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. 15
Why B is correct: There are 19 restaurants total, so the median is the 10th value when the employee counts are ordered. The first two groups account for 2 + 5 = 7 restaurants. The next group, 12 to 16 employees, brings the total to 11 restaurants. That means the 10th restaurant must fall in the 12 to 16 group. Of the choices, only 15 is in that interval.
Why the others are incorrect: 10 is in the 7 to 11 interval, and 22 and 26 are in the 22 to 26 interval, so none of those could be the median. - Correct answer: B. C = 50(2.6)^t
Why B is correct: An increase of 160% means each hour’s number of comments becomes 100% + 160% = 260% of the previous hour’s total, or 2.6 times as much. Since the article starts with 50 comments, the correct exponential model is C = 50(2.6)^t.
Why the others are incorrect: C = 50(1.6)^t uses the wrong growth factor. C = 50 + 1.6t and C = 50 + 2.6t are linear models, but repeated percent growth is exponential. - Correct answer: A. (x – 2)^2 + (y – 2)^2 = 36
Why A is correct: Circle A has center (-3, 2) and radius 4 because (x + 3)^2 + (y – 2)^2 = 16. Shifting 5 units right changes the center to (2, 2). Increasing the radius by a factor of 1.5 gives a new radius of 6, so r^2 = 36. The new equation is (x – 2)^2 + (y – 2)^2 = 36.
Why the others are incorrect: B has the wrong center, C has the wrong center and radius, and D shifts the circle too far right. - Correct answer: B. 52
Why B is correct: Since DE is parallel to BC, triangles ADE and ABC are similar. Because CE = 2AE, the full height AC = AE + CE = 3AE, so AE/AC = 1/3. Therefore DE/BC = 1/3. Since BC = 156, DE = 156/3 = 52.
Why the others are incorrect: 39, 78, and 104 do not match the similarity ratio implied by CE = 2AE. - Correct answer: B. (0, 6)
Why B is correct: Since g(x) = f(x)/(x + 1), use the table to find values of f(x). When x = -4, f(-4) = 2(-3) = -6. When x = 2, f(2) = 4(3) = 12. The line through (-4, -6) and (2, 12) has slope 3, so f(x) = 3x + 6. Therefore the y-intercept is (0, 6).
Why the others are incorrect: They do not match the linear function determined by the table. - Correct answer: C. -8
Why C is correct: Rewrite 2x – y = 5 as y = 2x – 5, so its slope is 2. Rewrite kx + 4y = 18 as y = (-k/4)x + 9/2, so its slope is -k/4. For the system to have no solution, the lines must be parallel with different intercepts, so the slopes must be equal: -k/4 = 2. Solving gives k = -8.
Why the others are incorrect: Any other value of k gives lines with different slopes, so the system would have one solution. - Correct answer: B. 6
Why B is correct: Use difference of squares: (x + 2)^2 – (x – 3)^2 = [(x + 2) – (x – 3)][(x + 2) + (x – 3)] = 5(2x – 1). Then 5(2x – 1) = 55, so 2x – 1 = 11, giving 2x = 12 and x = 6.
Why the others are incorrect: They do not satisfy the simplified equation. - Correct answer: A. 3200(0.85)^t
Why A is correct: A 15% decrease means the population is multiplied each year by 1 – 0.15 = 0.85. Starting from 3,200, the correct exponential model is 3200(0.85)^t.
Why the others are incorrect: 3200(1.15)^t represents growth, not decay. The other two are linear, but repeated percent decrease is exponential. - Correct answer: D. 25/2
Why D is correct: The slope of the line through (4, 17) and (10, 5) is (5 – 17)/(10 – 4) = -12/6 = -2. So h(x) = -2x + b. Using h(4) = 17 gives 17 = -8 + b, so b = 25. Thus h(x) = -2x + 25. The x-intercept occurs when 0 = -2x + 25, so x = 25/2.
Why the others are incorrect: They do not make the line cross the x-axis at the correct value. - Correct answer: C. 13
Why C is correct: Let the legs be x and x + 7. Since the area is 30, (1/2)x(x + 7) = 30, so x(x + 7) = 60. That gives x^2 + 7x – 60 = 0, which factors as (x + 12)(x – 5) = 0. So x = 5, and the legs are 5 and 12. The hypotenuse is sqrt(5^2 + 12^2) = sqrt(169) = 13.
Why the others are incorrect: They do not match the right triangle with legs 5 and 12. - Correct answer: C. 6
Why C is correct: Solve 3x – 5 = 2x + 1. Subtract 2x from both sides to get x – 5 = 1. Add 5, and x = 6.
Why the others are incorrect: They do not satisfy the equation. - Correct answer: B. 18
Why B is correct: The perimeter of a rectangle is 2(length + width). So 2(6 + 3) = 2(9) = 18.
Why the others are incorrect: They are not the correct total distance around the rectangle. - Correct answer: A. 250(1.08)^t
Why A is correct: An 8% increase means multiply by 1.08 each year. Starting from $250 gives the model 250(1.08)^t.
Why the others are incorrect: 250(0.08)^t is the wrong multiplier, and the linear expressions do not model repeated percent growth. - Correct answer: C. -3
Why C is correct: The x-intercept occurs when y = 0. Set 0 = 2x + 6, so 2x = -6 and x = -3.
Why the others are incorrect: They do not make y equal 0. - Correct answer: B. 8
Why B is correct: Use the Pythagorean theorem: a^2 + 6^2 = 10^2. Then a^2 + 36 = 100, so a^2 = 64 and a = 8.
Why the others are incorrect: They do not satisfy the right-triangle relationship. - Correct answer: A. y = -1/2 x + 6
Why A is correct: The slope through (0, 6) and (8, 2) is (2 – 6)/(8 – 0) = -4/8 = -1/2. The line crosses the y-axis at 6, so the equation is y = -1/2 x + 6.
Why the others are incorrect: B has the wrong slope sign, and C and D are too steep. - Correct answer: C. 21
Why C is correct: Square both sides of x + 2/x = 5: (x + 2/x)^2 = 25. This gives x^2 + 4 + 4/x^2 = 25. Subtract 4 to get x^2 + 4/x^2 = 21.
Why the others are incorrect: They come from incorrect expansion or arithmetic. - Correct answer: C. 12
Why C is correct: For infinitely many solutions, the two equations must describe the same line. Multiply 3x + 2y = 12 by 4 to get 12x + 8y = 48. So k must be 12.
Why the others are incorrect: They do not make the equations equivalent. - Correct answer: B. 24/5
Why B is correct: The triangle has legs 8 and 6, so the hypotenuse is 10. Its area is (1/2)(8)(6) = 24. If h is the altitude from the right angle to the hypotenuse, then the area is also (1/2)(10)(h). So 24 = 5h, giving h = 24/5.
Why the others are incorrect: They do not produce the correct area. - Correct answer: B. -14
Why B is correct: Since the zeros are 3 and -5, p(x) = a(x – 3)(x + 5). Given p(0) = -30, we get -30 = a(-3)(5) = -15a, so a = 2. Then p(2) = 2(2 – 3)(2 + 5) = 2(-1)(7) = -14.
Why the others are incorrect: They do not match the quadratic determined by the zeros and the value at 0. - Correct answer: B. 42
Why B is correct: Expand (x + 4)(x – 3) to get x^2 + x – 12. Since this equals 30, x^2 + x – 12 = 30. Add 12 to both sides to get x^2 + x = 42.
Why the others are incorrect: They come from an incorrect expansion or moving terms incorrectly. - Correct answer: C. y = -4/3 x + 2
Why C is correct: The slope through (0, 2) and (3, -2) is (-2 – 2)/(3 – 0) = -4/3. Since the line crosses the y-axis at 2, the equation is y = -4/3 x + 2.
Why the others are incorrect: A and D have the wrong slope sign, and B has the wrong slope magnitude.
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