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Cumulative Review: Algebra, Graphing, and Geometry

A free Pre-Algebra lesson from the “Cumulative Review and Test Prep” unit, with a worked example and practice problems including step-by-step solutions.

Later cumulative review connects symbolic algebra with graphs, geometry, data, and probability. The goal is to recognize which relationship is being used and solve with a clear sequence of steps. In Cumulative Review and Test Prep, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.

What you'll learn

Why it matters: Most real problems mix skills — a tip plus a tax, a discount plus a unit price, or an area plus a perimeter. Practicing them together is what test day and everyday math both look like.

Worked example

Problem. For y = 3x - 2, what is y when x = 5?

  1. Substitute x = 5.
  2. 3(5) - 2 = 15 - 2.
  3. y = 13.
  4. Connect the calculation back to Cumulative Review: Algebra, Graphing, and Geometry so the method, not just the arithmetic, is clear.

Answer: 13

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.

Practice problems

1. Solve 6x - 5 = 31.

Show solution
  1. Add 5: 6x = 36.
  2. Divide by 6: x = 6.

Answer: 6

2. Solve -2x > 10. Enter the boundary number.

Show solution
  1. Divide by -2 and flip the sign.
  2. x < -5, so the boundary number is -5.

Answer: -5

3. Which point lies on y = 2x + 3?

Choices: (4, 11) · (4, 8) · (11, 4) · (3, 4)

Show solution
  1. When x = 4, y = 2(4) + 3 = 11.

Answer: (4, 11)

4. Which graph matches x >= 2?

Choices: Closed circle at 2, shade right · Open circle at 2, shade right · Closed circle at 2, shade left · Open circle at 2, shade left

Show solution
  1. >= includes the boundary.
  2. Greater values are to the right.

Answer: Closed circle at 2, shade right

5. Reflect (-6, 2) across the x-axis.

Choices: (-6, -2) · (6, 2) · (6, -2) · (2, -6)

Show solution
  1. Reflecting across the x-axis changes the sign of y.
  2. The x-coordinate stays -6.

Answer: (-6, -2)

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