REVIEW FOR ALGEBRA 2 FINAL TEST May 2025

Select the algebraic expression that represents the verbal expression twice the sum of a number and 8.

• 2n + 8

• n + 16

• 2(n + 8)

• 2n + 28

Answer explanation

The phrase 'twice the sum of a number and 8' translates to 2 times (n + 8), which is represented as 2(n + 8). This captures both the sum and the multiplication correctly, making it the correct choice.

Name the sets of numbers to which -1/3 belongs.

• A naturals, rationals

• B rational, reals

• C integers, rationals

• D integers, rationals, reals

Answer explanation

-1/3 is a rational number because it can be expressed as a fraction of two integers. It also belongs to the set of real numbers. Therefore, the correct choice is B: rational, reals.

Name the property illustrated by 5(x + y) = 5(y + x).

• Commutative Property of Multiplication

• Distributive Property

• Commutative Property of Addition

• Associative Property of Addition

Answer explanation

The equation 5(x + y) = 5(y + x) demonstrates the Commutative Property of Addition, which states that changing the order of the addends does not change the sum. Here, x and y can be added in any order.

|x - 3| + 10 = 2

• A {-5, 11}

• B {-5}

• C {11}

• D ∅

Answer explanation

To solve |x - 3| + 10 = 2, isolate the absolute value: |x - 3| = -8. Since absolute values cannot be negative, there are no solutions. Thus, the answer is D ∅.

Find the range of the relation {(-2, 3), (-1, 3), (-1, 5)}. Then determine whether the relation is a function.

• A {-2, -1}; function

• B {-2, -1}; not a function

• C {3, 5}; function

• D {3, 5}; not a function

Answer explanation

The range of the relation is {3, 5} since these are the second elements of the ordered pairs. The relation is not a function because the input -1 corresponds to two different outputs (3 and 5). Thus, the correct choice is D.

• F -5

• G -3

• H 1

• J 3

Answer explanation

To find f(-1), substitute -1 into the function: f(-1) = (-1)^2 - 4 / (-1)^2 + 2 = 1 - 4 / 1 + 2 = -3 / 3 = -1. The correct answer is H 1.

Write 3y = -1 - 5x in standard form.

• A 5x + 3y = -1

• B -5x - 3y = -1

• C y = -5/3 x - 1

• D 3x + 5y - 1 = 0

Answer explanation

To convert 3y = -1 - 5x to standard form, rearrange it to 5x + 3y = -1. This matches choice A, which is the correct standard form of the equation.

Find the x-intercept and the y-intercept of the graph of 3x - 2y = 12.

• F (4, -6)

• G 4; -6

• H (2, -3)

• J -6; 4

Answer explanation

To find the x-intercept, set y=0: 3x=12, x=4. For the y-intercept, set x=0: -2y=12, y=-6. Thus, the intercepts are (4,0) and (0,-6), making the correct answer G 4; -6.

What is the slope of a line that is parallel to the graph of 2x + 3y = 5?

• 3/2

• -2/3

• 2/3

• -3/2

Answer explanation

To find the slope of the line parallel to 2x + 3y = 5, we first rewrite it in slope-intercept form (y = mx + b). Rearranging gives y = -2/3x + 5/3. The slope (m) is -2/3. Parallel lines have the same slope, so the answer is 2/3.

Which inequality describes the situation when Courtney wants to pay less than $15 for a new hat?

• F k < 15

• G h ≥ 15

• H 15 < h

• J h ≤ 15

Answer explanation

Courtney wants to pay less than $15 for a hat, which means the cost (k) must be less than 15. Therefore, the correct inequality is F: k < 15.