Digital SAT Math Practice Test with Answers (Part - 16)

Question 1 :

Objects R and S each travel at a constant speed. The speed of object R is half the speed of object S. Object R travels a distance of 4x inches in y seconds. Which expression represents the time, in seconds, it takes object S to travel a distance of 24x inches?

A)  12y

B)  3y

C)  16y

D)  6y

Answer :

Question 2 :

The weight of sample A is 468% of the weight of sample B, and the weight of sample A is 0.780% of the weight of sample C. If the weight of sample C is p% of the weight of sample B, what is the value of p?

Answer :

Question 3 :

If 4a/b = 6.7 and a/bn = 26.8, what is the value of n?

Answer :

Question 4 :

Let f(x) = (6x + 5)/(x + c) be the result of shifting g(x) = (ax + b)/(x + 4) up 7 units and left 8 units. What is the value of a + b + c?

Answer :

Question 5 :

The area of a rectangular region is increasing at a rate of 250 square feet per hour. Which of the following is closest to this rate in square meters per minute? (Use 1 meter = 3.28 feet.)

A)  0.39

B)  1.27

C)  13.67

D)  23.24

Answer :

Question 6 :

The number a is 70% less than the positive number b. The number c is 60% greater than a. The number c is how many times b?

Answer :

Question 7 :

P(t) = 290(1.04)^(4/6)t

The function P models the population, in thousands, of a certain city t years after 2005. According to the model, the population is predicted to increase by n% every 18 months. What is the value of n?

A)  0.38

B)  1.04

C)  4

D)  6

Answer :

Question 8 :

x² + x√t + y² - y - 65 = 0

The given equation, where t is a constant, defines a circle in the xy-plane. The radius of this circle is √83. What is the value of t?

A)  73

B)  71

C)  37

D)  35

Answer :

Question 9 :

f(x) = 27(1.20)^x/3

For the function f, the value of f(x) increases by p% for every increase of x by 6. What is the value of p?

Answer :

Question 10 :

A circle has equation (x − 2k)² + (y − 3k)² = 64, where k is a positive integer. The center of the circle lies inside the circle x² + y² = 64. If (a, b) is a point on the first circle, what is the least possible value of b?

A)  −5
B)  −2
C)  1
D)  14

Answer :

Question 11 :

A reseller buys certain books for a purchase price of 5.00 dollars each and then marks them each for sale at a consumer price that is 270% of the purchase price. After 4 months, any remaining books not yet sold are marked at a discounted price that is 70% off the consumer price. What is the discounted price of each of the remaining books, in dollars?

Answer :

Question 12 :

A circle in the xy-plane has the equation

x² + y² - (5k/2)x + 3hy + 25k²/16 + 9h²/4 - 37 = 0,

where k and h are positive constants. The center of the circle lies on the line y = -4x/3. What is the value of k/h?

A)  9/10

B)  10/9

C)  4/5

D)  5/4

Answer :

Question 13 :

The function h is defined by h(x) = -√(x² + bx + c), where b and c are constants. In the xy-plane, the graph of y = h(x) contains the points (3, 0) and (0, -√366). If h(m) = 0, what is the greatest possible value of m?

Answer :

Question 14 :

The function f is defined by

where a, b and c are constants. The graph of the function f in the xy-plane, where y = f(x) does not intersect the line x = 3. If f(-4) = f(2) = 0, what is the value of a + b + c?

Answer :

Question 15 :

A certain line in the xy-plane passes through the two points given in the table, where n is a constant. If the x-coordinate of the y-intercept of the line is n + 8, what is the y-coordinate of the y-intercept of the line?

Answer :

Question 16 :

The polynomial P(x) = (t² – 9)x³ + (4t – 1)x² + (6 – t)x + 8, where t is a constant, can be written in the form P(x) = (x + 2)Q(x) + 8 for some polynomial Q(x). What is the sum of all values of t?

A)  3.5

B)  3.75

C)  1.5

D)  2.25

Answer :

Question 17 :

In the guiven system of equations, w is a constant. In the xy-plane the graphs of these equations intersect at the point (q, 19), where q is a constant. What is the value of w?

–x – wy = –337

2x – wy = 47

Answer :

Question 18 :

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

Answer :

Question 19 :

(x – k)² = (k – 5a)(x – k)

In the given equation, a and k are constants, where k > 5a. The sum of the solutions to the equation is 3k + 32. What is the value of a?

Answer :

Question 20 :

A rare vinyl record was valued at $50 in 2004 and at $60.50 in 2006. The value increased by the same percent each year. Based on this model, what was the value, in dollars, of the record in 2012?

A)  92.00

B)  107.18

C)  129.69

D)  134.00

Answer :

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