Week 1 — Quiz (auto-graded) · Real Numbers, Exponents & Algebraic Expressions

Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Objective tested: Objective 1 — properties of real numbers, order of operations, integer-exponent rules, simplifying expressions.
Points: 10 (1 each) · Assignment group: Quizzes (15% of grade) · Due: end of Module 1.

This is the human-readable quiz with its vetted answer key and feedback. The import-ready Classic QTI is in F-quiz-week-01-qti.xml. AI is not permitted on quizzes (course AI policy). Every numeric answer below is pre-computed and independently re-verified (Python w01_verify.py, PASS).

Blueprint

No trick questions; distractors target the Week 1 misconceptions named in the lecture outline (sign-and-exponent slips, add-vs-multiply exponents, distributing a negative).

Questions, key, and feedback

Q1 (MC). Which of the following is an irrational number?
- A. √16
- B. √2 ✅
- C. 7/9
- D. 0.25
Feedback: √2 cannot be written as a ratio of integers, so it is irrational. √16 = 4, 7/9, and 0.25 = 1/4 are all rational. (√16 = 4 is the classic "looks irrational but isn't" trap.)

Q2 (MC). Using the order of operations, evaluate: 6 + 2 × 3²
- A. 24 ✅
- B. 72
- C. 42
- D. 144
Feedback: Exponent first (3² = 9), then multiply (2 × 9 = 18), then add (6 + 18 = 24). (B = added 6 + 2 first; C = multiplied 2 × 3 then squared; D = added inside then squared.)

Q3 (MC). Evaluate: −4²
- A. −16 ✅
- B. 16
- C. −8
- D. 8
Feedback: The exponent binds tighter than the negative sign: −4² means −(4²) = −(16) = −16. You would only get 16 from (−4)², where the parentheses square the negative too.

Q4 (Matching). Match each property of real numbers to the equation that illustrates it.
| Property | Correct equation |
|---|---|
| Commutative property of addition | a + b = b + a |
| Associative property of multiplication | (a · b) · c = a · (b · c) |
| Distributive property | a(b + c) = ab + ac |
| Additive identity | a + 0 = a |
Feedback: Commutative = order changes; associative = grouping changes; distributive = multiplication spread over a sum; identity = the value that leaves a number unchanged (0 for addition).

Q5 (MC). Simplify: x⁵ · x³
- A. x⁸ ✅
- B. x¹⁵
- C. x²
- D. 2x⁸
Feedback: Same base, multiplying → add the exponents: x⁵⁺³ = x⁸. (B multiplied the exponents; C subtracted them; D invented a coefficient.)

Q6 (MC). Simplify: (2x³)⁴
- A. 16x¹² ✅
- B. 8x¹²
- C. 16x⁷
- D. 2x¹²
Feedback: A power of a product raises each factor: (2)⁴ · (x³)⁴ = 16 · x¹² = 16x¹². (B used 2 × 4 = 8 instead of 2⁴; C added 3 + 4; D forgot to raise the 2.)

Q7 (MC). Rewrite using only positive exponents: 3x⁻² (the exponent −2 applies only to x)
- A. 3/x² ✅
- B. 1/(3x²)
- C. −3x²
- D. 3x²
Feedback: A negative exponent means reciprocal: x⁻² = 1/x². The coefficient 3 is not raised to −2, so 3x⁻² = 3/x². (B wrongly moved the 3 down; C treated −2 as a negative sign; D dropped the negative.)

Q8 (Multiple answer — select all that apply). Which of the following are equal to x⁶?
- A. x² · x⁴ ✅
- B. (x²)³ ✅
- C. x⁸ / x² ✅
- D. x² · x³
- E. (x³)³
Feedback: Add when multiplying (x²·x⁴ = x⁶), multiply for a power of a power ((x²)³ = x⁶), subtract when dividing (x⁸/x² = x⁶). D = x⁵ (2 + 3) and E = x⁹ (3 × 3), so neither is x⁶.

Q9 (True / False). −3² and (−3)² represent the same value.
- True
- False ✅
Feedback: False. −3² = −(3²) = −9, but (−3)² = (−3)(−3) = +9. The parentheses decide whether the negative gets squared.

Q10 (MC). Simplify: 5x − 2(3x − 4)
- A. −x + 8 ✅
- B. −x − 8
- C. −x − 4
- D. 11x − 8
Feedback: Distribute the −2 to both terms: −2(3x) = −6x and −2(−4) = +8. Then 5x − 6x + 8 = −x + 8. (B forgot to flip the sign on −4; C didn't distribute −2 across the −4; D subtracted 5x − 6x as +11x.)

Answer key (quick reference)

Quality gate (self-checked, computer-verified): each single-answer item has exactly one correct option; the matching item pairs all four properties one-to-one; the multiple-answer item keys A, B, C (and requires D, E unselected). Arithmetic pre-computed and independently re-verified (w01_verify.py): Q2 6+2·9 = 24; Q3 −(4²) = −16; Q5 x⁵⁺³ = x⁸; Q6 2⁴x¹² = 16x¹²; Q7 3x⁻² = 3/x²; Q8 x⁶ ✓ for A,B,C; Q9 −9 ≠ 9; Q10 5x−6x+8 = −x+8. All checks PASS. QTI parse confirmation: F-quiz-week-01-qti.xml parses as imsqti_xmlv1p2 with 10 items.

Item-bank entries (for variants + the midterm/final)

All ten items are tagged course=MATH120 · week=1 · objective=1 · topic=real-numbers-exponents-expressions and deposited in Item Bank: Week 1 — Real Numbers, Exponents & Expressions. The midterm (Week 8) and the per-term variant updates draw fresh items from this bank. (Tags: q1 irrational, q2 order-of-ops, q3 sign-exponent, q4 properties, q5 product-rule, q6 power-of-product, q7 negative-exponent, q8 exponent-equivalence, q9 sign-exponent-tf, q10 distribute-combine.)

Canvas placement block

canvas_object   = Quizzes::Quiz
title           = "Week 1 Quiz — Real Numbers, Exponents & Expressions"
assignment_group = "Quizzes"
points_possible = 10
grading_type    = points
due_offset_days = 6        # 6 days after module start
published       = true
shuffle_answers = true
provenance      = "~ Prof. Calloway's edition · Fall 2026 · built with thecoursemaker.com"