Digital SAT Math Questions and Answers

Problem 1 :

The functions f and g are defined by the given equations, where 1 ≤ x ≤ 5. Which of the following equations displays, as a constant or coefficient, the minimum value of the function it defines, where 1 ≤ x ≤ 5?

I.  f(x) = 2(0.8)(4)^{x – 4}

II.  f(x) = 64(0.3125)(0.5)^{x + 1}

A)  I only

B)  II only

C)  I and II

D)  Neither I nor II

Solution :

Problem 2 :

The total distance d, in meters, traveled by an object moving in a straight line can be modeled by a quadratic function that is defined in terms of t, where t is the time in seconds. At a time of 10.0 seconds, the total distance traveled by the object is 50.0 meters, and at a time of 20.0 seconds, the total distance traveled by the object is 200.0 meters. If the object was at a distance of 0 meters when t = 0, then what is the total distance traveled, in meters, by the object after 30.0 seconds?

Solution :

Problem 3 :

Solve for b :

Solution :

Problem 4 :

A pyramid has 6 edges. Each edge is 40 cm in length. If the surface area of the pyramid is k√3, what is the value of k?

Solution :

Problem 5 :

The quadratic function a(x + 4.5)² - d can be written as

(x - 9.5)(x + c)

If a is equal to 1, what is the value of d?

Solution :

Problem 6 :

f(x) = ax² + bx + c

In the given quadratic function, a and c are constants. The graph of y = f(x) in the xy-plane is a parabola that opens upward and has a vertex at the point (h, k), where h and k are constants. If k < 0 and f(-9) = f(3), which of the following must be true?

I. a ≥ 1

II. c < 0

A) I only

B) II only

C) I and II

D) Neither I nor II

Solution :

Problem 7 :

y = x² – 2x – 3

y = 2x – 3       

In the system of equations above, if x and y represent length and width of a rectangle respectively, then what is the area of the rectangle?

Solution :

Problem 8 :

Which of the following is equivalent to (√a + √b)^2/3, where a > 0 and b > 0?

A)  (a + b)³ .

B)  ³√(a + b)

C)  (a + 2√ab + b)^1/3

D)  ³√(a + 2ab + b)

Solution :

Problem 9 :

Two different points on a number line are both 3 units from the point with coordinate -4. The solution to which of the following equations gives the coordinates of both points?

A)  |x + 4| = 3

B)  |x - 4| = 3

C)  |x + 3| = 4

D)  |x - 3| = 4

Solution :

Problem 10 :

x² – ax + 12 = 0

In the equation above, a is a constant and a > 0. If the equation has two integer solutions, what is the smallest possible value of a?

Solution :

Problem 11 :

A line intersects two parallel lines, forming four acute angles and four obtuse angles. The measure of one of the acute angles is (7x – 610)º. The sum of the measures of one of the acute angles and three of the obtuse angles is (-14x + w)º. What is the value of w?

Solution :

Problem 12 :

f(x) = a(x - 3)² + b(x - 3)²

If f(10) = m and f(-4) = n, what is the value of

109(113)^{m - n} + 229(97)^{n - m}?

Solution :

Problem 13 :

In the figure shown, AD = 121/3 and AB = 11√130/3. What is the length of DC?

Solution :

Problem 14 :

w² + 12w - 40 = 0

Which of the following is a solution to the given equation?

A)  6 - 2√19

B)  2√19

C)  √19

D)  -6 + 2√19

Solution :

Problem 15 :

The given quartic function 54x⁴ + 219x² + 105 has factors in the form (k)(ax² + b)(cx² + d). If a, b, c, d and k are integers, what is the smallest possible value of ab?

Solution :

Problem 16 :

If y⁴ = 80 and z⁵ = 32, what is the value of y⁸ ⋅ z^-5?

A)  50

B)  64

C)  160

D)  200

Solution :

Problem 17 :

A rectangular prism has a height of 50 centimeters (cm). The base of the prism is a square and the surface area of the prism is S cm². If the prism is divided into two identical rectangular prisms by making a cut parallel to the square base, each resulting prism has a surface area of (³¹⁄₅₆)S cm². What is the side length, in cm, of each square base?

A)  5

B)  6

C)  12

D)  24

Solution :

Problem 18 :

In a school, there are 40 boys and some girls in a class. All the girls and 32 boys, which together account for 90% of the total number of students, went on a field trip. What is the percentage of girls in the class?

A)  25%

B)  40%

C)  50%

D)  60%

Solution :

Problem 19 :

A man walks around a rectangular field at 6 km per hour and completes one round in 2 hours. If the area of the field is 8 sq. km, what is the difference between its length and width?

A)  2.0 km

B)  3.5 km

C)  3.354 km

D)  4.5 km

Solution :

Problem 20 :

In the equation above, if x ≠ 0 and y ≠ 0, find the value of x/y.

Solution :

Problem 21 :

(5²² + 5²²)(4²² + 4²²) = x ⋅ 20²²

In the equation above, what is the value of x?

Solution :

Problem 22 :

Cube A has a volume of 64 cubic centimeters. Cube B has an edge length that is half the edge length of Cube A. Which of the following equations represents the relationship between volume, v, of Cube B in terms of the volume of Cube A?

A)  v = √64

B)  v = 64²

C)  v = 2(64)

D)  v = ⁶⁴⁄₂

Solution :

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