NJSLA Algebraic Concepts and Expressions 5 — Questions and Answers
Question 1: Which expression represents the perimeter of a square with side length (3x - 1)?
- 12x - 4 (Correct answer)
- 9x² - 6x + 1
- 6x - 2
- 12x + 4
Correct answer: 12x - 4
Perimeter of a square = 4s = 4(3x - 1) = 12x - 4.
Question 2: Simplify the expression: 2x + 3y - x + 5y
- x + 8y (Correct answer)
- x + 8y
- 3x + 8y
- x - 2y
Correct answer: x + 8y
Combine like terms: 2x - x = x and 3y + 5y = 8y, giving x + 8y.
Question 3: What value of n makes 5n - 8 = 3n + 4 true?
- 6 (Correct answer)
- 3
- 2
- 8
Correct answer: 6
Subtract 3n from both sides: 2n - 8 = 4; add 8: 2n = 12; divide by 2: n = 6.
Question 4: Which expression is equivalent to -(2x - 5)?
- -2x + 5 (Correct answer)
- -2x - 5
- 2x - 5
- 2x + 5
Correct answer: -2x + 5
Distributing the negative sign: -(2x - 5) = -2x + 5.
Question 5: The expression 16 - 4x² can be factored as:
- 4(2 - x)(2 + x) (Correct answer)
- 4(4 - x²)
- (4 - 2x)²
- 4(x - 2)(x + 2)
Correct answer: 4(2 - x)(2 + x)
Factor out 4: 4(4 - x²), then factor the difference of squares: 4(2 - x)(2 + x).
Question 6: In the expression 7a³b² - 3ab + 2b, how many terms are there?
- 3 (Correct answer)
- 2
- 4
- 6
Correct answer: 3
Terms are separated by addition or subtraction; there are 3 terms: 7a³b², -3ab, and 2b.
Question 7: Which of the following shows 4x² + 8x factored completely?
- 4x(x + 2) (Correct answer)
- 4(x² + 2x)
- x(4x + 8)
- 2x(2x + 4)
Correct answer: 4x(x + 2)
The GCF of 4x² and 8x is 4x, so 4x² + 8x = 4x(x + 2).
NJSLA Algebraic Concepts and Expressions 5
Which expression represents the perimeter of a square with side length (3x - 1)?