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 :

Problem 11 :

A circle with center (-7, -4) has a radius equal to 14. The equation x² + y² + ax + by + c = 0 represents the circle. What is the value of c?

Solution :

Problem 12 :

If k = l + m, which of the following is equivalent to the expression x² - l² - 2lm - m²?

A) (x + k)²

B) (x - k)²

C) (x - k)(x + k)

D) x² - kx - k²

Solution :

Problem 13 :

ax² + 148x + c

In the given expression, a and c are positive constants. If jx + k is a factor of the expression, where j and k are positive constants, what is the greatest possible value of ac?

Solution :

Problem 14 :

Lines c and d are perpendicular. If the equation of line c is y = mx + b and the lines intersect at point (7, 6). Which point lies on line d?

A) (7 + m, 7)

B) (2m, 8)

C) (7 + 2m, 4)

D) (7 - 3m, 3)

Solution :

Problem 15 :

What is the value of k, if the given equation only has one solution?

¼|x - 4| - 30 = 2k

Solution :

Problem 16 :

In the given pair of equations a and b are constants. The graph of this pair of equations in the xy-plane is a pair of perpendicular lines. Which of the following pairs of equations also represents a pair of perpendicular lines?

13x + 17y = 10

ax + by = 10

A) 39x + 17y = 10

ax – 3by = 10

B) 13x - 17y = 10

ax + by = 10

C) 65x + 17y = 10

5ax + by = 10

D) 52x + 34y = 10

2ax + 4by = 10

Solution :

Problem 17 :

Which equation correctly gives c in terms of d, e and f?

73/c = 73/d + 73/e + 73/f

A) c = d + e + f

B) c = def/(d + e + f)

C) c = (d + e + f)/def

D) c = def/(de + df + ef)

Solution :

Problem 18 :

For the exponential function f, the value of f(3) is k, where k is a constant. Which of the following equivalent forms of the function f shows the value of k as the coefficient or the base?

A) f(x) = 3(4)(4)^x + 1)

B) f(x) = 3,072(4)(4)^{x - 4}

C) f(x) = 12(4)(4)^x

D) f(x) = 768(4)(4)^{x - 3}

Solution :