DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 15)

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Problem 1 :

Which expression is equivalent to ⁷√(x⁹y⁹), where x and y are positive?

A) (xy)^7/9

B) (xy)^9/7

C) (xy)¹⁶

D) (xy)⁶³

Solution :

Problem 2 :

Which of the following equations is the most appropriate linear model for the data shown in the scatterplot?

A) y = -1.9x - 10.1

B) y = -1.9 + 10.1

C) y = 1.9x - 10.1

D) y = 1.9x + 10.1

Solution :

Problem 3 :

The graph of y = f(x) is shown, where the function f is defined by f(x) = ax³ + bx² + cx + d and a, b, c, and d are constants. For how many values of x does f(x) = 0?

A) One

B) Two

C) Three

D) Four

Solution :

Problem 4 :

Vivian bought party hats and cupcakes for $71. Each package of party hats cost $3, and each cupcake cost $1. If Vivian bought 10 packages of party hats, how many cupcakes did she buy?

Solution :

Problem 5 :

Bacteria are growing in a liquid growth medium. There were 300,000 cells per milliliter during an initial observation. The number of cells per milliliter doubles every 3 hours. How many cells per milliliter will there be 15 hours after the initial observation?

A) 1,500,000

B) 2,400,000

C) 4,500,000

D) 9,600,000

Solution :

Problem 6 :

Which expression is equivalent to 6x⁸y² + 12x²y²?

A) 6x²y²(2x⁶)

B) 6x²y²(x⁴)

C) 6x²y²(x⁶ + 2)

D) 6x²y²(x⁴ + 2)

Solution :

Problem 7 :

f(x) = 4x² + 64x + 262

The function g is defined by g(x) = f(x + 5). For what value of x does g(x) reach its minimum?

A) -13

B) -8

C) -5

D) -3

Solution :

Problem 8 :

In the xy-plane above, the parabola y = –kx² + 1 intersects the x- and y-axes at the points A, B and C. If ΔABC is an equilateral triangle, what is the value of k?

Solution :

Problem 9 :

In the xy-plane above, line ℓ is tangent to the graph of circle O and the value of sin∠ORP is 0.6. If the area of ΔOPR is 54, what is the radius of the circle?

Solution :

Problem 10 :

In the xy-plane above, points O, P and Q lie on the graph of y = 2x². If the area of triangle OPQ is 54, what is the length of PQ?

Solution :

Problem 11 :

The figure above shows three isosceles right triangles with sides of length 4, a and 25 respectively. If points A, B and C lie on ℓ, what is the value of a?

Solution :

Problem 12 :

If a + 2b = 1/2 and a – 2b =1/3, what is the value of 6a² – 24b²?

A) 1/3

B) 1/2

C) 1

D) 2

Solution :

Problem 13 :

In the xy-plane above, BC = AC and AB = 3√2. If the coordinates of point A are (1, 2), what are the coordinates of point B?

A) (3, 3)

B) (3, 4)

C) (4, 5)

D) (5, 6)

Solution :

Problem 14 :

If sec (3x + 10)° = csc (x – 20)°, which of the following could be the value of x?

A) 20

B) 25

C) 30

D) 35

Solution :

Problem 15 :

The equation P = 20,000(0.93)¹⁰ is being used to calculate the cost of money of an automobile. What does 0.93 represent in this situation equation?

A) 0.93% decay

B) 0.93% growth

C) 7% decay

D) 7% growth

Solution :

Problem 16 :

If x ≤ –10 or x ≥ 16, which of the following represents the values of x?

A) |x + 3| ≤ 13

B) |x + 3| ≥ 13

C) |x – 3| ≥ 13

D) |x – 3| ≤ 13

Solution :

Problem 17 :

If the vertex of y = ax² – ax + b has coordinates (2, –5), what is the y-intercept of this graph in the xy-plane?

A) (0, 2)

B) (0, 1)

C) (0, –1)

D) (0, –2)

Solution :

Problem 18 :

The lengths of three sides of triangle are different prime numbers if two of the sides have lengths 3 and 11 which of the following could be the length of third side?

I. 7

II. 13

III. 17

A) I only

B) II only

C) I and II only

D) I, II and III

Solution :

Problem 19 :

In the system of equations above, a is a constant. If the system has no solution, what is the value of a ?

A) ⅔

B) 2

C) 8

D) 24

Solution :

Problem 20 :

If 27⁸¹ = 3^x, what is the value of x?

A) 27

B) 84

C) 100

D) 243

Solution :

Problem 21 :

In the figure above, line m is parallel to line n and is perpendicular to line r. If y = 2x, what is the value of y?

Solution :

Problem 22 :

A salad dressing supplier ensures that there are 7.5 ounces of salad dressing in every container. How many containers would be required to hold 150 ounces of salad dressing?

Solution :