2025 Spring Semester Exam Review – Algebraic Reasoning

Rewrite the following logarithmic equation in exponential form: log₃ 81 = 4

• 4³ = 81

• 3⁴ = 81

• 81⁴ = 3

• 81³ = 4

Tags

CCSS.HSF.BF.B.5

Evaluate: log₉27

• 2/3

• 3/2

• 2

• -2

log₃11p³

• log₃11 + 3 log₃p

• log₃11 - 3 log₃p

• log₃11 + 3 log₂p

• 11 log₃2p³

Solve: 3log₃x – 7 = -1

• 8

• 2

• 9

• 81

Tags

CCSS.HSF.BF.B.5

Solve: log₃x = 4

• 20

• 27

• 81

• 1.25

Tags

CCSS.HSF.BF.B.5

• x³y³z⁵

• xy³z

• x²y³z³

• xy²z²

Tags

CCSS.HSA.APR.D.7

Refer to the graph shown. Which of the following correctly describes the domain (D) and range (R) of the function?

• D: All Real Numbers R: All Real Numbers

• D: -9 ≤ x ≤ 0 R: -3 ≤ y ≤ 3

• D: -3 ≤ x ≤ 3 R: -9 ≤ y ≤ 0

• D: -2 ≤ x ≤ 2 R: -4 ≤ y ≤ -1

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

Simplify √800

• 4√10

• 20√40

• 8√100

• 20√2

Solve by factoring: x² – 7x + 12

• 7, 5

• -3, -4

• -7, 5

• 3, 4

Tags

CCSS.HSA-REI.B.4B

Solve by Factoring: 6x² + 21x – 12 = 0

• {1/2, -4}

• {1/2, 4}

• {3, -4}

• {-2, 4}

Tags

CCSS.HSA-REI.B.4B