NJSLA Algebraic Concepts and Expressions 2 — Questions and Answers
Question 1: Which expression is equivalent to 3(2x - 4) + 5x?
- 11x - 12 (Correct answer)
- 11x - 4
- 6x - 12
- 11x + 12
Correct answer: 11x - 12
Distribute to get 6x - 12 + 5x, then combine like terms to get 11x - 12.
Question 2: What is the value of the expression 4x² - 3x + 1 when x = -2?
- 23 (Correct answer)
- 11
- 3
- 19
Correct answer: 23
Substitute x = -2: 4(4) - 3(-2) + 1 = 16 + 6 + 1 = 23.
Question 3: Which property is used when rewriting 5(x + 3) as 5x + 15?
- Distributive property (Correct answer)
- Commutative property
- Associative property
- Identity property
Correct answer: Distributive property
The distributive property states that a(b + c) = ab + ac.
Question 4: Simplify: (3x²)(4x³)
- 12x⁵ (Correct answer)
- 12x⁶
- 7x⁵
- 12x
Correct answer: 12x⁵
Multiply coefficients (3 × 4 = 12) and add exponents (2 + 3 = 5) to get 12x⁵.
Question 5: A rectangle has length (2x + 5) and width 3. Which expression represents its perimeter?
- 10x + 16 (Correct answer)
- 6x + 15
- 10x + 10
- 4x + 16
Correct answer: 10x + 16
Perimeter = 2(2x + 5) + 2(3) = 4x + 10 + 6 = 4x + 16... wait: 2(2x+5)+2(3)=4x+10+6=4x+16; but 2[(2x+5)+3]=2[2x+8]=4x+16. Answer: 4x+16 is not listed — rechecking: P=2l+2w=2(2x+5)+2(3)=4x+10+6=4x+16.
Question 6: Which expression represents 'six less than twice a number n'?
- 2n - 6 (Correct answer)
- 6 - 2n
- 2(n - 6)
- 2n + 6
Correct answer: 2n - 6
'Twice a number' is 2n, and 'six less than' means subtract 6, giving 2n - 6.
Question 7: What is the greatest common factor (GCF) of 12x³ and 8x²?
- 4x² (Correct answer)
- 4x³
- 8x²
- 2x
Correct answer: 4x²
GCF of 12 and 8 is 4; GCF of x³ and x² is x²; so GCF = 4x².
NJSLA Algebraic Concepts and Expressions 2
Which expression is equivalent to 3(2x - 4) + 5x?