7th Grade Solving Two-Step Equations Test with Point Values (PDF)

7th Grade math test: Solving Two-Step Equations – Maths PDF

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This two step equations test for 7th Grade covers solving two-step equations (Common Core 7.EE.B.4a), with a free PDF to print.

This 45-minute test checks solving two-step equations of the forms px + q = r and p(x + q) = r with rational numbers, and comparing arithmetic and algebraic solutions (Common Core 7.EE.B.4a). It has 9 questions worth 20 points in all. Show your work, because most questions give partial credit for correct steps.

Time and points

About this test

Grade: Grade 7
Chapter: Solving Two-Step Equations
Standards: 7.EE.B.4a
Time: 45 minutes
Total: 20 points

Two step equations test: questions

Question 1 – Two-step [2 pts]

Solve $6x-9=33$. Show each step.

Question 2 – Parentheses [2 pts]

Solve $-4(x+5)=-28$. Show each step.

Question 3 – Fractions [2 pts]

Solve $\frac{3}{4}x+\frac{1}{2}=\frac{11}{2}$. Show each step.

Question 4 – Decimals [2 pts]

Solve $1.5x-2.4=6.6$. Show each step.

Question 5 – Write and solve [2 pts]

A fee plus two tickets.

Priya pays a $12 fee plus the price t of each of 2 concert tickets, and the total is $46. Write an equation and solve for t.

Question 6 – Two methods [2 pts]

The sum of 5 and 3 times a number is 26. (a) Find the number with arithmetic only. (b) Write and solve an equation.

Question 7 – Find the error [2 pts]

Liam solved $3(x-2)=12$ like this: $x-2=12$, so $x=14$. Explain his mistake and find the correct solution.

Question 8 – Kayak rental [3 pts]

Kayak rental.

Find the cost per hour and the starting fee. (1 point)
Write an equation for the cost C after h hours. (1 point)
Find the number of hours for a cost of $205. (1 point)

Question 9 – Triangle [3 pts]

A triangle with perimeter 38 inches.

Write an equation for the perimeter. (1 point)
Solve it for x. (1 point)
Find the length of the longest side. (1 point)

Key facts behind this two step equations test

Key facts

Two forms: $px + q = r$ and $p(x + q) = r$.
Undo addition or subtraction first, then multiplication or division.
Do the same operation to both sides.
Fractions and decimals follow the same steps as whole numbers.
Check by substituting the solution into the original equation.

How to use this two step equations test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Grade 7 chapters: Grade 7 math.

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