Algebra 1 Literal Equations and Formulas Test Solutions and Scoring (PDF)

Algebra 1 math test solutions: Literal Equations and Formulas – Maths PDF

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This literal equations test answers for Algebra 1 covers literal equations and formulas (Common Core A-CED.A.4, A-REI.A.1), with a free PDF to print.

Grade the literal equations test with this key. Every question lists the points available and how to split them between method and result. Students who show clear work should receive partial credit, even if the final answer is not correct. The test totals 20 points in all.

Algebra 1 · Common Core State Standards: A-CED.A.4, A-REI.A.1

Literal equations test answers: worked solutions

Question 1 – Solve for a side [2 pts]

a) Divide by $lh$: $w = \frac{V}{lh}$.

b) Subtract $b$, then divide by $x$: $m = \frac{y – b}{x}$.

Scoring: 1 point for each correct formula.

Question 2 – Standard form [2 pts]

Subtract $4x$: $5y = 20 – 4x$. Divide by 5: $y = 4 – \frac{4}{5}x$.

$y = 4 – \frac{4}{5}x$

Scoring: 1 point for isolating the y term; 1 point for dividing every term by 5.

Question 3 – Trapezoid height [2 pts]

Multiply by 2: $2A = h(a + b)$. Divide by $a + b$.

$h = \frac{2A}{a + b}$

Scoring: 1 point for clearing the fraction; 1 point for dividing by the whole sum.

Question 4 – Variable on both sides [2 pts]

Subtract $bx$ and add 3: $ax – bx = 10$. Factor: $x(a – b) = 10$.

$x = \frac{10}{a – b}$

Scoring: 1 point for collecting x terms; 1 point for factoring and dividing.

Question 5 – Find the principal [2 pts]

Divide both sides by $rt$: $P = \frac{I}{rt}$.

Substitute: $P = \frac{225}{0.05(3)} = \frac{225}{0.15} = 1500$.

$P = \frac{I}{rt}$; $1,500

Scoring: 1 point for the formula; 1 point for $1,500.

Question 6 – Interest rate [2 pts]

$r = \frac{I}{Pt} = \frac{270}{1500(3)} = \frac{270}{4500} = 0.06$.

$r = \frac{I}{Pt}$; 6%

Scoring: 1 point for the rearranged formula; 1 point for 6%.

Question 7 – Trapezoid base [3 pts]

Top base 11 feet.

a) $b_{1} = \frac{2A}{h} – b_{2}$.

b) $b_{1} = \frac{2(54)}{6} – 7 = 18 – 7 = 11$.

11 feet

Scoring: part a, 1 point for clearing the fraction and 1 point for isolating b₁; part b, 1 point.

Question 8 – Rectangle width [3 pts]

Width 10 meters.

a) $w = \frac{P – 2l}{2}$.

b) $w = \frac{50 – 30}{2} = 10$ m.

c) $A = lw = 15 \cdot 10 = 150$ m².

10 m; 150 m²

Scoring: 1 point per part.

Question 9 – Find the error [2 pts]

After subtracting $3x$ the equation is $2y = 12 – 3x$. The student forgot to divide every term, including $12$ and $3x$, by 2.

$y = 6 – \frac{3}{2}x$

Scoring: 1 point for the explanation; 1 point for the correct equation.

Total score

Total

20 points

Key facts behind this literal equations test answers

Key facts

A literal equation contains two or more variables, like a formula.
Solve for a variable by applying inverse operations to both sides.
Treat the other letters as if they were numbers.
When the variable appears in two terms, collect those terms and factor.
The answer is an expression, not necessarily a number.

How to use this literal equations 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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