NJSLA Algebraic Concepts and Expressions Questions and Answers — Questions and Answers
Question 1: A taxi service charges a flat fee of $3.00 plus an additional $2.50 per mile. Which expression represents the total cost, in dollars, for a ride of *m* miles?
- 3m + 2.50
- 3 + 2.50m (Correct answer)
- (3 + 2.50)m
- 5.50m
Correct answer: 3 + 2.50m
The total cost is the sum of the one-time flat fee and the variable cost that depends on the miles traveled. The flat fee is a constant $3.00. The per-mile cost is $2.50 multiplied by the number of miles, *m*, which is written as 2.50m. Therefore, the correct expression is 3 + 2.50m.
Question 2: Which of the following expressions is equivalent to 5(2x - 3) + 4x?
- 10x - 15
- 14x - 3
- 14x - 15 (Correct answer)
- 6x - 15
Correct answer: 14x - 15
To find the equivalent expression, first apply the distributive property to 5(2x - 3). This means multiplying 5 by both 2x and -3, which results in 10x - 15. The expression then becomes 10x - 15 + 4x. Next, combine the like terms, 10x and 4x, which sum to 14x. The constant term -15 remains, making the final simplified expression 14x - 15.
Question 3: What is the value of the expression 3a² - (b + 4) when a = 3 and b = 5?
- 14
- 26
- 2
- 18 (Correct answer)
Correct answer: 18
Substitute the given values into the expression: 3(3)² - (5 + 4). Following the order of operations (PEMDAS), first evaluate the exponent: 3² = 9. Then, solve the operation inside the parentheses: 5 + 4 = 9. The expression becomes 3(9) - 9. Next, perform the multiplication: 3 * 9 = 27. Finally, perform the subtraction: 27 - 9 = 18.
Question 4: In the algebraic expression 7y - 4z + 12, which statement is true?
- The expression contains three terms. (Correct answer)
- 12 is a coefficient.
- y is a constant.
- -4 is a variable.
Correct answer: The expression contains three terms.
Terms in an algebraic expression are separated by addition or subtraction signs. The expression 7y - 4z + 12 has three distinct parts separated by these signs: 7y, -4z, and 12. Therefore, it has three terms. A coefficient is a number multiplied by a variable (like 7 and -4), a constant is a number by itself (12), and a variable is a letter representing an unknown value (y and z).
Question 5: Which algebraic expression correctly represents the phrase "eight less than the product of a number, n, and three"?
- 8 - 3n
- 3(n - 8)
- 8 < 3n
- 3n - 8 (Correct answer)
Correct answer: 3n - 8
First, translate "the product of a number, n, and three," which means 3 multiplied by n, or 3n. The phrase "eight less than" indicates subtraction from the previously established quantity. Therefore, you subtract 8 from 3n, resulting in the expression 3n - 8.
Question 6: A rectangular garden has a length that is 5 feet longer than its width, *w*. The perimeter of a rectangle is found using the formula P = 2(length + width). Which of the following expressions represents the perimeter of the garden?
- w(w + 5)
- 4w + 10 (Correct answer)
- 2w + 5
- 2w + 10
Correct answer: 4w + 10
First, define the dimensions. The width is *w*. The length is "5 feet longer than its width," so length = w + 5. Substitute these into the perimeter formula: P = 2((w + 5) + w). Simplify inside the parentheses by combining like terms: P = 2(2w + 5). Finally, use the distributive property to get the simplified expression: P = 4w + 10.
NJSLA Algebraic Concepts and Expressions Questions and Answers
A taxi service charges a flat fee of $3.00 plus an additional $2.50 per mile.
Which expression represents the total cost, in dollars, for a ride of *m* miles?