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Unit 1: Algebraic Expressions & Equations

Study guide for CLEP CLEP Precalculus — Unit 1: Algebraic Expressions & Equations. Practice questions, key concepts, and exam tips.

215

Practice Questions

14

Flashcards

4

Key Topics

Key Concepts to Study

Polynomial operations and factoring
Rational expressions and equations
Systems of equations and inequalities
Complex numbers and quadratic formula

Sample Practice Questions

Try these 5 questions from this unit. Sign up for full access to all 215.

Q1MEDIUM

Determine the range of h(x) = {-x if x ≤ 1, $x^{3}$ if x > 1}?

A) (-∞, ∞)
B) [0, ∞)
C) (-∞, 0)
D) (-1, 1)
E) [1, ∞)
Show Answer

Answer: A — "(-∞, ∞)" is correct because h(x) has no bounds.

Q2EASY

What is the focus of a parabola with equation x² = 20y?

A) (0,4)
B) (0,5)
C) (0,2)
D) (0,6)
E) (0,8)
Show Answer

Answer: B — (0,5) is correct because the standard equation of a parabola with vertex (0,0) and focus (0,p) is x² = 4py, and since x² = 20y, 4p = 20, so p = 20/4 = 5.

Q3MEDIUM

If sec(x) = 2, what is the value of cos(x)?

A) 0.25
B) 0.5
C) 0.75
D) 1
E) 1.5
Show Answer

Answer: B — 0.5 is correct because sec(x) is the reciprocal of cos(x), so cos(x) = 1 / sec(x) = 1 / 2 = 0.5.

Q4EASY

What is the tabular representation of the function f(x) = 3x - 2 for x-values -2, -1, 0, 1, 2?

A) x: -2, -1, 0, 1, 2; f(x): -8, -5, -2, 1, 4
B) x: -2, -1, 0, 1, 2; f(x): -6, -3, 0, 3, 6
C) x: -2, -1, 0, 1, 2; f(x): -4, -1, 2, 5, 8
D) x: -2, -1, 0, 1, 2; f(x): -2, 1, 4, 7, 10
E) x: -2, -1, 0, 1, 2; f(x): 0, 3, 6, 9, 12
Show Answer

Answer: A — x: -2, -1, 0, 1, 2; f(x): -8, -5, -2, 1, 4 is correct because the function f(x) = 3x - 2 is evaluated at each x-value to obtain the corresponding f(x) values, resulting in the given table.

Q5MEDIUM

If h(x) = |x| + 2, what is h(-5)?

A) 3
B) 5
C) 7
D) 9
E) 11
Show Answer

Answer: C — 7 is correct because since h(x) = |x| + 2, then h(-5) = |-5| + 2 = 5 + 2 = 7.

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Study Tips for Unit 1: Algebraic Expressions & Equations

  • Focus on understanding concepts, not memorizing facts — CLEP tests application
  • Practice with timed questions to build exam-day speed
  • Review explanations for wrong answers — they reveal common misconceptions
  • Use flashcards for key terms, practice questions for deeper understanding

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