7th Grade Equivalent Linear Expressions Test with Point Values (PDF)

7th Grade math test: Equivalent Linear Expressions – Maths PDF

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This grade 7 equivalent expressions test for 7th Grade covers equivalent linear expressions (Common Core 7.EE.A.1, 7.EE.A.2), with a free PDF to print.

This 45-minute test checks adding, subtracting, factoring, and expanding linear expressions, and rewriting expressions in equivalent forms (Common Core 7.EE.A.1-2). 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: Equivalent Linear Expressions
Standards: 7.EE.A.1, 7.EE.A.2
Time: 45 minutes
Total: 20 points

Grade 7 equivalent expressions test: questions

Question 1 – Combine like terms [2 pts]

Simplify \(9x-4+2x+10\).

Question 2 – Area model [2 pts]

A rectangle model.

Write the area of the whole rectangle as a product, and as a sum of the areas of the two parts.

Question 3 – Distribute [2 pts]

Expand and simplify \(-3(2y-7)+5\).

Question 4 – Factor [2 pts]

Factor \(18x+24\) using the greatest common factor.

Question 5 – Subtract [2 pts]

Simplify \((5x-2)-(3x-8)\).

Question 6 – Rational coefficients [2 pts]

Simplify \(\frac{2}{3}x-\frac{1}{6}x\).

Question 7 – Equivalent? [2 pts]

Evaluate each expression.

Complete the table. Tell which two expressions are equivalent and explain how the table shows it.

Question 8 – Rectangle [3 pts]

A rectangle.

Write the perimeter as a simplified expression. (1 point)
Find the perimeter when \(w=12\). (1 point)
A second rectangle has width 5 and the same length, \(w+8\). Write its area as a product and expand it. (1 point)

Question 9 – Discount and tax [3 pts]

A jacket costs \(p\) dollars. A store takes 20% off, then the buyer pays 5% tax. (a) Write the price after the discount as a single product. (b) Write the final cost as a single product. (c) Find the final cost when \(p=60\).

Key facts behind this grade 7 equivalent expressions test

Key facts

Like terms have the same variable part and can be combined by adding coefficients.
Distributive property: \(a(b + c) = ab + ac\).
Factor by pulling out the greatest common factor: \(6x + 12 = 6(x + 2)\).
Subtracting an expression means adding its opposite.
Adding \(5\%\) tax to a price p gives \(p + 0.05p = 1.05p\).

How to use this grade 7 equivalent expressions 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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