BetterGrades Algebra · Unit A1 · Review

Quantities, Variables, and Mathematical Objects: cumulative review

Quantities, Variables, and Mathematical Objects: cumulative review for Quantities, Variables, and Mathematical Objects, with an explicit attempt-first assessment blueprint.

Assessment

25 concrete questions

Suggested time: 35-60 minutes.

Grading boundary: mixed self-check + selected deterministic checks

Cumulative share: 25% prior units

Each question is fully authored and linked to a lesson skill. Detailed scoring criteria and worked solutions stay protected until a substantive attempt is submitted.

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Open-response checkA1.3

How many terms does $3x + 6$ have?

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Open-response checkA1.3

Identify base and exponent in $(x-4)^{3}$ .

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Open-response checkA1.3

A student calls $2$ and $x$ terms in $2x+3$ . Repair the language.

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Open-response checkA1.3

Draw or describe an expression tree for $4 - 2(x+1)$ .

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Open-response checkA1.3

Identify numerator, denominator, and restriction in $\frac{x+5}{2x}$ .

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Open-response checkA1.3

Rewrite $7 - 3x$ as an addition expression.

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Open-response checkA1.3

Explain why preserving structure matters when evaluating $2(x+3)^{2}$ .

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Open-response checkA1.3

Describe the terms, factors, coefficients, and outermost operation in $-2x^{3} + 5x - 9$ .

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Open-response checkA1.3

Compare $4(x - 3)^{2}$ and $(4x - 3)^{2}$ by describing their operation trees.

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Open-response checkA1.3

Which pairs are like terms: $6ab^{2}, -3a^{2}b, 5ab^{2}, 8ba^{2}$ ?

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Open-response checkA1.3

Explain why $x$ cannot be cancelled in $\frac{x + 7}{x},$ but can be cancelled in $\frac{x(x + 7)}{x}$ for $x \ne 0$ .

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Open-response checkA1.4

Evaluate $5x - 7$ at $x = 4$ .

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Open-response checkA1.4

Evaluate $x^{2} + 2x$ at $x = -3$ .

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Open-response checkA1.4

Evaluate $3a^{2}b$ for $a = -2$ and $b = 5$ .

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Open-response checkA1.4

Evaluate $\frac{m-n}{m+n}$ for $m=5, n=2$ .

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Open-response checkA1.4

Evaluate C $= 2\pi r$ for $r = 3$ cm.

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Open-response checkA1.4

Evaluate $d =$ rt for $r = \frac{55 mi}{hr}$ and $t = 2.5$ hr.

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Open-response checkA1.4

If $p = x-4,$ rewrite $p^{2}+3p$ in terms of $x$ .

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Open-response checkA1.4

Simplify the previous expression.

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Open-response checkA1.4

If $y = 3x+2$ and $x=4,$ find $y$ .

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Open-response checkA1.4

If $f(t)=t^{2}-1,$ find $f(\frac{1}{2})$ .

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Open-response checkA1.4

A student evaluates $x^{2}$ at $x=-5$ as $-25$ . Repair the work.

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Open-response checkA1.4

Why is $4(2x+1)$ required when $y=2x+1$ is substituted into $4y$ ?

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Open-response checkA1.4

Evaluate $P=2l+2w$ for $l=5.2$ m, $w=3.1 m$ .

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Open-response checkA1.4

For $g(x)=|x-3|,$ find $g(-2)$ .

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