Digital SAT Math Practice Test with Answers (Part - 17)

Question 1 :

Let f(x) be a quadratic function with real coefficients such that

2x² – 12x + 20 ≤ f(x) ≤ 3x² – 18x + 29

for all real numbers x. If f(1) = 12, find the value of f(27).

Answer :

Question 2 :

The graph of g(x) is shown.

If g(x + 28) = ⅒(x - a)²(x - b)²(x - c), where a, b and c are constants, which of the following could be the value of b?

A)  31

B)  3

C)  -2

D)  -25

Answer :

Question 3 :

g(x) = ¹⁄₁₆[9(2)^x + 7]

When the given equation is graphed in the xy-plane, g(x) is greater than k for all values of x, where k is a constant. What is the largest possible value of k?

A)  0

B)  7/16

C)  2

D)  There is not enough information to determine the value of k.

Answer :

Question 4 :

For positive numbers x and y, x + y = 8 and xy = 12. What is the value of the following expression?

A)  40/7

B)  43/7

C)  146/21

D)  22/3

Answer :

Question 5 :

The diagram shows lines m and n intersected by transversal t. The measure of ∠3 is (5x + 18)° and the measure of ∠6 is (8x - 15)°. Which of the following additional information is sufficient to conclude that lines m and n are parallel?

A)  ∠2 ≅ ∠3

B)  ∠5 ≅ ∠7 = 180°

C)  m∠1 + m∠4 = 180°

D)  m∠3 and m∠6 are alternate interior angles.

Answer :

Question 6 :

In right triangle XYZ, angles X and Z are acute. Point R lies on XZ such that YR ⊥ XZ. If sin(∠XZY) = 12/13, what is the value of YR/XR?

Answer :

Question 7 :

In rectangle PQRS, diagonal QS has length √2500. The perimeter of the rectangle is 140 units. If PQ is greater than QR, what is the value of PQ - QR?

Answer :

Question 8 :

A circle has center (h, c), where h and c are constants. The points (h + 8, c) and (h + 2, k) lie on the circle. If k > c, what is the value of k - c?

A)  2

B)  √15

C)  √60

D)  8

Answer :

Question 9 :

In an xy-plane, the graph of the equation y = m^x – n passes through the points (a, 9) and (2a, 219). What could be a value of n?

A)  14

B)  6

C)  –6

D)  –14

Answer :

Question 10 :

6 + 7r = pw

7r – 5w = 5w + 11

In the given system of equations, p is a constant. If the system has no solution, what is the value of p?

Answer :

Question 11 :

In the figure BD and AC intersect at point D, BD = 16 and CD = 12. What is the value of tan A?

Answer :

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