Core Academic Skills Assessment Mathematics: Algebra and Functions Questions and Answers — 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?
- C(p) = 15p + 0.05
- C(p) = 15 + 0.05p (Correct answer)
- C(p) = 15.05p
- C(p) = 15 + 5p
Correct answer: C(p) = 15 + 0.05p
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)?
- 6
- 18
- 22 (Correct answer)
- -2
Correct answer: 22
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
- x > 8
- x < 8 (Correct answer)
- x > -2
- x < -2
Correct answer: x < 8
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?
- 8s + 5l = 120 6s + 7l = 136 (Correct answer)
- 8s + 6l = 120 5s + 7l = 136
- s + l = 13 s + l = 136
- 14s + 12l = 256 s + l = 1
Correct answer: 8s + 5l = 120 6s + 7l = 136
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)?
- 3x² + 13x - 10 (Correct answer)
- 3x² - 13x - 10
- 3x² + 17x + 10
- 4x + 3
Correct answer: 3x² + 13x - 10
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.
Question 6: The population of a town is modeled by the function P(t) = 12,000(1.03)ᵗ, where 't' is the number of years since 2010. Which of the following statements BEST describes the population's growth?
- The population decreases by 3% each year.
- The population grows by 103 people each year.
- The population grows by 3% each year. (Correct answer)
- The initial population in 2010 was 1.03.
Correct answer: The population grows by 3% each year.
This is an exponential growth function of the form P(t) = P₀(1+r)ᵗ, where P₀ is the initial amount and 'r' is the growth rate. Here, P₀ = 12,000. The growth factor is 1.03, which can be written as 1 + 0.03. Therefore, the growth rate 'r' is 0.03, which is equivalent to a 3% annual growth.
Core Academic Skills Assessment Mathematics: Algebra and Functions Questions and Answers
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?