Algebra 1 Structure of Algebraic Expressions Test Solutions and Scoring (PDF)

Algebra 1 math test solutions: Structure of Algebraic Expressions – Maths PDF

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This algebra 1 expressions test answers for Algebra 1 covers structure of algebraic expressions (Common Core A-SSE.A.1a, A-SSE.A.1b), with a free PDF to print.

Use this key to grade the expressions test. Each solution shows the full work, and the scoring note explains how the points are awarded. The test totals 20 points. Give partial credit for correct steps, even when the final answer is wrong.

Algebra 1 · Common Core State Standards: A-SSE.A.1a, A-SSE.A.1b

Algebra 1 expressions test answers: worked solutions

Question 1 – Parts of an expression [2 pts]

a) The constant term is 12.

b) The coefficient of $x$ is -7 (the sign stays with the term).

Scoring: 1 point for each part. Award no point for 7 in part b.

Question 2 – Evaluate [2 pts]

$2(-3)^{2} – 3(-3) + 1 = 2(9) + 9 + 1 = 28$.

Scoring: 1 point for correct substitution with the exponent applied before multiplying; 1 point for the correct value.

Question 3 – Combine like terms [2 pts]

$(9a + 2a) + (-4 + 10) = 11a + 6$.

$11a + 6$

Scoring: 1 point for each correct term.

Question 4 – Distribute and subtract [2 pts]

First product.

$10x – 15 – 4x + 4$, then combine: $6x – 11$.

$6x – 11$

Scoring: 1 point for distributing both factors correctly (including the sign of $-4(-1)$); 1 point for the final expression.

Question 5 – Streaming plan [2 pts]

a) 2.5 is the coefficient of $w$: the plan adds $2.50 each week (the table rises from $12.49 to $14.99).

b) 9.99 is the constant: a one-time charge of $9.99 paid at the start.

Scoring: 1 point for each correct interpretation with units.

Question 6 – Write expressions [2 pts]

a) $2n + 7$.

b) $6(n + 4)$, since the sum is a group multiplied by 6.

Scoring: 1 point for each expression. Part b needs the parentheses.

Question 7 – Write as a product [2 pts]

Both terms share the quantity $(x + 4)$, so $(3 + 2)(x + 4) = 5(x + 4)$.

At $x = 1$: $5(5) = 25$.

$5(x + 4)$; 25

Scoring: 1 point for the product; 1 point for the value.

Question 8 – Perimeter [3 pts]

Perimeter 6x + 18.

a) $2(2x + 3) + 2(x + 6) = 4x + 6 + 2x + 12 = 6x + 18$.

b) $6(5) + 18 = 48$.

$6x + 18$; 48

Scoring: part a, 1 point for setting up the perimeter and 1 point for simplifying; part b, 1 point.

Question 9 – Compare plans [3 pts]

a) Plan A charges $3.50 per gigabyte.

b) $(20 + 2g) – (12 + 3.5g) = 20 + 2g – 12 – 3.5g = 8 – 1.5g$.

c) $8 – 1.5(4) = 2$: at 4 gigabytes Plan B costs $2 more.

3.50 per GB; $8 – 1.5g$; $2 more

Scoring: 1 point per part.

Total score

Total

20 points

Key facts behind this algebra 1 expressions test answers

Key facts

Terms are separated by + and – signs, and each term keeps its own sign.
A coefficient multiplies a variable; a constant has no variable.
Like terms have the same variable part and can be combined by adding coefficients.
A grouped expression such as (x + 3) can be treated as one factor.
In a model, a coefficient is often a rate and a constant is a starting amount.

How to use this algebra 1 expressions test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Algebra 1 chapters: Algebra 1 math.

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