Core Academic Skills Assessment Mathematics: Algebra and Functions Questions and Answers

Question 1

A printing company charges a flat fee of $15 for setup, plus $0.05 per page for a printing job. Which of the following functions, C(p), represents the total cost for a job that requires 'p' pages to be printed?

Accepted Answer

C(p) = 15 + 0.05p

Answer

The total cost is the sum of the fixed setup fee and the variable cost per page. The fixed fee is $15. The variable cost is $0.05 multiplied by the number of pages, 'p'. Therefore, the correct function is C(p) = 15 + 0.05p.

Question 2

If f(x) = 3x² - 4x + 2, what is the value of f(-2)?

Accepted Answer

22

Answer

To find f(-2), substitute -2 for x in the function: f(-2) = 3(-2)² - 4(-2) + 2. Follow the order of operations: f(-2) = 3(4) - (-8) + 2. Then, f(-2) = 12 + 8 + 2, which equals 22.

Question 3

Solve the following inequality for x:  2(x + 3) > 4x - 10

Accepted Answer

x < 8

Answer

First, distribute the 2 on the left side: 2x + 6 > 4x - 10. Next, get the x terms on one side by subtracting 4x from both sides: -2x + 6 > -10. Then, subtract 6 from both sides: -2x > -16. Finally, divide by -2. Remember to reverse the inequality sign when dividing by a negative number: x < 8.

Question 4

A conference hall has two seating plans. Plan A uses 8 small tables and 5 large tables to seat 120 people. Plan B uses 6 small tables and 7 large tables to seat 136 people. If 's' is the number of seats at a small table and 'l' is the number of seats at a large table, which system of equations correctly represents this situation?

Accepted Answer

8s + 5l = 120
6s + 7l = 136

Answer

For Plan A, the total number of seats is the sum of seats from small tables (8s) and large tables (5l), which equals 120. This gives the equation 8s + 5l = 120. For Plan B, the total is from 6 small tables (6s) and 7 large tables (7l), equaling 136. This gives the equation 6s + 7l = 136. The other options incorrectly combine or represent the given information.

Question 5

Which of the following is equivalent to the expression (3x - 2)(x + 5)?

Accepted Answer

3x² + 13x - 10

Answer

To multiply the binomials, use the FOIL method (First, Outer, Inner, Last). First: (3x)(x) = 3x². Outer: (3x)(5) = 15x. Inner: (-2)(x) = -2x. Last: (-2)(5) = -10. Then, combine the like terms (15x and -2x): 3x² + 15x - 2x - 10 = 3x² + 13x - 10.

Core Academic Skills Assessment Practice Test

Core Academic Skills Assessment Practice Test

Core Academic Skills Assessment Mathematics: Algebra and Functions Questions and Answers