NJSLA Algebraic Concepts and Expressions 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?

Accepted Answer

3 + 2.50m

Answer

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?

Accepted Answer

14x - 15

Answer

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?

Accepted Answer

18

Answer

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?

Accepted Answer

The expression contains three terms.

Answer

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"?

Accepted Answer

3n - 8

Answer

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.

NJSLA Exam Practice Test

NJSLA Exam Practice Test

NJSLA Algebraic Concepts and Expressions Questions and Answers