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Unit 1 of 5

Unit 1: Algebraic Foundations

Study guide for CLEP CLEP College Algebra — Unit 1: Algebraic Foundations. Practice questions, key concepts, and exam tips.

274

Practice Questions

32

Flashcards

11

Key Topics

Key Concepts to Study

real numbers
order of operations
absolute value
exponent rules
radicals
factoring
complex numbers
imaginary unit
operations with complex numbers
factorials
binomial theorem

Sample Practice Questions

Try these 5 questions from this unit. Sign up for full access to all 274.

Q1MEDIUM

Determine the value of x for which f(x) = 0, given f(x) = 2x - 5.

A) 2.5
B) 0
C) -1.5
D) 5
E) -2.5
Show Answer

Answer: A — 2.5 is correct because 2(2.5) - 5 = 0, so the function equals zero when x is 2.5.

Q2EASY

What is the value of 2^3?

A) 4
B) 10
C) 12
D) 8
E) 6
Show Answer

Answer: D — 8 is correct because 2^3 means 2 multiplied by itself 3 times, so 2*2*2 = 8.

Q3EASY

What is the value of |2x+1| when x = -1?

A) 0
B) 3
C) 1
D) -1
E) -3
Show Answer

Answer: C — 1 is correct because substituting x = -1 into |2x+1| yields |2(-1)+1| = |-2+1| = |-1|, and the absolute value of -1 is 1.

Q4MEDIUM

What is the 5th term of the sequence defined by the recurrence relation a_n = 2a_(n-1) + 1, where a_1 = 1?

A) 15
B) 16
C) 31
D) 32
E) 63
Show Answer

Answer: C — 31 is correct because applying the recurrence relation, we get a_2 = 2*1 + 1 = 3, a_3 = 2*3 + 1 = 7, a_4 = 2*7 + 1 = 15, and a_5 = 2*15 + 1 = 31.

Q5EASY

What is the inverse of f(x) = 2x?

A) f^{-1}(x) = 2x
B) f^{-1}(x) = x/3
C) f^{-1}(x) = 3x
D) f^{-1}(x) = x/2
E) f^{-1}(x) = x^2
Show Answer

Answer: D — x/2 is correct because to find the inverse of f(x) = 2x, we swap x and y to get x = 2y, then solve for y, which gives y = x/2.

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Study Tips for Unit 1: Algebraic Foundations

  • 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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