DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 6)

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Problem 1 :

When the linear function y = f(x) is graphed in the xy-plane, the graph contains the corresponding values of x and f(x) shown in the table above. Which of the following could represent the function?

A) f(x) = 3x + 12

B) f(x) = 3x + 15

C) f(x) = 15x + 12

D) f(x) = 15x + 15

Solution :

Problem 2 :

The height of a rocket launched from a rooftop can be modeled by the equation h = -16s² + 64s + 21, where h is the height of the rocket above the ground, in feet, and s is the number of seconds since the rocket was launched. Which of the following represents the height, in feet, of the rooftop from which the rocket was launched?

A) 0

B) 16

C) 21

D) 64

Solution :

Problem 3 :

If h(–1) = 3 and h(0) = 5 in linear function h, which of the following is the equation of function h?

A) h(x) = 2x + 5

B) h(x) = 2x + 3

C) h(x) = 2x

D) h(x) = 3x + 5

Solution :

Problem 4 :

Which of the following equations correctly expresses r in terms of p and s if the relationship between the numbers p, r, and s can be expressed as p = 13r – 6s?

Solution :

Problem 5 :

Right triangle ABC has sides of the following lengths : AB = 165, BC = 280, and AC = 325. Another triangle, LMN, is similar to ABC such that A corresponds to L and B corresponds to M. What is the value of cos(L)?

Solution :

Problem 6 :

If x² = y³, for what value of z does x^3z = y⁹?

A) -1

B) 0

C) 1

D) 2

Solution :

Problem 7 :

A quadratic function models the height, in feet, of an object above the ground in terms of time, in seconds, after the object was launched. According to the model, the object was launched from a height of 8 feet and reached its maximum height of 1800 feet 16 seconds after it was launched. Based on the model, what was the height in feet, of the object 24 seconds after it was launched?

Solution :

Problem 8 :

x(4k – 15) + 19 = 53x + 47

In the given equation, k is a positive integer. If the given equation has exactly one solution, what cannot be the value of k?

A) 17

B) 19

C) 53

D) 68

Solution :

Problem 9 :

A bank offers 5% compound interest calculated on half yearly basis. A customer deposits $1600 each on 1st January and 1st July of a year, the amount he would have gained by way of interest is :

A) $120

B) $121

C) $122

D) $123

Solution :

Problem 10 :

If 2 = p³, then which of the following is equal to 8p?

A) p⁶

B) p⁸

C) p¹⁰

D) 8√2

Solution :

Problem 11 :

If p² – q² = x and y = 2pq, which of the following is equivalent to x² + y²?

A) (p² + q²)²

B) (p² – q²)²

C) p⁴ – q⁴

D) p⁴ + q⁴

Solution :

Problem 12 :

The volume of a right circular cone is 33 cubic feet. What is the volume, in cubic feet, of a right circular cone with half the radius and twice the height of the cone?

A) 16.5

B) 33

C) 49.6

D) 66

Solution :

Problem 13 :

8(p – 1) = 5(p² – 1) – 6(p – 1)

If p > 1, what is the solution of the equation above?

Solution :

Problem 14 :

The expression is equivalent to (3x + 2)/(x + 2)², where a and b are constants and x ≠ 2. What is the value of b?

Solution :

Problem 15 :

In the figure above, line ℓ is parallel to line m. What is the value of k?

Solution :

Problem 16 :

If m + 6 divided by 2 is 4 less than 4m, what is the value of m?

A) 2

B) 3

C) 4

D) 5

Solution :

Problem 17 :

If a line contains the points (0, 0) and (12, 16), then the line will also contain which of the following points?

A) (2, 3)

B) (3, 2)

C) (3, 4)

D) (4, 3)

Solution :

Problem 18 :

sin x = sin y

In the equation above, x and y are measured in radians. Which of the following could be x in terms of y?

A) π/2 - y

B) π/2 + y

C) y - π/2

D) π - y

Solution :

Problem 19 :

The equation (2x - b)(7x + b) = 14x² - cx - 16 is true for all values x, where b and c are constants. If b is greater than 0, what is the value of c?

A) -20

B) 20

C) 28

D) 36

Solution :

Problem 20 :

Battery A runs out of energy after 132 minutes. Battery runs out of energy twice as fast. Battery C runs out of energy three times as fast as Battery B. If used one at a time, what is the total number of minutes that all the three batteries can provide energy for?

Solution :