SAT Math Problems and Solutions

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Problem 1 :

The table gives the volume of two similar cylinders. If the radius of cylinder A is 9 cm. What is the value of j – k?

Volume = πr²h

Surface Area = 2πr² + 2πrh

Solution :

Problem 2 :

y = –3x² – 58

y = px - 46

In the given system of equations, p is a constant. The graphs of the equations in the given system intersect at exactly one point, (x, y) in the xy-plane. Which of the following could be the value of x?

A) -2

B) -4

C) 12

D) 16

Solution :

Problem 3 :

ax² + bx + c = 0

The quadratic equation above has two real roots and sum of those two roots is –4. If a > 0, then which of the following is true?

A) a ≥ c/4

B) a > c/4

C) c ≥ a/4

D) c > a/4

Solution :

Problem 4 :

(x + 7) is a factor of the quadratic function y = f(x), and x = c is a positive zero of the function. If the minimum of the function is (63/8, k), what is the value of c?

Solution :

Problem 5 :

For two acute angles, ∠A and ∠B, cos A = sin B. The measures, in degrees, of ∠A and ∠B are 13x + 10 and 48 + 3x, respectively. What is the value of x?

Solution :

Problem 6 :

A baseball coach charges each athlete $150 for the first month and $95 for each additional month. Which of the following functions correctly represents the total revenue R(m), in dollars, for m months and n athletes, where m and n are positive integers?

A) R(m) = 95mn + 55

B) R(m) = 95mn + 150

C) R(m) = 95mn + 55n

D) R(m) = 95mn + 150n

Solution :

Problem 7 :

f(x) = -7x + b

For the given function f(x), which of the following gives the equation for the function f(x) + 20, given that the point (-4, 0) lies on the graph of f(x) - 20?

A) f(x) = -7x - 28

B) f(x) = -7x - 8

C) f(x) = -7x + 8

D) f(x) = -7x + 12

Solution :

Problem 8 :

The positive number a is 480% of the number b, and a is 70% of the number c. If c is p% of b, which of the following is closest to the value of p?

A) 267

B) 336

C) 550

D) 685

Solution :

Problem 9 :

f(x) = a^x – b

The exponential function given above passes through the points (c, 8) and (2c, 350). What is a possible value of b?

Solution :

Problem 10 :

For the function f, for every increase of 1/2 in the value of x, the value of f(x) increases by a factor of c, where c is a constant. Which of the following forms of function f displays the value of c as the base or coefficient?

A) f(x) = 56(2)^6x

B) f(x) = 56(8)^2x

C) f(x) = 56(64)^x

D) f(x) = 56(4,096)^x/2

Solution :