Algebra and Trigonometry 7th Edition Test Bank by Robert F. Blitzer | Verified Solutions & Exam Practice Questions | Complete Study Guide

Algebra and Trigonometry 7th Edition
Test Bank by Robert F. Blitzer |
Verified Solutions & Exam Practice
Questions | Complete Study Guide
ALGEBRA AND TRIGONOMETRY — 7TH EDITION

Robert F. Blitzer | Complete -Question Exam

All Chapters: P through 11



BOOK CHAPTERS AT A GLANCE

• Chapter P — Prerequisites: Fundamental Concepts of Algebra

• Chapter 1 — Equations and Inequalities

• Chapter 2 — Functions and Graphs

• Chapter 3 — Polynomial and Rational Functions
• Chapter 4 — Exponential and Logarithmic Functions

• Chapter 5 — Trigonometric Functions

• Chapter 6 — Analytic Trigonometry

• Chapter 7 — Additional Topics in Trigonometry

• Chapter 8 — Systems of Equations and Inequalities

• Chapter 9 — Matrices and Determinants

• Chapter 10 — Conic Sections and Analytic Geometry

• Chapter 11 — Sequences, Induction, and Probability




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CHAPTER P — PREREQUISITES: FUNDAMENTAL CONCEPTS OF ALGEBRA
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,Question 1 Which of the following is an example of a rational number?

A. √2

B. π

C. 3/4

D. √5

E. √3

CORRECT ANSWER: C — 3/4 RATIONALE: A rational number is any number that
can be expressed as the quotient of two integers. 3/4 = 0.75, a terminating decimal,
making it rational. √2, π, √5, and √3 are all irrational.



Question 2 Simplify: 3x² + 5x − 2x² + 4x

A. x² + 9x

B. 5x² + 9x

C. x² − 9x

D. x² + 9x

E. 2x² + 9x

CORRECT ANSWER: D — x² + 9x RATIONALE: Combine like terms: (3x² − 2x²) = x²
and (5x + 4x) = 9x. Result: x² + 9x.


Question 3 Which property is illustrated by: a(b + c) = ab + ac?

A. Commutative Property

B. Associative Property

C. Identity Property

D. Inverse Property

E. Distributive Property

,CORRECT ANSWER: E — Distributive Property RATIONALE: The Distributive
Property states that multiplying a factor by a sum is the same as multiplying the factor
by each addend separately: a(b + c) = ab + ac.


Question 4 Evaluate: (−3)⁴

A. −81

B. −12

C. 12

D. 81

E. 27

CORRECT ANSWER: D — 81 RATIONALE: (−3)⁴ = (−3)(−3)(−3)(−3) = 9 × 9 = 81.
The even exponent makes the result positive.


Question 5 Write 0.000078 in scientific notation.

A. 7.8 × 10⁻⁴

B. 7.8 × 10⁴

C. 78 × 10⁻⁶

D. 0.78 × 10⁻⁴

E. 7.8 × 10⁻⁵

CORRECT ANSWER: E — 7.8 × 10⁻⁵ RATIONALE: Move the decimal 5 places to the
right to get 7.8. Since the original number is less than 1, the exponent is negative: 7.8 ×
10⁻⁵.



Question 6 Simplify: √(50)

A. 10√2

B. 25√2

C. 5√10
D. 2√5

, E. 5√2

CORRECT ANSWER: E — 5√2 RATIONALE: √50 = √(25 × 2) = √25 · √2 = 5√2.



Question 7 Simplify: (x³)⁴
A. x⁷

B. x¹²·⁴

C. 4x³

D. x³⁺⁴

E. x¹²

CORRECT ANSWER: E — x¹² RATIONALE: Using the power rule of exponents: (xᵐ)ⁿ
= xᵐⁿ. So (x³)⁴ = x^(3×4) = x¹².


Question 8 Factor completely: x² − 9

A. (x − 3)²

B. (x + 9)(x − 1)

C. (x − 9)(x + 1)

D. (x + 9)(x − 9)

E. (x + 3)(x − 3)

CORRECT ANSWER: E — (x + 3)(x − 3) RATIONALE: x² − 9 is a difference of two
squares: a² − b² = (a + b)(a − b). Here a = x and b = 3.


Question 9 Simplify the rational expression: (x² − 4)/(x − 2)

A. x − 2

B. x + 4

C. x²

D. (x + 2)(x − 2)²

E. x+2