SAT Math Practice Tests

Question 1

1. If (x)/(3) + 5 = 11, what is the value of x? (A) 6 (B) 18 (C) 33 (D) 48

Question 2

1. A bakery uses 450 grams of flour for every 6 loaves of bread it makes. At this rate, how many grams of flour are needed to make 22 loaves of bread? (type your answer)

Question 3

Two horizontal parallel lines, line ℓ on top and line m below, are crossed by a transversal that slants up to the right. At the intersection with line ℓ, the angle between line ℓ to the left of the intersection and the transversal above line ℓ is marked 118°. At the intersection with line m, the angle between line m to the right of the intersection and the transversal above line m is marked x°.

1. In the figure, line ell is parallel to line m. What is the value of x? (A) 28 (B) 59 (C) 62 (D) 118

Question 4

1. Which expression is equivalent to (2x^2 + 5x - 3) - (x^2 - 4x + 6)? (A) x^2 + 9x - 9 (B) x^2 + x - 9 (C) x^2 + x + 3 (D) x^2 + 9x + 3

Question 5

A line in the xy-plane labeled y = f(x). The line passes through the points (0, −2), (1, 0), and (2, 2).

1. The graph of the linear function f is shown. Which equation defines f? (A) f(x) = -2x - 2 (B) f(x) = (1)/(2)x - 2 (C) f(x) = 2x + 1 (D) f(x) = 2x - 2

Question 6

Dot plot of the number of training runs completed by 20 runners: 2 runs, 1 dot; 3 runs, 2 dots; 4 runs, 6 dots; 5 runs, 3 dots; 6 runs, 5 dots; 7 runs, 3 dots.

1. The dot plot shows the number of training runs completed last week by each of the 20 runners in a marathon training group. What is the median number of training runs for these runners? (A) 4 (B) 4.5 (C) 5 (D) 5.5

Question 7

1. A group of friends is going to a jazz club. Each ticket costs $18, and the group will also pay a single $12 parking fee. The group can spend at most $150 in total. Which inequality represents the possible numbers of tickets, t, the group can buy? (A) 12t + 18 ≤ 150 (B) 18t ≤ 150 + 12 (C) 18t + 12 ≥ 150 (D) 18t + 12 ≤ 150

Question 8

1. The function f is defined by f(x) = ax^2 + 7, where a is a constant. If f(3) = 25, what is the value of f(-2)? (type your answer)

Question 9

1. If (x, y) is the solution to the system of equations 3x + 2y = 16 and x - 2y = 0, what is the value of x - y? (A) 2 (B) 4 (C) 6 (D) 8

Question 10

1. At 7:00 a.m., a bike-sharing station had 48 bikes. Bikes were then taken from the station at a constant rate, and no bikes were returned. At 7:40 a.m., the station had 20 bikes. Which function gives the number of bikes, b(t), at the station t minutes after 7:00 a.m., for 0 ≤ t ≤ 40? (A) b(t) = 20 + 0.7t (B) b(t) = 48 - 28t (C) b(t) = 48 - 0.7t (D) b(t) = 48 + 0.7t

Question 11

Right triangle ABC with the right angle at C. Leg CA is horizontal with length 15, and leg CB is vertical with length 8.

1. In right triangle ABC shown, what is the value of cos B? (A) (8)/(17) (B) (8)/(15) (C) (15)/(17) (D) (17)/(8)

Question 12

1. What is the greatest solution to the equation (x - 3)^2 = 2x - 6? (type your answer)

Question 13

1. A runner's weekly training plan consists of e easy runs and ell long runs. Each easy run is 4 kilometers. The equation 4e + 10ell = 58 represents a week in which the runner covers a total of 58 kilometers. What is the best interpretation of the number 10 in this context? (A) The number of long runs the runner completes in the week (B) The distance, in kilometers, of each long run (C) The total distance, in kilometers, of all the long runs in the week (D) The total distance, in kilometers, the runner covers in the week

Question 14

A parabola opening upward labeled y = f(x). It crosses the x-axis at (−1, 0) and (5, 0), has its vertex at (2, −9), and crosses the y-axis at (0, −5).

1. The graph of the quadratic function f is shown. Which of the following could define f? (A) f(x) = (x - 1)(x + 5) (B) f(x) = (x + 1)(x - 5) (C) f(x) = (x - 2)^2 + 9 (D) f(x) = (x + 2)^2 - 9

Question 15

1. In the equation 3(2x - k) = 6x + 12, k is a constant. For what value of k does the equation have infinitely many solutions? (A) -12 (B) -4 (C) 4 (D) 12

Question 16

1. A marine survey classified 280 coral colonies by reef zone and by whether the colony showed bleaching. The results are shown in the table. If one of the bleached colonies is selected at random, what is the probability that it is from the shallow zone? (A) (6)/(35) (B) (2)/(7) (C) (2)/(5) (D) (3)/(5)

Question 17

1. The equation (ax + 3)(2x + b) = 6x^2 + cx - 12 is true for all values of x, where a, b, and c are constants. What is the value of c? (type your answer)

Question 18

1. In the xy-plane, line k passes through the point (4, 1) and is perpendicular to the graph of 2x - 5y = 7. What is the y-coordinate of the y-intercept of line k? (A) -9 (B) -(3)/(5) (C) (13)/(5) (D) 11

Question 19

1. The area A(t), in square meters, covered by living coral on a restored section of reef is modeled by A(t) = 850(1.12)^(t)/(2), where t is the number of years since the restoration began. Which statement best describes how the area changes according to the model? (A) The area increases by 6% every year. (B) The area increases by 12% every year. (C) The area increases by 12% every 2 years. (D) The area increases by 24% every 2 years.

Question 20

1. In the xy-plane, the graph of x^2 + y^2 - 6x + 10y + 18 = 0 is a circle. What is the radius of the circle? (A) 4 (B) 3√(2) (C) 8 (D) 16

Question 21

1. In the xy-plane, the graphs of y = x^2 - 4x + c and y = 2x - 1, where c is a constant, intersect at exactly one point. What is the value of c? (type your answer)

Question 22

1. Two researchers each selected a random sample of visitors to a national park and asked whether they had visited the park before. In the first sample, 62% had visited before, with an associated margin of error of 4.5 percentage points. In the second sample, 57% had visited before, with an associated margin of error of 3 percentage points. Based on both samples, which of the following is a plausible value for the percent of all visitors to the park who had visited before? (A) 56% (B) 59% (C) 62% (D) 64%

Question 1 (harder Module 2)

1. In the xy-plane, a line has a y-intercept of (0, 6) and passes through the point (4, -2). What is the x-coordinate of the x-intercept of the line? (A) -3 (B) -2 (C) (1)/(3) (D) 3

Question 2 (harder Module 2)

1. The frequency table shows the number of goals a soccer team scored in each of the 20 matches it played in one season. What is the mean number of goals the team scored per match? (type your answer)

Question 3 (harder Module 2)

1. Which expression is equivalent to (x^2 - 9)/(x^2 + x - 6) for x ≠ -3 and x ≠ 2? (A) (x + 3)/(x - 2) (B) (x - 3)/(x - 2) (C) (x - 3)/(x + 2) (D) (3)/(2)

Question 4 (harder Module 2)

A solid line in the xy-plane passes through (0, −2) and (3, 0). The region above the line is shaded, and the shaded region includes the line.

1. The shaded region shown, including the line, represents the solutions to which inequality? (A) 2x - 3y ≥ 6 (B) 3x - 2y ≤ 6 (C) 2x - 3y ≤ 6 (D) 3x - 2y ≥ 6

Question 5 (harder Module 2)

Triangle ABC with point D on side AB and point E on side AC. Segment DE is drawn across the triangle. AD = 6, DB = 4, and DE = 9.

1. In the figure, point D lies on overlineAB, point E lies on overlineAC, and overlineDE is parallel to overlineBC. What is the length of overlineBC? (type your answer)

Question 6 (harder Module 2)

1. A jazz club sold 240 tickets for a concert. Advance tickets cost $15 each, and tickets bought at the door cost $22 each. The total revenue from ticket sales was $4,020. How many tickets were bought at the door? (A) 60 (B) 180 (C) 240 (D) 420

Question 7 (harder Module 2)

Scatterplot of 12 runners with average weekly training distance from 32 to 78 kilometers on the x-axis and marathon finish time from 195 to 252 minutes on the y-axis. The points trend downward. A line of best fit, y = −1.2x + 290, is drawn.

1. The scatterplot shows the average weekly training distance x, in kilometers, and the marathon finish time y, in minutes, for 12 runners. A line of best fit for the data is also shown, and its equation is y = -1.2x + 290. Based on the line of best fit, if a runner increases the average weekly training distance from 40 kilometers to 65 kilometers, the predicted finish time decreases by approximately what percent? (A) 1.2% (B) 12% (C) 14% (D) 30%

Question 8 (harder Module 2)

1. The function g is defined by g(x) = √(2x + k), where k is a constant. If g(6) = 5, what is the value of g(18)? (type your answer)

Question 9 (harder Module 2)

1. What value or values of x satisfy the equation √(x + 7) = x - 5? (A) 2 only (B) 9 only (C) 2 and 9 (D) There is no solution.

Question 10 (harder Module 2)

1. The linear function f satisfies f(3) = -4 and f(-1) = 8. The function g is defined by g(x) = f(x - 2) + 3. For what value of x is g(x) = 0? (type your answer)

Question 11 (harder Module 2)

1. In the equation x^2 + bx + 16 = 0, b is a positive constant. If the equation has exactly one real solution, what is that solution? (A) -8 (B) -4 (C) 4 (D) 8

Question 12 (harder Module 2)

1. Each student at a language school is enrolled in either the morning program or the evening program, and 40% of the students are in the morning program. Of the students in the morning program, 30% also take an online course, and of the students in the evening program, 45% also take an online course. If a student who takes an online course is selected at random, what is the probability that the student is in the evening program? (A) (27)/(100) (B) (9)/(20) (C) (3)/(5) (D) (9)/(13)

Question 13 (harder Module 2)

1. In a laboratory, a colony of coral polyps triples in number every 4 days. The colony starts with 250 polyps. Which function gives the number of polyps, P(w), in the colony w weeks after the start? (A) P(w) = 250(3)^(w)/(4) (B) P(w) = 250(3)^(4w)/(7) (C) P(w) = 250(3)^(7w)/(4) (D) P(w) = 250(3)^4w

Question 14 (harder Module 2)

1. Two acute angles have measures (3a - 10)° and (a + 16)°, and sin((3a - 10)°) = cos((a + 16)°). What is the value of a? (A) 13 (B) 21 (C) 24 (D) 43.5

Question 15 (harder Module 2)

1. A bike-sharing program offers two plans. With a membership, a rider pays $180 per year plus $0.05 per minute of riding. Without a membership, a rider pays $1.00 per ride plus $0.15 per minute of riding. Each of a certain rider's rides lasts 20 minutes. What is the least number of rides the rider could take in a year for the membership plan to cost less than the plan without a membership? (type your answer)

Question 16 (harder Module 2)

1. For x > 0, the expression fracsqrt[3]x^2 · sqrt[4]x^3√(x) is equivalent to x^k, where k is a constant. What is the value of k? (type your answer)

Question 17 (harder Module 2)

1. A jazz club increased its cover charge by 25%. Later, the club decreased the new cover charge by p%. The final cover charge is 10% less than the original cover charge. What is the value of p? (A) 10 (B) 15 (C) 28 (D) 35

Question 18 (harder Module 2)

1. A circle has a diameter of 24 centimeters. A sector of this circle has an area of 24π square centimeters. What is the measure, in radians, of the central angle of the sector? (A) (π)/(12) (B) (π)/(6) (C) (π)/(3) (D) 2π

Question 19 (harder Module 2)

1. A solar installer is covering a flat roof with two sizes of panels. Each small panel has an area of 1.7 square meters, and each large panel has an area of 2.2 square meters. The total area of the panels can be at most 120 square meters, and at least 60 panels must be installed. What is the maximum number of large panels that can be installed? (A) 24 (B) 30 (C) 36 (D) 54

Question 20 (harder Module 2)

A parabola opening upward labeled y = f(x), with vertex at (2, −3) and y-intercept (0, 5). It also passes through (4, 5).

1. The graph of y = f(x) is shown, where f(x) = ax^2 + bx + c and a, b, and c are constants. What is the value of b? (A) -8 (B) -4 (C) 4 (D) 8

Question 21 (harder Module 2)

1. Two right circular cylinders are similar. The ratio of the volume of the smaller cylinder to the volume of the larger cylinder is 8 : 27. The total surface area of the smaller cylinder is 48π square inches. What is the total surface area, in square inches, of the larger cylinder? (A) (64)/(3)π (B) 32π (C) 72π (D) 108π

Question 22 (harder Module 2)

1. In the system of equations 3x + ky = 5 and kx + 12y = 10, k is a constant. For which value of k does the system have no solution? (A) -6 (B) 0 (C) 6 (D) 36