Digital SAT Math Practice Test with Answers (Part - 14)

Question 1 :

2x + 9y = 7

The given equation is one equation in a system of two linear equations. If the system of equations has at least one solution, which of the following equations could be the other equation in the system?

I.  3x + 13.5y = 10.5

II.  3x - 13.5y = 10.5

A)  I only

B)  II only

C)  I and II

D)  Neither I nor II

Answer :

Question 2 :

y = ax² - 72x + c

y = x² -bx + 18

In the system of equations above, a, b and c are integer constants, and the two equations have the same x-intercepts. if the x-intercepts are integer values, what is the value of c?

A)  8

B)  9

C)  36

D)  144

Answer :

Question 3 :

The graph of y = f(x) + 4 is shown. Which equation defines function f ?

A)  f(x) = -3^x + 1

B)  f(x) = -3^x + 5

C)  f(x) = -3^x + 8

D)  f(x) = -3^x + 9

Answer :

Question 4 :

Two lines intersect at exactly one point, forming two acute angles and two obtuse angles. The measure of one of these angles is (9x - 140)°. Which of the following could NOT be the sum of the measures of any two of these angles?

A)  (-18x + 280)°

B)  (-18x + 640)°

C)  (18x - 280)°

D) 180°

Answer :

Question 5 :

A scientist measured the lengths of 240 gray seals from Muskeget Island and 120 gray seals from Sable Island. The scientist determined that the mean length of the 240 gray seals from Muskeget Island was 88 inches and the mean length of the 120 gray seals from Sable Island was 94 inches. What was the mean length of all 360 gray seals the scientist measured for this study?

A)  89

B)  90

C)  91

D)  92

Answer :

Question 6 :

Circle A in the xy-plane has the equation (x + 5)² + (y - 5)² = 25. Circle B has the same center as circle A. The radius of circle B is two times the radius of circle A. The equation defining circle B in the xy-plane is (x + 5)² + (y - 5)² = k., where k is a constant. What is the value of k?

Answer :

Question 7 :

x² + 7x + 5 = 0

One solution to the given equation can be written as x = (-7 + √k)/2, where k is a constant. What is the value of k?

Answer :

Question 8 :

In triangle QRS shown, QR is less than RS. Which expression represents the length QS?

A)  18cos Q

B)  18sin Q

C)  18/cos Q

D)  18/sin Q

Answer :

Question 9 :

The cost to rent a bus from Company X is $950 for the first 3 hours and an additional $50 per hour for each hour after the first 3 hours. If the total cost to rent the bus from Company X for t hours, where t > 3, is $1,150, which equation represents this situation?

A)  950(t - 3) + 50t = 1,150

B)  950(3t) + 50t = 1,150

C)  950 + 50(t - 3) = 1,150

D)  950 + 50(3t) = 1,150

Answer :

Question 10 :

The population of the town of Smithville doubled every 75 years from 1659 to 1959. The population of this town was 240,000 in 1959. What was the population of this town in 1659?

Answer :

Question 11 :

Which of the following expressions is equivalent to the expression above? 

Answer :

Question 12 :

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

Answer :

Question 13 :

In the given equation, k and n are constants and n is greater than 1. The equation has no solution. What is the value of k?

Answer :

Question 14 :

57x² + (57b + a)x + ab = 0

In the given equation, a and b are positive constants. The product of the solutions to the given equation is kab, where k is a constant. What is the value of k?

A)  1/57

B)  1/19

C)  1

D)  57

Answer :

Question 15 :

In triangle ABC, AB = BC. Points D and E lie on line segments AB and BC, respectively, such that line segments DE and AC are parallel. Point O is the midpoint of line segment DE, and the measure of ∠OAC is 30°. Point F lies on line segment AC, and line segment BF passes through point O. If AB = 81 and AO = BO, what is the length of line segment BE?

Answer :

Question 16 :

The function f is defined by f(x) = 4x + k(x – 1), where k is a constant, and f(5) = 32. What is the value of f(10)?

Answer :

Question 17 :

In the figure, EG and AD intersect at point F, and line 𝓁 is parallel to line j. If EF = 0.5CD and FG = 2.25CD, which of the following must be true?

I.  AB = 2.25EF

II.  FG = 0.5AB

III.  EF/FG = AF/FD

A)  I only

B)  II only

C)  I and II

D)  II and III

Answer :

Question 18 :

Which expression is NOT a factor of 1120x⁴ – 43750?

A)  4x² + 25

B)  2x² – 5

C)  2x + 5

D)  70

Answer :

Question 19 :

x² + y² = 36

y = mx + b/4

In the given system of equations, m and b are constants. In the xy-plane, the graphs of the equations in the given system intersect at the point (–5, y), where y < 0. Which expression represents the value of b?

A)  -5m/4 + √11/4

B)  5m/4 - √11/4

C)  -20m + 4√11

D)  20m - 4√11

Answer :

Question 20 :

How many liters of a 25% saline solution must be added to 3 liters of a 10% saline solution to obtain a 15% saline solution?

Answer :

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