Complete this realistic 22-question, 35-minute timed SAT Math module and focus on algebra, functions, percentages, quadratics, and problem-solving skills so you can build accuracy, confidence, and speed under timed pressure.
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- Correct answer: B. The number of riders is 94% of the previous year’s total each year.
Why: In R(t) = 1200(0.94)^t, the 0.94 is the yearly multiplier. That means each year’s ridership is 94% of the previous year’s ridership. - Correct answer: C. 16
Why: The center is (4, -2) and the line is y = 4, so the distance from the center to the line is 6. Half the chord is √(10² – 6²) = √64 = 8, so the full chord is 16. - Correct answer: D. 29
Why: Set the equations equal:
x² – 8x + k = 4x – 7
x² – 12x + (k + 7) = 0
For exactly one solution, the discriminant must be 0:
(-12)² – 4(1)(k + 7) = 0
144 – 4k – 28 = 0
116 – 4k = 0
k = 29 - Correct answer: B. 23
Why: From x + 1/x = 5, square both sides:
x² + 2 + 1/x² = 25
x² + 1/x² = 23 - Correct answer: D. 13√7
Why: Since sin A = 12/13, the triangle follows the 5-12-13 ratio. Let the sides be 5k, 12k, and 13k. The area is:
1/2(5k)(12k) = 210
30k² = 210
k² = 7
k = √7
So the hypotenuse is 13√7. - Correct answer: B. y = 7.5x + 24
Why: Multiplying each y-value by 3 multiplies both the slope and the y-intercept by 3.
y = 2.5x + 8 becomes y = 7.5x + 24. - Correct answer: A. 11
Why: Factor the numerator:
x² + 7x + 12 = (x + 3)(x + 4)
So for x ≠ -4,
f(x) = (x + 3)(x + 4)/(x + 4) = x + 3
f(8) = 11 - Correct answer: A. x ≤ 37
Why: Substitute y = 20:
40x + 75(20) ≤ 3000
40x + 1500 ≤ 3000
40x ≤ 1500
x ≤ 37.5
Since x must be a whole number, x ≤ 37. - Correct answer: C. sin(62°)/cos(62°)
Why: tan A = sin A / cos A. Since A = 62°, tan A = sin(62°)/cos(62°). - Correct answer: C. 12
Why: Since ∠Q = 90° and QS = QR, the triangle is 45-45-90. The hypotenuse equals leg times √2:
SR = 6√2 · √2 = 12 - Correct answer: C. 36.06
Why: Use the distance formula:
√(12² + 34²) = √1300 ≈ 36.06 - Correct answer: B. ∠YCD = ∠YZD
Why: Inscribed angles that intercept the same arc are equal. - Correct answer: C. y = 75(0.84)^x
Why: A 16% decrease means multiply by 0.84 each hour. Starting value is 75. - Correct answer: A. x ≤ 31
Why: Substitute y = 20:
40x + 65(20) ≤ 2550
40x + 1300 ≤ 2550
40x ≤ 1250
x ≤ 31.25
Since x must be a whole number, x ≤ 31. - Correct answer: C. 14
Why: cos A = adjacent/hypotenuse = AC/AB = 1/2
7/AB = 1/2
AB = 14 - Correct answer: D. 0.799
Why: In similar right triangles, angle E is complementary to angle A’s partner, so sin E = cos A = 0.799. - Correct answer: D. AB = 3√2, BC = 3
Why: cos B = √2/2 means a 45-45-90 triangle. Since AC = 3, the other leg BC = 3, and the hypotenuse AB = 3√2. - Correct answer: B. 24 miles
Why: Use the Pythagorean theorem:
x² + 7² = 25²
x² + 49 = 625
x² = 576
x = 24 - Correct answer: B. The two angles must be equal.
Why: Inscribed angles intercepting the same arc are equal. - Correct answer: B. After 3 hours, the substance has a mass of about 61 grams.
Why: M(3) = 84(0.9)^3 = 84(0.729) = 61.236, which is about 61. - Correct answer: B. x – 2
Why: Factor:
7x² – 14x = 7x(x – 2)
Then divide by 7x:
(7x(x – 2))/(7x) = x – 2 - Correct answer: A. 7/2
Why: Solve |x – 2| = 5 – x
Case 1: x ≥ 2
x – 2 = 5 – x
2x = 7
x = 7/2Case 2: x < 2
-(x – 2) = 5 – x
-x + 2 = 5 – x
2 = 5
ImpossibleSo the only solution is 7/2.
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