Arizona State University MAT117 College
Algebra – Final Exam \ (150+ Questions And
Answers with Rationales)
EXAM OVERVIEW
MAT117 College Algebra is an adaptive course often
delivered through ALEKS. The course develops skills in
linear, quadratic, general polynomial, exponential, and
logarithmic functions. The proctored final exam covers
topics from modules A, B, C, and D and typically accounts
for 40% of the overall course grade.
Key Topics Covered on the Final Exam:
• Exponents, Scientific Notation, and Polynomials
• Factoring and Rational Expressions
• Linear Equations, Inequalities, and Systems
• Functions, Domain, Range, and Transformations
• Quadratic Functions and Equations
• Polynomial Functions (Zeros, Multiplicity, End
Behavior)
, • Rational Functions (Asymptotes, Domain, Graphing)
• Exponential and Logarithmic Functions
• Inverse Functions and Function Composition
• Applications (Word Problems, Modeling, Regression)
PART 1: EXPONENTS, SCIENTIFIC NOTATION &
POLYNOMIALS (Questions 1-20)
Question 1
Simplify the expression using the rules of
exponents: (𝑥 3 𝑦 2 )4 .
• A) 𝑥 7 𝑦 6
• B) 𝑥 12 𝑦 8
• C) 𝑥 12 𝑦 6
• D) 𝑥 7 𝑦 8
• Answer: B
• Rationale: When raising a power to a power,
multiply the
exponents: ( 𝑥 3 )4 = 𝑥 12 and ( 𝑦 2 )4 = 𝑦 8 . So the
expression simplifies to 𝑥 12 𝑦 8 .
,Question 2
𝑥5
Simplify the expression: .
𝑥2
• A) 𝑥 3
• B) 𝑥 7
• C) 𝑥 2.5
• D) 𝑥 10
• Answer: A
• Rationale: When dividing like bases, subtract the
exponents: 𝑥 5−2 = 𝑥 3 .
Question 3
Convert 45,000,000 to scientific notation.
• A) 4.5 × 106
• B) 4.5 × 107
• C) 4.5 × 108
• D) 45 × 106
• Answer: B
, • Rationale: Move the decimal point 7 places to the
left to get 4.5, so 45,000,000 = 4.5 × 107 .
Question 4
Convert 3.2 × 10−4 to standard form.
• A) 0.00032
• B) 0.0032
• C) 0.032
• D) 32000
• Answer: A
• Rationale: A negative exponent means move the
decimal 4 places to the left: 3.2 × 10−4 = 0.00032.
Question 5
Multiply: (2𝑥 + 3)(𝑥 − 4).
• A) 2𝑥 2 − 8𝑥 + 3𝑥 − 12
• B) 2𝑥 2 − 5𝑥 − 12
• C) 2𝑥 2 + 5𝑥 − 12
• D) 2𝑥 2 − 11𝑥 − 12
Algebra – Final Exam \ (150+ Questions And
Answers with Rationales)
EXAM OVERVIEW
MAT117 College Algebra is an adaptive course often
delivered through ALEKS. The course develops skills in
linear, quadratic, general polynomial, exponential, and
logarithmic functions. The proctored final exam covers
topics from modules A, B, C, and D and typically accounts
for 40% of the overall course grade.
Key Topics Covered on the Final Exam:
• Exponents, Scientific Notation, and Polynomials
• Factoring and Rational Expressions
• Linear Equations, Inequalities, and Systems
• Functions, Domain, Range, and Transformations
• Quadratic Functions and Equations
• Polynomial Functions (Zeros, Multiplicity, End
Behavior)
, • Rational Functions (Asymptotes, Domain, Graphing)
• Exponential and Logarithmic Functions
• Inverse Functions and Function Composition
• Applications (Word Problems, Modeling, Regression)
PART 1: EXPONENTS, SCIENTIFIC NOTATION &
POLYNOMIALS (Questions 1-20)
Question 1
Simplify the expression using the rules of
exponents: (𝑥 3 𝑦 2 )4 .
• A) 𝑥 7 𝑦 6
• B) 𝑥 12 𝑦 8
• C) 𝑥 12 𝑦 6
• D) 𝑥 7 𝑦 8
• Answer: B
• Rationale: When raising a power to a power,
multiply the
exponents: ( 𝑥 3 )4 = 𝑥 12 and ( 𝑦 2 )4 = 𝑦 8 . So the
expression simplifies to 𝑥 12 𝑦 8 .
,Question 2
𝑥5
Simplify the expression: .
𝑥2
• A) 𝑥 3
• B) 𝑥 7
• C) 𝑥 2.5
• D) 𝑥 10
• Answer: A
• Rationale: When dividing like bases, subtract the
exponents: 𝑥 5−2 = 𝑥 3 .
Question 3
Convert 45,000,000 to scientific notation.
• A) 4.5 × 106
• B) 4.5 × 107
• C) 4.5 × 108
• D) 45 × 106
• Answer: B
, • Rationale: Move the decimal point 7 places to the
left to get 4.5, so 45,000,000 = 4.5 × 107 .
Question 4
Convert 3.2 × 10−4 to standard form.
• A) 0.00032
• B) 0.0032
• C) 0.032
• D) 32000
• Answer: A
• Rationale: A negative exponent means move the
decimal 4 places to the left: 3.2 × 10−4 = 0.00032.
Question 5
Multiply: (2𝑥 + 3)(𝑥 − 4).
• A) 2𝑥 2 − 8𝑥 + 3𝑥 − 12
• B) 2𝑥 2 − 5𝑥 − 12
• C) 2𝑥 2 + 5𝑥 − 12
• D) 2𝑥 2 − 11𝑥 − 12
