MATH 110 Module 1 Exam Questions and Answers
Portage Learning — 2026/2027 Edition
Comprehensive Module 1 Examination | Introductory College Mathematics
Total Questions: 50 | Sections: 5 | Cognitive Levels: 30% Recall, 50% Application, 20% Analysis
Format: Multiple Choice (A–D) | Each question includes answer & rationale
Instructions: Read each question carefully. Select the single best answer from options A–D. The correct answer is
marked *[CORRECT]*, followed by a brief rationale referencing the Portage Learning MATH 110 curriculum and
college-level mathematics standards. Show your work for full credit on calculation problems.
Section 1: Basic Arithmetic & Number Operations
Q1: Evaluate the expression using the order of operations (PEMDAS): 12 + 6 × (8 − 3) ÷ 5
A. 16
B. 18 *[CORRECT]*
C. 20
D. 22
Correct Answer: B
Rationale: Apply PEMDAS: first parentheses (8−3=5), then 6×5=30, then 30÷5=6, finally 12+6=18. Choice A omits the
parenthetical subtraction; C performs addition before multiplication; D ignores the division step entirely.
Q2: Compute: (−15) + 8 − (−7) + (−4)
A. −4 *[CORRECT]*
B. −2
C. −20
D. 4
Correct Answer: A
Rationale: Combine integers: (−15)+8 = −7; −7 −(−7) = −7+7 = 0; 0 +(−4) = −4. Portage Learning MATH 110
emphasizes that subtracting a negative is equivalent to adding a positive. Choice B mishandles the sign on −7; C incorrectly
accumulates negatives; D ignores the final −4.
Q3: Which property of numbers is illustrated by: 7 × (3 + 9) = 7×3 + 7×9 ?
A. Commutative Property of Multiplication
B. Associative Property of Addition
C. Distributive Property *[CORRECT]*
D. Identity Property of Addition
Correct Answer: C
Rationale: The Distributive Property states a(b+c) = ab + ac, distributing multiplication over addition. Commutative (A)
reorders operands; Associative (B) regroups operations without distributing; Identity (D) involves adding 0 or multiplying by 1.
MATH 110 — Module 1 Examination | Page 1
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Q4: Divide: 4,056 ÷ 12
A. 338 *[CORRECT]*
B. 336
C. 342
D. 338 R 6
Correct Answer: A
Rationale: Long division: 4056 ÷ 12 = 338 exactly (12 × 338 = 4056). Choice B misplaces a digit during subtraction; C
overshoots the quotient; D incorrectly leaves a remainder when the division is exact.
Q5: Simplify using exponent rules: 24 × 23 ÷ 25
A. 4 *[CORRECT]*
B. 2
C. 8
D. 16
Correct Answer: A
Rationale: Using am·an = am+n and am÷an = am−n: 24+3−5 = 22 = 4. Choice B treats exponents additively without applying
base; C adds all exponents as positive; D multiplies bases.
Q6: Evaluate: √225 + √81
A. 18
B. 24 *[CORRECT]*
C. 21
D. 27
Correct Answer: B
Rationale: √225 = 15 (since 15×15=225) and √81 = 9, so 15 + 9 = 24. Choice A confuses 225 with 144 (√144=12); C uses
√196=14; D mistakenly sums radicands (√306) before taking root.
Q7: Evaluate using PEMDAS: 50 − 23 × 3 + (12 ÷ 4)2
A. 31 *[CORRECT]*
B. 5
C. 13
D. 37
Correct Answer: A
Rationale: Order: parentheses → 12÷4 = 3, then 32 = 9; exponents → 23 = 8; multiply → 8×3 = 24; final → 50 − 24 + 9 =
31. Choice B does multiplication after subtraction; C ignores the squared term; D computes 2×3 instead of 23×3.
Q8: Which equation demonstrates the Inverse Property of Addition?
A. 5 + 0 = 5
B. 5 + (−5) = 0 *[CORRECT]*
C. 5 × 1 = 5
D. 5 × (1/5) = 1
Correct Answer: B
Rationale: The Inverse Property of Addition states that any number plus its additive inverse equals zero: a + (−a) = 0. Choice
A is the Identity Property of Addition; C is the Identity Property of Multiplication; D is the Inverse Property of Multiplication.
MATH 110 — Module 1 Examination | Page 2
Portage Learning — 2026/2027 Edition
Comprehensive Module 1 Examination | Introductory College Mathematics
Total Questions: 50 | Sections: 5 | Cognitive Levels: 30% Recall, 50% Application, 20% Analysis
Format: Multiple Choice (A–D) | Each question includes answer & rationale
Instructions: Read each question carefully. Select the single best answer from options A–D. The correct answer is
marked *[CORRECT]*, followed by a brief rationale referencing the Portage Learning MATH 110 curriculum and
college-level mathematics standards. Show your work for full credit on calculation problems.
Section 1: Basic Arithmetic & Number Operations
Q1: Evaluate the expression using the order of operations (PEMDAS): 12 + 6 × (8 − 3) ÷ 5
A. 16
B. 18 *[CORRECT]*
C. 20
D. 22
Correct Answer: B
Rationale: Apply PEMDAS: first parentheses (8−3=5), then 6×5=30, then 30÷5=6, finally 12+6=18. Choice A omits the
parenthetical subtraction; C performs addition before multiplication; D ignores the division step entirely.
Q2: Compute: (−15) + 8 − (−7) + (−4)
A. −4 *[CORRECT]*
B. −2
C. −20
D. 4
Correct Answer: A
Rationale: Combine integers: (−15)+8 = −7; −7 −(−7) = −7+7 = 0; 0 +(−4) = −4. Portage Learning MATH 110
emphasizes that subtracting a negative is equivalent to adding a positive. Choice B mishandles the sign on −7; C incorrectly
accumulates negatives; D ignores the final −4.
Q3: Which property of numbers is illustrated by: 7 × (3 + 9) = 7×3 + 7×9 ?
A. Commutative Property of Multiplication
B. Associative Property of Addition
C. Distributive Property *[CORRECT]*
D. Identity Property of Addition
Correct Answer: C
Rationale: The Distributive Property states a(b+c) = ab + ac, distributing multiplication over addition. Commutative (A)
reorders operands; Associative (B) regroups operations without distributing; Identity (D) involves adding 0 or multiplying by 1.
MATH 110 — Module 1 Examination | Page 1
, MATH 110 Module 1 Exam — Portage Learning 2026/2027 Page 2
Q4: Divide: 4,056 ÷ 12
A. 338 *[CORRECT]*
B. 336
C. 342
D. 338 R 6
Correct Answer: A
Rationale: Long division: 4056 ÷ 12 = 338 exactly (12 × 338 = 4056). Choice B misplaces a digit during subtraction; C
overshoots the quotient; D incorrectly leaves a remainder when the division is exact.
Q5: Simplify using exponent rules: 24 × 23 ÷ 25
A. 4 *[CORRECT]*
B. 2
C. 8
D. 16
Correct Answer: A
Rationale: Using am·an = am+n and am÷an = am−n: 24+3−5 = 22 = 4. Choice B treats exponents additively without applying
base; C adds all exponents as positive; D multiplies bases.
Q6: Evaluate: √225 + √81
A. 18
B. 24 *[CORRECT]*
C. 21
D. 27
Correct Answer: B
Rationale: √225 = 15 (since 15×15=225) and √81 = 9, so 15 + 9 = 24. Choice A confuses 225 with 144 (√144=12); C uses
√196=14; D mistakenly sums radicands (√306) before taking root.
Q7: Evaluate using PEMDAS: 50 − 23 × 3 + (12 ÷ 4)2
A. 31 *[CORRECT]*
B. 5
C. 13
D. 37
Correct Answer: A
Rationale: Order: parentheses → 12÷4 = 3, then 32 = 9; exponents → 23 = 8; multiply → 8×3 = 24; final → 50 − 24 + 9 =
31. Choice B does multiplication after subtraction; C ignores the squared term; D computes 2×3 instead of 23×3.
Q8: Which equation demonstrates the Inverse Property of Addition?
A. 5 + 0 = 5
B. 5 + (−5) = 0 *[CORRECT]*
C. 5 × 1 = 5
D. 5 × (1/5) = 1
Correct Answer: B
Rationale: The Inverse Property of Addition states that any number plus its additive inverse equals zero: a + (−a) = 0. Choice
A is the Identity Property of Addition; C is the Identity Property of Multiplication; D is the Inverse Property of Multiplication.
MATH 110 — Module 1 Examination | Page 2
