Algebra 1 Solving Linear Equations in One Variable Test with Point Values (PDF)

Algebra 1 math test: Solving Linear Equations in One Variable – Maths PDF

This algebra 1 linear equations test for Algebra 1 covers solving linear equations in one variable (Common Core A-REI.A.1, A-REI.B.3, A-CED.A.1), with a free PDF to print.

Algebra 1 linear equations test (Algebra 1) – first page of the printable PDF
Take this 20-point, 45-minute test to measure your skill with linear equations in one variable (A-REI.B.3 and A-CED.A.1). Read each question carefully, show your work, and check units and signs before you move on. If you get stuck, skip the question and return to it at the end.

Time and points

About this test
  • Grade: Algebra 1
  • Chapter: Solving Linear Equations in One Variable
  • Standards: A-REI.A.1, A-REI.B.3, A-CED.A.1
  • Time: 45 minutes
  • Total: 20 points

Algebra 1 linear equations test: questions

Question 1 – One-step and two-step [2 pts]

  1. Solve \(x – 9 = 14\). (1 point)
  2. Solve \(5x + 8 = -17\). (1 point)

Question 2 – Both sides [2 pts]

Solve \(7x – 4 = 3x + 20\).

Question 3 – Distribute [2 pts]

Solve \(4(2x – 3) = 3x + 13\).

Question 4 – Fraction coefficient [2 pts]

Solve \(\frac{3}{4}x + 2 = 11\).

Question 5 – Types of solutions [2 pts]

Describe the solutions of each equation as one solution, no solution, or infinitely many solutions.

  1. \(5(x – 1) = 5x – 5\) (1 point)
  2. \(2x + 3 = 2x – 4\) (1 point)

Question 6 – Tape diagram [2 pts]

2929xxx8
Question 6 diagram.

The tape diagram shows three equal parts \(x\) and one part 8 with a total of 29. Write an equation and solve it.

Question 7 – Rectangle perimeter [3 pts]

x + 6x
Perimeter 44 inches.

The rectangle has width \(x\) inches and length \(x + 6\) inches. Its perimeter is 44 inches.

  1. Write an equation for the perimeter. (1 point)
  2. Solve the equation. (1 point)
  3. State the length and width. (1 point)

Question 8 – Equal savings [3 pts]

WeeksJamalSofia0$120$455$195$14510$270$245
Savings after 0, 5, and 10 weeks.

Jamal has $120 and saves $15 each week. Sofia has $45 and saves $20 each week.

  1. Write an equation to find the number of weeks \(w\) when they have the same amount. (1 point)
  2. Solve the equation. (1 point)
  3. Find how much each has then. (1 point)

Question 9 – Find the error [2 pts]

A student solved \(3(x + 4) = 21\) by writing \(3x + 4 = 21\) and got \(x = \frac{17}{3}\). Identify the error and find the correct solution.

View solution

Key facts behind this algebra 1 linear equations test

Key facts
  • Do the same operation to both sides of an equation to keep it balanced.
  • Undo addition and subtraction first, then multiplication and division.
  • With variables on both sides, collect variable terms on one side and constants on the other.
  • A false statement such as 6 = 5 means no solution; a true statement such as 8 = 8 means infinitely many.
  • Check a solution by substituting it into the original equation.

How to use this algebra 1 linear 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.

Prepare for the test

All Algebra 1 chapters: Algebra 1 math.

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