and y = 5, what is the value of x?A. 2
B. 3
C. 4
D. 5Correct answer: C. 4
Why C is correct:
Substitute y = 5 into x + y = 9: x + 5 = 9, so x = 4.Why the others are incorrect:
A. 2 + 5 = 7
B. 3 + 5 = 8
D. 5 + 5 = 105. Question:
In a right triangle, one leg has length 9 and the hypotenuse has length 15. What is the length of the other leg?
A. 6
B. 9
C. 12
D. 18Correct answer: C. 12
Why C is correct:
Use the Pythagorean theorem:
x² + 9² = 15²
x² + 81 = 225
x² = 144
x = 12Why the others are incorrect:
A. 6² + 9² = 117, not 225
B. 9² + 9² = 162, not 225
D. A leg cannot be longer than the hypotenuse6. Question:
Solve for x: |x – 1| = 1, where x > 1.A. 2
B. 3
C. 4
D. 5Correct answer: A. 2
Why A is correct:
|x – 1| = 1 gives x – 1 = 1 or x – 1 = -1, so x = 2 or x = 0. Since x > 1, only x = 2 works.Why the others are incorrect:
B. |3 – 1| = 2
C. |4 – 1| = 3
D. |5 – 1| = 47. Question:
A class charges a 10 dollar registration fee plus 5 dollars per session. If the total cost is 35 dollars, how many sessions were attended?A. 4
B. 5
C. 6
D. 7Correct answer: B. 5
Why B is correct:
Set up the equation: 10 + 5s = 35. Then 5s = 25, so s = 5.Why the others are incorrect:
A. 10 + 5(4) = 30
C. 10 + 5(6) = 40
D. 10 + 5(7) = 458. Question:
What is the slope of the line through the points (1, 2) and (3, 6)?A. 2
B. 4
C. 5
D. 6Correct answer: A. 2
Why A is correct:
Slope = (6 – 2) / (3 – 1) = 4 / 2 = 2.Why the others are incorrect:
B. Too large
C. Too large
D. Too large9. Question:
A taxi charges 2 dollars to start a ride and 3 dollars per mile. What is the total cost, in dollars, of a 2-mile ride?A. 5
B. 6
C. 7
D. 8Correct answer: D. 8
Why D is correct:
Cost = 2 + 3(2) = 2 + 6 = 8.Why the others are incorrect:
A. Too low
B. Too low
C. Too low10. Question:
If 2x + 3/x = 7, what is the value of 4x² + 9/x²?
A. 25
B. 37
C. 43
D. 49Correct answer: B. 37
Why B is correct:
Square both sides:
(2x + 3/x)² = 7²
4x² + 12 + 9/x² = 49
4x² + 9/x² = 37Why the others are incorrect:
A, C, and D come from squaring incorrectly or forgetting the middle term.11. Question:
In the system 2x + y = -5 and y = x + 1, what is the value of x?A. -2
B. -3
C. 3
D. 5Correct answer: A. -2
Why A is correct:
Substitute y = x + 1 into 2x + y = -5:
2x + (x + 1) = -5
3x + 1 = -5
3x = -6
x = -2Why the others are incorrect:
B. Too small
C. Positive, but x must be negative
D. Positive, but x must be negative12. Question:
A theater has 20 rows. Each row has either 18 or 22 seats. If there are 404 seats in all, how many rows have 22 seats?A. 8
B. 9
C. 10
D. 11Correct answer: D. 11
Why D is correct:
If all 20 rows had 18 seats, there would be 20(18) = 360 seats.
There are 404 – 360 = 44 extra seats.
Each 22-seat row adds 4 more seats than an 18-seat row, so 44 / 4 = 11 rows.Why the others are incorrect:
A. Too few extra-seat rows
B. Too few extra-seat rows
C. Too few extra-seat rows13. Question:
Which equation represents the line that passes through the points (0, -7) and (4, 5)?A. y = -3x + 7
B. y = 3x – 7
C. y = 3x + 7
D. y = -3x – 7Correct answer: B. y = 3x – 7
Why B is correct:
Slope = (5 – (-7)) / (4 – 0) = 12 / 4 = 3.
Since the line passes through (0, -7), the y-intercept is -7.
So the equation is y = 3x – 7.Why the others are incorrect:
A. Wrong slope and wrong sign on the intercept
C. Correct slope but wrong y-intercept
D. Wrong slope, though it has the correct intercept14. Question:
A line passes through (2, 5) and is perpendicular to the line y = 2x + 1. Which equation could represent the line?A. y = (1/2)x – 6
B. y = -2x + 6
C. y = 2x – 6
D. y = -(1/2)x + 6Correct answer: D. y = -(1/2)x + 6
Why D is correct:
The given line has slope 2, so a perpendicular line has slope -1/2.
Use point (2, 5):
5 = -(1/2)(2) + b
5 = -1 + b
b = 6
So the equation is y = -(1/2)x + 6.Why the others are incorrect:
A. Wrong slope
B. Wrong slope
C. Wrong slope15. Question:
A streaming service charges a 12 dollar monthly fee plus 5 dollars per premium add-on. If the total bill was 42 dollars, how many premium add-ons were purchased?A. 4
B. 5
C. 6
D. 7Correct answer: C. 6
Why C is correct:
Set up the equation: 12 + 5a = 42.
Then 5a = 30, so a = 6.Why the others are incorrect:
A. 12 + 5(4) = 32
B. 12 + 5(5) = 37
D. 12 + 5(7) = 4716. Question:
In the xy-plane, a circle has center (3, -4) and radius 10. The horizontal line y = 2 intersects the circle at points A and B. What is the length of AB?
A. 8
B. 12
C. 16
D. 20Correct answer: C. 16
Why C is correct:
The distance from the center to the line is 2 – (-4) = 6.
Half the chord is √(10² – 6²) = √64 = 8.
So the full chord length is 16.Why the others are incorrect:
A and B are too short, and D would be the diameter only if the line passed through the center.17. Question:
A line has slope 4 and passes through the point (2, 1). Which equation represents the line?A. y = 4x – 7
B. y = 4x + 7
C. y = -4x – 7
D. y = -4x + 7Correct answer: A. y = 4x – 7
Why A is correct:
Use y = mx + b with slope 4:
1 = 4(2) + b
1 = 8 + b
b = -7
So the equation is y = 4x – 7.Why the others are incorrect:
B. Wrong y-intercept
C. Wrong slope
D. Wrong slope18. Question:
What is the slope of the line through the points (-1, 4) and (3, 24)?A. 2
B. 3
C. 4
D. 5Correct answer: D. 5
Why D is correct:
Slope = (24 – 4) / (3 – (-1)) = 20 / 4 = 5.Why the others are incorrect:
A. Too small
B. Too small
C. Too small19. Question:
A quantity starts at 72 and decreases by 15% each hour. Which expression represents the quantity after t hours?
A. 72(0.15)ᵗ
B. 72(0.85)ᵗ
C. 72(1.15)ᵗ
D. 72 – 0.15tCorrect answer: B. 72(0.85)ᵗ
Why B is correct:
A 15% decrease means the quantity keeps 85% of its value each hour.
So the multiplier is 0.85, and the model is 72(0.85)ᵗ.Why the others are incorrect:
A uses the percent instead of the decay factor.
C represents growth, not decay.
D is linear, not exponential.20. Question:
A theater has 18 rows. Each row has either 16 or 20 seats. If there are 324 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 18 rows had 16 seats, there would be 18(16) = 288 seats.
There are 324 – 288 = 36 extra seats.
Each 20-seat row adds 4 more seats than a 16-seat row, so 36 / 4 = 9 rows.Why the others are incorrect:
A. Too few
B. Too few
D. Too many21. Question:
In a right triangle, one leg has length 12 and the hypotenuse has length 20. What is the length of the other leg?
A. 8
B. 12
C. 16
D. 18Correct answer: 16
Why 16 is correct:
Use the Pythagorean theorem:
x² + 12² = 20²
x² + 144 = 400
x² = 256
x = 1622. Question:
A line passes through (3, 14/3) and is perpendicular to the line y = 3x – 5. Which equation could represent the line?A. y = (1/3)x + 2
B. y = -3x + 2
C. y = 3x – 2
D. y = -(1/3)x + 17/3Correct answer: D. y = -(1/3)x + 17/3
Why D is correct:
The given line has slope 3, so a perpendicular line has slope -1/3.
Use point (3, 14/3):
14/3 = -(1/3)(3) + b
14/3 = -1 + b
14/3 = -3/3 + b
b = 17/3
So the equation is y = -(1/3)x + 17/3.Why the others are incorrect:
A. Wrong slope
B. Wrong slope
C. Wrong slopeNext Step:
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