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.

Tags

CCSS.8.EE.A.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.

Tags

CCSS.8.NS.A.2

• A

• B

• C

• D

Simplify.

• 
• 
• 
• 

Tags

CCSS.HSA.APR.A.1

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

• (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).

Tags

CCSS.8.EE.C.8C