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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.

137

Practice Questions

132

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 137.

Q1MEDIUM

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 — The sequence is defined by a recurrence relation that doubles the previous term and adds 1, starting with a_1 = 1. The correct calculation yields a_5 = 2a_4 + 1 = 2(15) + 1 = 31, making option "32" the correct choice.

Q2MEDIUM

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

A.

f−1f^{-1}(x) = 2x

B.

f−1f^{-1}(x) = x/2

C.

f−1f^{-1}(x) = x/3

D.

f−1f^{-1}(x) = 3x

E.

f−1f^{-1}(x) = x2x^{2}

Show Answer

Answer: B — 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.

Q3MEDIUM

Simplify 2(x - 3) + 5(x + 2)

A.

7x - 4

B.

7x - 6

C.

7x - 1

D.

7x + 4

E.

7x + 1

Show Answer

Answer: D — 7x + 4 is correct because distributing and combining like terms in 2(x - 3) + 5(x + 2) yields 2x - 6 + 5x + 10, which simplifies to 7x + 4.

Q4MEDIUM

Which function represents a tiered pricing structure?

A.

f(x) = { 10 if x < 5, 20 if x >= 5 }

B.

f(x) = 2x

C.

f(x) = 4x - 2

D.

f(x) = x3x^{3}

E.

f(x) = 3x23x^{2}

Show Answer

Answer: A — "f(x) = { 10 if x < 5, 20 if x >= 5 }" is correct because it has different prices for different tiers.

Q5EASY

What is the conjugate of the complex number 2 - 5i?

A.

2 + 5i

B.

5 - 2i

C.

-2 + 5i

D.

2 - 5i

E.

-2 - 5i

Show Answer

Answer: A — 2 + 5i is correct because the conjugate of a complex number a + bi is a - bi, so for 2 - 5i, the conjugate is 2 + 5i.

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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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