CSET CSET Mathematics: Number Theory and Algebra 2 — Questions and Answers
Question 1: Which of the following best describes a rational number?
- A number that cannot be expressed as a fraction
- Any number that can be written as p/q where p and q are integers and q ≠ 0 (Correct answer)
- A non-repeating, non-terminating decimal
- Any real number on the number line
Correct answer: Any number that can be written as p/q where p and q are integers and q ≠ 0
A rational number is any number expressible as the ratio p/q of two integers where the denominator is not zero.
Question 2: What is the slope of a line perpendicular to y = (2/3)x + 5?
- 2/3
- −2/3
- 3/2
- −3/2 (Correct answer)
Correct answer: −3/2
Perpendicular lines have slopes that are negative reciprocals; the negative reciprocal of 2/3 is −3/2.
Question 3: Which of the following is an example of the associative property of addition?
- a + b = b + a
- (a + b) + c = a + (b + c) (Correct answer)
- a + 0 = a
- a(b + c) = ab + ac
Correct answer: (a + b) + c = a + (b + c)
The associative property states that grouping of addends does not change the sum: (a + b) + c = a + (b + c).
Question 4: Solve for x: 3(x − 4) = 2x + 7
- x = 5
- x = 11
- x = 19 (Correct answer)
- x = 3
Correct answer: x = 19
3x − 12 = 2x + 7, so x = 19.
Question 5: What is the degree of the polynomial 4x³ − 7x² + x − 9?
- 1
- 2
- 3 (Correct answer)
- 4
Correct answer: 3
The degree of a polynomial is the highest exponent of the variable, which is 3 here.
Question 6: Which of the following correctly factors x² − 9?
- (x − 3)²
- (x + 3)²
- (x − 3)(x + 3) (Correct answer)
- (x + 9)(x − 1)
Correct answer: (x − 3)(x + 3)
x² − 9 is a difference of two squares: x² − 3² = (x − 3)(x + 3).
CSET CSET Mathematics: Number Theory and Algebra 2
Which of the following best describes a rational number?