Function Operations Quiz
Algebra II Standard AR.4.B
Function Operations Practice
Assessment Score
/ 100
Name:
Date:
Period:
Directions: Show all algebraic steps clearly in the workspace provided for each problem. Select the single best answer choice.
1
Given \(p(x) = 2x^2 + 5x - 8\) and \(q(x) = 7x + 4\), what is \((p + q)(x)\)?
Addition
A \(2x^2 + 12x - 4\)
B \(2x^2 + 12x - 12\)
C \(14x^2 - 4\)
D \(2x^2 - 2x - 12\)
Show Your Work:
2
If \(p(x) = 7x - 9\) and \(q(x) = x^2 + 8\), what is \(r(x) = (p \cdot q)(x)\)?
Perform the operations and express the polynomial in standard form.
Multiplication
A \(7x^3 - 9x^2 + 56x - 72\)
B \(7x^3 - 72\)
C \(7x^3 + 47x^2 - 72\)
D \(7x^3 - 9x^2 + 56x + 72\)
Show Your Work:
Confidence Rating:
1 (Review needed) 2 (Somewhat confident) 3 (Mastered)
Page 1 of 2 • Student Copy
Teacher Resource Formative Assessment
Diagnostic Key & Distractor Analysis
Quick Answer Key
1: A 2: A
Each distractor below was engineered around specific, high-frequency student algebraic errors. Use student answer selections to identify immediate intervention targets.
1 Polynomial Addition: \((p+q)(x)\)
Correct: A \((2x^2 + 12x - 4)\)
Correct Procedure: Group like terms: \(2x^2 + (5x + 7x) + (-8 + 4) = 2x^2 + 12x - 4\).
A
Correct Answer: Correctly combines linear terms and constants while preserving the quadratic term.
B
Integer Sign Error: Student evaluated \(-8 + 4\) as \(-(8+4) = -12\) rather than \(-4\). Indicates weakness in integer arithmetic with opposite signs.
C
Exponent Confusion with Like Terms: Student incorrectly added exponents when combining linear terms (\(5x + 7x = 12x^2\)), then combined \(2x^2 + 12x^2 = 14x^2\). Confuses product rule with addition rule.
D
Operation Reversal (Subtraction): Student calculated \((p - q)(x) = 2x^2 + (5x - 7x) + (-8 - 4) = 2x^2 - 2x - 12\). Indicates symbol confusion between addition and subtraction of functions.
2 Polynomial Multiplication: \((p \cdot q)(x)\)
Correct: A \((7x^3 - 9x^2 + 56x - 72)\)
Correct Procedure: Distribute both terms: \(7x(x^2 + 8) - 9(x^2 + 8) = 7x^3 + 56x - 9x^2 - 72\). Arrange in standard descending degree form.
A
Correct Answer: Correctly applies full distributive property (FOIL/box method) and writes in standard form.
B
Omission of Cross-Terms ("Freshman's Dream"): Student multiplied only first terms and last terms: \((7x)(x^2) + (-9)(8) = 7x^3 - 72\), missing outer and inner distributions completely.
C
Illegal Combining of Unlike Terms: Student distributed correctly to get \(-9x^2 + 56x\), but then erroneously merged unlike terms as \(+47x^2\). Reflects confusion between degree types.
D
Negative Sign Distribution Failure: Student distributed \(-9\) to \(x^2\) as \(-9x^2\), but neglected the negative when multiplying \(-9 \times 8\), getting \(+72\) instead of \(-72\).
Targeted Remediation Recommendations
If students chose Item 1 (B or C): Review vertical alignment of polynomials to prevent cross-degree addition, and enforce using number lines or algebra tiles for integer subtraction.
If students chose Item 2 (B or D): Mandate the 2×2 Box/Area Model method. The grid structure forces students to fill all 4 product cells and visually prevents dropped signs.
Function Operations Misconception Diagnostic Page 2 of 2 • Teacher Key
