Act Algebra Math Review

Kai is designing a parabolic arch for a bridge. What is the domain and range of the quadratic function that models the arch?

• D: ℝ R: y ≤ 4

• D: -5 ≤ x ≤ 2 R: -6≤ y ≤ 4

• D: ℝ R: ℝ

• D: -3 ≤ x ≤ 1 R: 0≤ y ≤ 4

Answer explanation

The correct choice is D: ℝ for domain, indicating all real numbers, and R: y ≤ 4 for range, which shows the maximum value of the quadratic function is 4, consistent with its vertex being at or below this point.

Emma is planning a garden and wants to create a rectangular area where the length is 5 meters more than the width. The area of the garden is 24 square meters. Solve for the dimensions of the garden by factoring.

• Width = 8 meters; Length = 3 meters

• Width = 3 meters; Length = 8 meters

• Width = 24 meters; Length = 1 meter

• Width = 12 meters; Length = -7 meters

Answer explanation

To solve the equation by factoring, we find the roots. The factors lead to x = -8 and x = 3, which match the correct choice. Thus, the solution is x = -8; x = 3.

Ava is designing a garden and wants to create a rectangular flower bed. The area of the flower bed is represented by the equation 5x^2 - 2x = 1, where x is the width in meters. Solve for x using the quadratic formula and round your answers to the nearest tenth.

• x = -2.9; x = 6.9

• x = 3.4; x = -1.4

• x = 0.7; x = -0.3

• x = 0.5; x = -0.1

Answer explanation

Using the quadratic formula, we find the roots of the equation. The calculations yield x = 0.7 and x = -0.3, which match the correct answer choice. Thus, the correct answers are x = 0.7; x = -0.3.

Evaluate 10 to the 0 power

• 1

• 10

• 0

• 100

Answer explanation

10⁰ is equivalent to 1 because any non-zero number raised to the power of 0 equals 1. Therefore, the correct answer is 1.

Aria is trying to find out between which two whole numbers the square root of 277 lies. Can you help her?

• 15 and 16

• 16 and 17

• 18 and 19

• 14 and 15

Answer explanation

The square root of 277 is approximately 16.64. Since 16^2 = 256 and 17^2 = 289, the square root lies between 16 and 17. Thus, the correct answer is 16 and 17.

• A

• B

• C

• D

Simplify.

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Grace is trying to simplify the expression ∛54 for her math homework. What is the simplest form of this expression?

• 3∛6

• 9∛2

• 3∛2

• 3∛3

Answer explanation

To simplify ∛54i, we can express 54 as 27 * 2. Thus, ∛54i = ∛(27 * 2)i = ∛27 * ∛2 * i = 3∛2 * i. The simplest form is 3∛2.

Answer explanation

Substituting y=x into y=2x-1 gives x=1. Then, y=1. The solution is (1,1), which matches the correct answer.

• (14,4) 

• (4,14)

• (4, 0)

• (0,4)

Answer explanation

To solve the system, substitute y from the first equation into the second: 5x - 6 = 4x - 2. Solving gives x = 4. Substitute x back to find y: y = 5(4) - 6 = 14. Thus, the solution is (4, 14).