SAT Math Practice Test

Topic 2.1 · Concept check

If 4(x − 3) = 2x + 10, what is the value of x?

Topic 2.1 · Apply it

A line passes through the points (2, 5) and (6, 17). Which equation represents the line?

Topic 2.1 · Concept check

If 2x + 3y = 12 and x − y = 1, what is the value of x + y?

Topic 2.1 · Apply it

A gym charges a one-time $40 sign-up fee plus $25 per month. Which equation gives the total cost C, in dollars, for m months of membership?

Topic 2.1 · Apply it

The height h, in centimeters, of a plant w weeks after it was measured is modeled by h = 1.5w + 12. What is the best interpretation of 1.5 in this context?

Topic 2.1 · Concept check

Which inequality describes all solutions to 5 − 2x > 11?

Topic 2.1 · Apply it

In the system 3x + ky = 7 and 6x + 10y = 5, k is a constant. For what value of k does the system have no solution?

Topic 2.1 · Apply it

Line ℓ has equation y = −(2/3)x + 4. Line m is perpendicular to line ℓ and passes through (0, −1). Which is an equation of line m?

Topic 2.1 · Apply it

A theater sold 150 tickets for a total of $1,520. Adult tickets cost $12 and student tickets cost $8. How many adult tickets were sold?

Topic 2.1 · Concept check

At what point does the graph of 3x − 4y = 24 cross the x-axis?

Topic 2.1 · Concept check

If (2/3)n = 18, what is the value of (1/2)n?

Topic 2.1 · Apply it

For the linear function f, f(2) = 7 and f(5) = 16. What is the value of f(10)?

Topic 2.1 · Apply it

In the equation 3(2x − a) = 6x − 12, a is a constant. If the equation has infinitely many solutions, what is the value of a?

Topic 2.1 · Apply it

A tank holds 500 liters of water and drains at a constant 20 liters per minute. After how many minutes will the tank hold 140 liters?

Topic 2.1 · Apply it

A student earns $15 per hour tutoring and $10 per hour walking dogs and wants to earn at least $300 this month. If t is hours tutoring and d is hours walking dogs, which inequality represents this situation?

Topic 2.2 · Concept check

What is the positive solution to x² − 5x − 14 = 0?

Topic 2.2 · Concept check

If f(x) = 2x² − 3x + 1, what is the value of f(−2)?

Topic 2.2 · Apply it

A colony of bacteria starts with 500 bacteria and doubles every 3 hours. Which function gives the number of bacteria P after t hours?

Topic 2.2 · Concept check

Which expression is equivalent to (x + 3)² − (x − 3)²?

Topic 2.2 · Concept check

What is the minimum value of y = (x − 4)² − 9?

Topic 2.2 · Apply it

For what value of c does the equation x² + 6x + c = 0 have exactly one real solution?

Topic 2.2 · Apply it

What are all the solutions to √(x + 7) = x − 5?

Topic 2.2 · Concept check

If (x² − 9)/(x + 3) = 5 and x ≠ −3, what is the value of x?

Topic 2.2 · Concept check

Which expression is equivalent to (16x⁸)^1/2, for x > 0?

Topic 2.2 · Apply it

The value V, in dollars, of a car t years after it was bought is modeled by V = 24,000(0.85)^t. Which statement best describes the car's value?

Topic 2.2 · Apply it

The function f is defined by f(x) = x², and g(x) = f(x − 2) + 3. What is the vertex of the graph of g?

Topic 2.2 · Concept check

What is the sum of the solutions to 2x² − 8x + 3 = 0?

Topic 2.2 · Apply it

In the polynomial p(x) = x³ − 2x² + kx − 6, k is a constant. If x − 3 is a factor of p(x), what is the value of k?

Topic 2.2 · Apply it

The function h is defined by h(x) = a·b^x, where a and b are positive constants. If h(0) = 5 and h(2) = 45, what is the value of h(3)?

Topic 2.2 · Apply it

Which point is a solution to the system y = x² − 4 and y = 2x − 1?

Topic 2.3 · Apply it

A jacket that normally costs $80 is on sale for 25% off. A 10% sales tax is then added to the sale price. What is the final cost of the jacket?

Topic 2.3 · Apply it

There are 2.54 centimeters in 1 inch and 12 inches in 1 foot. How many centimeters long is a board that is 3 feet long?

Topic 2.3 · Data analysis

A student who prefers online classes is chosen at random. What is the probability that the student is in grade 11?

Topic 2.3 · Data analysis

A data set contains the values 3, 5, 7, 9 and 26. Which statement about the data set is true?

Topic 2.3 · Data analysis

In a random sample of 400 voters in a city of 60,000 voters, 240 said they support a new park. The margin of error for the sample proportion is 4 percentage points. Which conclusion is most reasonable?

Topic 2.3 · Data analysis

For a group of students, the line of best fit relating minutes spent reading per day, x, to vocabulary test score, y, is y = 2.4x + 15. Based on this line, how much higher is the predicted score for each additional 5 minutes of reading per day?

Topic 2.3 · Apply it

The number of members in a club increased from 40 to 58. By what percent did the number of members increase?

Topic 2.4 · Concept check

A right triangle has legs of length 9 and 12. What is the perimeter of the triangle?

Topic 2.4 · Apply it

A circle in the xy-plane has equation x² + y² − 6x + 4y − 12 = 0. What is the radius of the circle?

Topic 2.4 · Concept check

In right triangle ABC, angle C is the right angle and sin A = 5/13. What is tan A?

Topic 2.4 · Apply it

Triangle DEF is similar to triangle ABC, with DE corresponding to AB. If AB = 6, DE = 15 and the area of triangle ABC is 20, what is the area of triangle DEF?

Topic 2.4 · Concept check

A circle has radius 9. What is the area of a sector of the circle with a central angle of 120°?

Topic 2.4 · Concept check

A right circular cone has radius 3 and height 8. What is its volume?

Topic 2.4 · Apply it

Two parallel lines are cut by a transversal. Two same-side interior angles measure (3x + 10)° and (2x + 20)°. What is the measure of the larger angle?