SAT Math Practice Test with Answers

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Question 1 :

5x² – 40px + 5y² + 70py = 325p²

In the xy-plane, the graph of the given equation is a circle, where p is a constant. The center of the circle is (–8, 14). If a square is incribed in the circle, what is the area of the square ?

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Question 2 :

The speed of an object is increasing at a rate of 33 inches per second squared. What is the rate, in miles per hour squared?

Use (12 inches = 1 foot) and (5,280 feet = 1 mile)

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Question 3 :

In the given system of equations, g and h are constants. The system has no solution. The ratio g to h is equivalent to the ratio 15 to k, where k is a constant. What is the value of k?

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Question 4 :

Which of the following expressions has 6x – 5b as a factor, where b is a positive integer constant?

A) 24x² – 22x – 15b

B) 24x² + 18x – 15b

C) 24x² + 36x – 15b

D) 24x² – 484x – 15b

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Question 5 :

The function f is defined by f(x) = a √(-x + b), where a and b are constants. In the xy-plane, the graph of y = f(x) passes through the point (5, 0), and f(–12) > f(–7). Which of the following must be true?

A) a < f(b)

B) a > b

C) f(3) < f(-2b)

D) a < b

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Question 6 :

The table shows three values of x and their corresponding values of y for the linear relationship between x and y. The x-intercept of the line occurs when x = -4. The number d is a negative constant. The number k is a constant. What is the value of dk?

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Question 7 :

f(x) = ax² – 7x + c

The function f is defined above, where a and c are constants. The graph of y = f(x) is a parabola that has a vertex at the point (h, k), where h and k are constants. If f(-9) = f(-2) and c > 0, which of the following must be true?

I. a < – 3/4

II. k > 16

A) I only

B) II only

C) I and II

D) Neither I nor II

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Question 8 :

The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. A triangle has side lengths of 4x + 20, 2x + 8 and 7x – 11. Which inequality represents all possible values of x?

A) x < 39

B) 8 < 2x < 78

C) 3 < x < 38

D) 23 < 5x < 195

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Question 9 :

In the given circle, point B is the center. Point A, C and D lie on the circle. Point B lies on line segment AC. Line EA is tangent to the circle at point A. The diameter of the circle is 240 cm. The length of segment BE is twice that of segment AB. If minor arc CD is kπ cm, what is the value of k?

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Question 10 :

A circle is centered at point O with coordinates (0, 0) in the xy-plane. The circle contains point A with coordinates (25, 0) and point B with coordinates (k, 24), where k is a negative constant. What is the value of cosine ∠AOB?

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Question 11 :

At a movie theater, there are a total of 350 customers. Each customer is located in either theater A, theater B, or theater C. If one of these customers is selected at random, the probability of selecting a customer who is located in theater A is 0.48, and the probability of selecting a customer who is located in theater B is 0.24. How many customers are located in theater C?

A) 28

B) 40

C) 84

D) 98

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Question 12 :

3 consecutive even integers are ordered from smallest to largest. 5 times the first integer is at least 9 more than the sum of the second and third integers. What is the minimum possible value for the second integer?

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Question 13 :

In triangle ABC, the measure of angle B is 90°, AB is a leg with a length of 12, and segment AC contains the point D. Which of the following must be true?

I. BC = 12tan(∠CAB)

II. cos(∠ABD) – sin(∠DBC) = 0

III. m∠ABD = m∠BDC

A) I and II only

B) II and III only

C) I and III only

D) I, II and III

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Question 14 :

In the xy-plane, the graph of x² + 6x + y² + 2y = 15 is a circle. Line k is a tangent to this circle at the point (a, b) and has a slope of 3/4. What is a possible of b?

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Question 15 :

A square pyramid has a volume of 400 cubic inches and a slant height of 13 inches. If each side of the square base and height are integers in inches, what is the surface area of the pyramid in square inches?

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Question 16 :

The frequency table above summarizes data set A. Data set B is created by multiplying all of the values in data set A by 2. Which of the following must be true?

I. The difference between the mean and median of data set B is 0.

II. The standard deviation of data set B is equal to the standard deviation of data set A.

III. The range of data set B is double the range of data set A.

A) I and II only

B) II and III only

C) I and III only

D) I, II and III

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Question 17 :

In triangle ABC, the measure of angle B is 90°, BD is an altitude of the triangle. The length of BC is 10 and m∠ABD = 60°. What is the length of AD?

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Question 18 :

The function h(x) is defined by h(x) = a^x + b, where a and b are positive constants. The graph of y = h(x) in the xy-plane passes through the points (0, 4) and (2, 12). What is the value of ab?

A) 8

B) 9

C) 12

D) 15

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Question 19 :

The perimeter of a right isosceles triangle is 52 + 52√2. What is the length of hypotenuse?

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Question 20 :

Rectangle ABCD is similar to rectangle WXYZ. The area of rectangle ABCD is 486 square units, and the area of rectangle WXYZ is 54 square units. The length of the longest side of rectangle ABCD is 27 units. What is the length, in units, of the longest side of rectangle WXYZ?

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