Digital SAT Math Practice Test with Answers (Part - 5)

Question 1 :

y = 4x² + 15

y = mx + 6

In the above system, the parabola and line intersect at exactly one point. What is the slope of the line m?

A)  6

B)  9

C)  12

D)  15

Answer :

Question 2 :

An hourglass timer is filled with 1200 tiny beads that flow from the top container to the bottom container at a constant rate. It took one hour, when all the beads have reached the bottom container. How many minutes did it take, when 520 beads have reached the bottom cotainer?

Answer :

Question 3 :

Jane is performing an experiment in which she combines potassium and water to produce potassium hydroxide. The amount of water w, in milliliters needed to create a chemical reaction between potassium and water can be modeled by the equation w = 1.6a + 10, where a is the amount of potassium hydroxide, in grams, Jane wishes to produce from the reaction. According to the model, how much more potassium hydroxide, in grams is produced for each additional milliliter of water used in the reaction?

A)  0.6

B)  0.625

C)  0.875

D)  1.6

Answer :

Question 4 :

Evolutionary biologists measure a species’ effective population N_e to assess its health and evolutionary patterns. The formula above relates N_e to N_f, the number of females capables of breeding, and N_m, the number of males capable of breeding. Which of the following expresses the number of females capable of breeding in terms of the effective population and the number of males capable of breeding?

Answer :

Question 5 :

Tammy picks three sides of a rectangle and adds their lengths to get 140 cm. Gladys picks three sides of the same rectangle and adds their lengths to get 100 cm. What is the perimeter of the rectangle in cm?

A)  120

B)  140

C)  150

D)  160

Answer :

Question 6 :

In the system of equations of above, p and q are constants. The system of equations has more than one solution. What is the value of q?

Answer :

Question 7 :

The sum of the roots of a cubic polynomial, g(x) = ax³ + bx² + cx + d is 6. If g(x) can be expressed as (x² – 4x + 4)(x + k), what is the value of a + b + c + d?

Answer :

Question 8 :

The function f is defined by f(x) = ax² + bx + c, where a, b and c are constants. The graph of y = f(x) in the xy-plane passes through the points (7, 0) and (-3, 0). If a is an integer greater than 1, which of the following could be the value of a + b?  

A)  -6

B)  -3

C)  4

D)  5

Answer :

Question 9 :

An equilateral triangle with side length k is inscribed into a circle. Which of the following defines the radius, r, in terms k?

A)  k/2

B)  k√3/6

C)  k√3/3

D)  k√3/2

Answer :

Question 10 :

If x > 0 and a = 2 in the equation above, what is the value of x?

A)  4

B)  5

C)  6

D)  7

Answer :

Question 11 :

In the given figure, BC is the diameter of the circle. If the length of BC is equal to 132 and the length of AB is equal to √363, what is the value of BC/BD?

Answer :

Question 12 :

x^2/3 - 4x^1/3 - 5 = 0

What positive value of x staisfies the equation above?

Answer :

Question 13 :

64x² – (16a + 4b)x + ab = 0

In the given equation, a and b are positive constants. The sum of the solutions to the given equation is k(4a + b), where k is a constant. What is the value of k?  

Answer :

Question 14 :

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?

Answer :

Question 15 :

For all x ≥ 3, f(x) = √(x - 3)/2. If f(n) = 3, what is the value of n?

Answer :

Question 16 :

If -4k + 12 ≥ -24, what is the maximum possible value of 3k?

Answer :

Question 17 :

When 3x² + x + 2 is divided by x - 1, the result can be expressed as ax + b + c/(x - 1), where a , b and c are constants. What is the value of a + b + c?

Answer :

Question 18 :

Juan’s restaurant serves burritos during lunch and dinner. On a typical day, 25 percent more burritos are sold during lunch than dinner. If x represents the number of burritos sold during lunch, the total number of burritos sold on a typical day can be represented by the expression ax, where a is a constant. What is the value of a in the expression?

Answer :

Question 19 :

Kevin has collected m coins. Ellie has collected half as many as Kevin, but 5 more than Robert. In terms of m, how many coins has Robert collected?

A)  2m - 5

B)  m/2 + 5

C)  2m + 5

D)  m/2 - 5

Answer :

Question 20 :

A)  g(x) = x²(x + 2)²

B)  g(x) = x³(x - 2)²

C)  g(x) = x²(x + 2)(x - 2)

D)  g(x) = (x + 2)²(x - 2)²

Answer :

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