Digital SAT Math Practice Test with Answers (Part - 11)

Question 1 :

The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms. in 5 hours, what is the speed of the first train?

A)  10 Km/hr

B)  50 Km/hr

C)  70 Km/hr

D)  80 Km/hr

Answer :

Question 2 :

Answer :

Question 3 :

The functions f and g are defined by f(x) = x² + 2 and g(x) = 4x – 3. If a > 0, for what values of a does g[f(a)] = 41?

Answer :

Question 4 :

John is a member of a recreational bowling league. His bowling scores from 2006 to 2015 can be modeled by the equation p = 80.5 + 16.8t, where t represents the number of years since he joined the league in 2006 and p represents the average number of points he scored per game. Which of the following is the best interpretation of the number 16.8 in the equation?

A)  The total number of points John scored in 2006.

B)  The average number of points John scored per game in 2006.

C)  The yearly increase in the average number of points John scored per game.

D)  The average number of games John played each year. 

Answer :

Question 5 :

Bob can finish painting a house in 4 days. Carl can finish painting a house in 6 days. Which of the following equations can be used to find the number of days d that Bob and Carl would need to finish painting one house working together?

Answer :

Question 6 :

In the xy-plane, line k and line j are perpendicular and intersect at the point (3, 9). If line k is defined by the equation y = mx + b, where m and b are constants and m > 1, which of the following points lies on line j?

A)  (4, 9 - 1/m)

B)  (4, 9 + 1/m)

C)  (4, 9 - m)

D)  (4, 9 + m)

Answer :

Question 7 :

P(t) = 350(1.44)^(8a/n)t

The function P models the population, in thousands, of a certain city, t years after 2010. According to the module, the population is predicted to increase by 20% every n months. What is the value of a?

A)  1/16

B)  2/3

C)  3/4

D)  4/5

Answer :

Question 8 :

-4x² + 112x + 42 = -px + w

In the equation given, p and w are constants. The solution set of the equation is {w/2, -w/2}. What is a possible value of w?

Answer :

Question 9 :

The function is defined by f(x) = ½x + a, where a is a constant. If f(a) = 3, what is the value of f(8)?

A)  6

B)  7

C)  8

D)  9

Answer :

Question 10 :

A car is traveling along a highway at 80 miles per hour. Before it exits the highway and enters a residential area, it must slow down to meet the residential speed limit of 30 miles per hour. If it decelerates so that its speed drops by 2 miles per hour every second, how many seconds will it take the car to slow down to the residential speed limit?

Answer :

Question 11 :

Given :

(a + b)³ = a³ + 3ab(a + b) + b)³ 

x = 3^1/3 + 3^-1/3

What is the value of 3x³ - 9x ?

A)  10

B)  12

C)  15

D)  16

Answer :

Question 12 :

Every day, Dave eats either a sandwich or pizza for lunch. Over 42 days, Dave had pizza 3 times for every 4 times he had a sandwich. Over the next x days, he had pizza 3 times for every 2 times he had sanwich. If at the end of this entire period he had pizza as many times as he had a sandwich, what is the value of x?

Answer :

Question 13 :

A printer’s input capacity is the maximum number of sheets of paper the printer can hold at one time. The table below gives the distribution of input capacities for a randomly selected group of printers.

If the median input capacity of these printers is 400 pages, what is the maximum possible value of x?

Answer :

Question 14 :

In the xy-plane, the line defined by the equation y = 3x – 5 passes through the vertex of a parabola with x-intercepts of 3 and 15. What is the y-coordinate of the vertex of the parabola?

Answer :

Question 15 :

The initial price of a computer is a dollars. For each month that passes by, the price is reduced to 10 percent less than the price for the previous month. Based on this information, the price P of the computer can be modeled by the equation

P = a(r)ⁿ

Where n is the number of months that have passed and r is a constant. The price of the computer decreases by n percent every 3 months. What is the value of n?

Answer :

Question 16 :

A)  5/2

B)  5/4

C)  15/13

D)  16/15

Answer :

Question 17 :

In the xy-plane above, a circle is tangent to line ℓ, the x-axis and the y-axis. If the radius of the circle is 5, what is the value of t?

A)  7

B)  8

C)  9

D)  10

Answer :

Question 18 :

In the figure above, D is the midpoint of AB and E is the midpoint of BC. The area of trapezoid ADEC is how many times the area of triangle DBE?

A)  2

B)  2.5

C)  3

D)  3.5

Answer :

Question 19 :

In the xy-plane above, line segment AB is the diagonal of a rectangle. If the area of the rectangle is 20, what is the slope of AB?

A)  1.25

B)  1.5

C)  2.5

D)  5

Answer :

Question 20 :

There are 50 tennis balls, 20 of which are blue, in a container. After x blue tennis balls are removed, 25% of the tennis balls in the container are blue. What is the value of x?

Answer :

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