Algebra 1 Literal Equations and Formulas Worksheet (PDF)

Algebra 1 math worksheet: Literal Equations and Formulas – Maths PDF

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

Use these 20 problems to master literal equations and formulas (Common Core A-CED.A.4). You will rearrange area, perimeter, interest, temperature, distance, and volume formulas to isolate a chosen variable, then substitute given values to solve real problems. They move from quick warm-ups to multistep word problems, so slow down on the last six and check that each answer makes sense.

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

Literal equations worksheet: exercises 1 to 10

Exercise 1 – Distance formula

Solve $d = rt$ for $t$.

Exercise 2 – Perimeter of a square

Solve $P = 4s$ for $s$.

Exercise 3 – Area of a rectangle

Solve $A = lw$ for $w$.

Exercise 4 – Circumference

Solve $C = 2\pi r$ for $r$.

Exercise 5 – Solve for b

Solve $y = mx + b$ for $b$.

Exercise 6 – Solve for x

Steps.

Solve $y = mx + b$ for $x$.

Exercise 7 – Perimeter of a rectangle

Solve $P = 2l + 2w$ for $l$.

Exercise 8 – Area of a triangle

A triangle.

Solve $A = \frac{1}{2}bh$ for $h$.

Exercise 9 – Temperature formula

Solve $F = \frac{9}{5}C + 32$ for $C$.

Exercise 10 – Volume of a prism

Solve $V = lwh$ for $h$.

Exercises 11 and up

Exercise 11 – General linear form

Solve $ax + b = c$ for $x$.

Exercise 12 – Standard form to slope-intercept

The line $3x + 2y = 12$.

Solve $3x + 2y = 12$ for $y$.

Exercise 13 – Variable on both sides

Solve $ax + b = cx + d$ for $x$. Assume $a \neq c$.

Exercise 14 – Surface area of a cylinder

Solve $S = 2\pi r^{2} + 2\pi rh$ for $h$.

Exercise 15 – Trapezoid

A trapezoid with area 60.

Solve $A = \frac{1}{2}(b_{1} + b_{2})h$ for $b_{1}$, then find $b_{1}$ when $A = 60$, $h = 6$, and $b_{2} = 8$.

Exercise 16 – Simple interest

Simple interest is $I = Prt$. Sofia earns $180 in interest on $1,500 at a rate of $r = 0.04$ (4%). Solve the formula for $t$, then find the number of years.

Exercise 17 – Convert a temperature

A weather app shows 77°F. Use the formula $C = \frac{5}{9}(F – 32)$ to find the temperature in degrees Celsius.

Exercise 18 – Fence length

Dog run, perimeter 46 feet.

A rectangular dog run has perimeter 46 feet and width 9 feet. Solve $P = 2l + 2w$ for $l$, then find the length.

Exercise 19 – Road trip speed

Diego drives 330 miles in 5.5 hours. Solve $d = rt$ for $r$ and find his average speed in miles per hour.

Exercise 20 – Slope formula

The slope formula is $m = \frac{y_{2} – y_{1}}{x_{2} – x_{1}}$. Solve it for $y_{2}$, then find $y_{2}$ when $m = 3$, $x_{1} = 1$, $x_{2} = 5$, and $y_{1} = 2$.

Exercise 21 – Soup can

A cylinder-shaped can has volume $V = \pi r^{2}h$. A can has radius 3 inches and volume $90\pi$ cubic inches. Solve the formula for $h$ and find the height.

Key facts behind this literal equations worksheet

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 worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

All Algebra 1 chapters: Algebra 1 math.

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