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Algebra I Readiness and Final Test

A free Algebra I lesson from the “Algebra I Readiness and Final Test” unit, with a worked example and practice problems including step-by-step solutions.

The Algebra I readiness test is a cumulative assessment across expressions, equations, inequalities, formulas, functions, linear relationships, systems, exponents, polynomials, factoring, quadratics, and applications.

What you'll learn

Why it matters: Cumulative Algebra I work reflects how real modeling problems mix skills: defining variables, choosing forms, solving, graphing, and interpreting answers together.

Worked example

Problem. A line has slope 2 and passes through (3, 8). Write it in slope-intercept form.

  1. Use point-slope form: y - 8 = 2(x - 3).
  2. Distribute: y - 8 = 2x - 6.
  3. Add 8 to get y = 2x + 2.

Answer: y = 2x + 2

Practice problems

1. Simplify 3(2x - 5) + 4x.

Show solution
  1. Course Review: First identify exactly what the question is asking: Simplify 3(2x - 5) + 4x.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Distribute first: 6x - 15.
  4. Combine 6x + 4x = 10x.
  5. Check the result by substituting or estimating: the response should match 10x - 15 and make sense in the original problem.

Answer: 10x - 15

2. Solve 4x - 9 = 31.

Show solution
  1. Course Review: First identify exactly what the question is asking: Solve 4x - 9 = 31.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Add 9: 4x = 40.
  4. Divide by 4: x = 10.
  5. Check the result by substituting or estimating: the response should match 10 and make sense in the original problem.

Answer: 10

3. Solve -5x < 20. Enter the boundary number.

Show solution
  1. Course Review: First identify exactly what the question is asking: Solve -5x < 20. Enter the boundary number.
  2. For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
  3. Divide by -5 and flip.
  4. x > -4.
  5. Check the result by substituting or estimating: the response should match -4 and make sense in the original problem.

Answer: -4

4. Solve A = lw for l.

Choices: l = A/w · l = Aw · l = w/A · l = A - w

Show solution
  1. Course Review: First identify exactly what the question is asking: Solve A = lw for l.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Divide both sides by w.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: l = A/w

5. Use d = rt. If d = 315 and t = 5, what is r?

Show solution
  1. Course Review: First identify exactly what the question is asking: Use d = rt. If d = 315 and t = 5, what is r?
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. r = d/t.
  4. 315/5 = 63.
  5. Check the result by substituting or estimating: the response should match 63 and make sense in the original problem.

Answer: 63

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