SAT Math Practice Problems with Answers

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Problem 1 :

In a triangle ABC, sin A = cos B and the length of side AB is 8. Which of the following represents the length of side AC?

A) 8/tan B

B) 8 tan B

C) 8/sin B

D) 8 sin B

Answer :

Problem 2 :

f(x) = 5(0.92)³^x

The function is defined by the given equation. The equation can be reqritten as f(x) = 5(1 - p/100)^x, where p is a constant. Which of the following is closest to the value of p?

A) 8

B) 12

C) 22

D) 24

Answer :

Problem 3 :

The concentration of a chemical compound is equal to the amount of the substance in the container, in moles, divided by the volume of the solution, in cubic centimeters. A chemist has two containers of different sizes (filled to the brim with solution!) each in the shape of a cube. The edge length of the larger container is 4 times the edge length of the smaller container. Each cube contains 144 moles of a substance. The concentration of the compound in the larger container is 3 moles per cubic centimeter. What is the positive difference between the larger container’s volume and the smaller container’s volume, in cubic centimeters?

Answer :

Problem 4 :

A line intersects two parallel lines, forming four acute angles and four obtuse angles. The measure of one these eight angles is (7x – 250)°. The sum of measures of four of the eight angles is k°. Which of the following could NOT be equivalent to k, for all values of x?

A) –14x + 1,540

B) 14x – 320

C) –28x + 1,720

D) 360

Answer :

Problem 5 :

The function f is defined by f(x) = ax² + bx + c, where a, b and c are constants. The graph of y = f(x) is a parabola where f(-11) = f(-1). If b is an integer less than -3, what is the greatest possible value of a + b?

Answer :

Problem 6 :

3x² + 18x + 3y² – 6y – 15 = 0

The equation above gives the graph of a circle in the xy-plane. If the circle is inscribed in a square, what is the area of the square?

Answer :

Problem 7 :

A table of popular movie theater chains is shown above. A movie theater chain is considered a BIG chain, if it has more than 6,000 screens. The ratio of BIG chain screens to all screens is k to 5. If Wanda (a smaller chain) has a total of x thousand screens, which expression represents k in terms of x?

Answer :

Problem 8 :

Answer :

Problem 9 :

The effectiveness of onlinemath4all YouTube channel on student DSAT Math score improvement is being studied. A psychometrician selected 152 students for the study. The students were obtained from two randomly selected schools of 76 students each. The students from one school received access to many onlinemath4all videos, while the students from the second school did not use onlinemath4all’s videos (they were encouraged to seek other sources). How should the experiment be changed to allow the reasearcher to conclude whether onlinemath4all videos have an effect on DSAT math score improvement?

A) All 152 students should receive acess to onlinemath4all’s videos.

B) One of the schools should study without a calculator.

C) Half of the students from each school should be randomly assigned to each study plan.

D) No changes to the experiment are needed.

Answer :

Problem 10 :

Which of the following could be the equation of the graph shown in the xy-plane?

A) y = – (1/15)(x – 6)(x – 4)²(x + 1)

B) y = – (1/15)(x – 6)²(x – 4)(x + 1)²

C) y = – (1/15)(x + 6)(x + 4)²(x + 1)

D) y = – (1/15)(x + 6)²(x + 4)(x – 1)²

Answer :

Problem 11 :

An equilateral triangle is inscribed in a circle with a diameter of 16. Which of the following gives the area of the equilateral triangle?

A) 6√3

B) 24√3

C) 32√3

D) 48√3

Answer :

Problem 12 :

The given equation ax² + 88x + c = 0, where a and c are constants has no real solutions and a factor of kx + j. What is the least possible value of ac?

Answer :

Problem 13 :

f(t) = 34,000(1.07)^6t

The given function f models the balance of an investment account, in dollars, t years after it is opened. Which statement is the best interpretation of (1.07)^6t?

A) Every 6 years, the balance increases by 2,380 dollars.

B) Every 6 years, the balance increases by 7% of the previous 6 years balance.

C) Every 2 months, the balance increases by 2,380 dollars.

D) Every 2 months, the balance increases by 7% of the previous 2 months balance.

Answer :

Problem 14 :

The quadratic function a(x + 4.5)² - d can be rewritten as (x - 9.5)(x + c). If a is equal to 1, what is the value of d?

Answer :

Problem 15 :

g(x) is a quadratic function. In the xy-plane, the graph of y = g(x) passes through the points (12, 540) and (16, 908). If g(0) = 12, what is the value of g(24)?

Answer :

Problem 16 :

The surface area of rectangle prism A is 312 m². The surface area of area of rectangle prism B is 11,232 m². Rectangular prism A has a volume of 224 m³. If both rectangular prisms are similar, what is the volume of rectangular prism B?

Answer :

Problem 17 :

The given figure shows lines a and b intersected by line k. Which of the following is sufficient to prove that a and b are parallel?

A) 180 – y = x

B) x = 180 – z

C) y + z = 180 – x

D) 180 – z = y

Answer :

Problem 18 :

The function f is defined by f(x) = ax² + bx + c, where a, b and c are constants. The graph of y = f(x) in the xy-plane passes through the points (13, 0) and (-6, 0). Which of the following is the value of a + b in terms of a?