DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 234)

Problem 1 :

x² – 4x + 2 = 0

If a and b are the roots of the equation above, what is the value of (a + 1)(b + 1)?

A)  5

B)  6

C)  7

D)  10

Solution :

Problem 2 :

If a⁵ = 10 and a⁷ = 2/p, which of the following is an expression for p?

A)  2a²

B)  5/a² 

C)  1/5a²

D)  a²/100

Solution :

Problem 3 :

A movie theater sold n tickets today. Some of these were adult tickets and the rest were child tickets. An adult ticket costs twelve dollars and a child ticket costs eight dollars. If the theater sold $2000 worth of tickets and the number of child tickets sold is c, which of the following could be the value of n?

A)  n = 2000/c

B)  n = (500 - 4c)/3

C)  n = (500 - c)/3

D)  n = (500 + c)/3

Solution :

Problem 4 :

f(x) = x(x + 2)(x – 3)

In the function f(x) above, which of the following about the graph of f in the xy-plane could not be true?

A)  The graph of f rises to the right as x approaches positive infinity.

B)  The function f falls to the left as x approaches negative infinity.

C)  The function f has three distinct real zeros.

D)  The graph of f has a negative y-intercept.

Solution :

Problem 5 :

In the xy-plane above, the graphs of f(x) and g(x) are shown. The graph of g(x) is the result of a translation of f(x). If f(x) = x²(x - 2), which of the following is an equation of g(x)?

A)  g(x) = (x - 2)³ + 2(x - 2) - 2

B)  g(x) = (x + 2)³ - 2(x + 2)² - 2

C)  g(x) = (x - 2)³ - 2(x - 2)² - 2

D)  g(x) = (x + 2)³ - 2(x + 2)² - 2

Solution :

Problem 6 :

(3x + 2y)²

If the expression above can be written as

ax² + bxy + cy²,

where a, b and c are constants, find the value of

a + b + c

Solution :

Problem 7 :

What is one possible value of x for which the function g above is undefined?

Solution :

Problem 8 :

At a certain pizza restaurant, 8 ounces of cheese is enough for 2/3 of a pizza. Given that there are 16 ounces in a pound, how many pizzas can be produced with 12 pounds of cheese?

Solution :

Problem 9 :

 y - 3x ≤ 4

y + 2x ≥ 45

In the xy-plane, a point with coordinates (h, k) lies in the solution set of the system of inequalities above. What is the minimum possible value of h?

Solution :

Problem 10 :

Call center A handle 20% fewer calls than call center B. Call center B handles 20% fewer calls than call center C. If call center A handles 1,200 calls, how many calls does call center C handle?

Solution :

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