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Pre-Algebra Final Exam

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.

The final exam samples every unit: integers, factors, fractions, ratios, percents, decimals, scientific notation, roots, real numbers, proportions, unit conversions, expressions, equations, inequalities, the coordinate plane, linear functions, slope, angle relationships, area, circles, volume, the Pythagorean theorem, transformations, data and statistics, probability, sampling, and word problems. 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

Worked example

Problem. A right triangle has legs 9 and 12. What is the length of the hypotenuse?

  1. Use the Pythagorean theorem: a^2 + b^2 = c^2.
  2. 9^2 + 12^2 = 81 + 144 = 225.
  3. c = sqrt(225) = 15.
  4. Connect the calculation back to Pre-Algebra Final Exam so the method, not just the arithmetic, is clear.

Answer: 15

Practice problems

1. Compute -5 + 12.

Show solution
  1. Final Review: First identify exactly what the question is asking: Compute -5 + 12.
  2. For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
  3. Different signs: 12 - 5 = 7.
  4. Check the result by substituting or estimating: the response should match 7 and make sense in the original problem.
  5. Write the final response in the form requested by the prompt.

Answer: 7

2. Compute 1/2 + 1/4.

Show solution
  1. Final Review: First identify exactly what the question is asking: Compute 1/2 + 1/4.
  2. For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
  3. Rewrite 1/2 as 2/4.
  4. 2/4 + 1/4 = 3/4.
  5. Check the result by substituting or estimating: the response should match 3/4 and make sense in the original problem.

Answer: 3/4

3. Find 10% of 70.

Show solution
  1. Final Review: First identify exactly what the question is asking: Find 10% of 70.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. 10% is 0.10.
  4. 0.10 x 70 = 7.
  5. Check the result by substituting or estimating: the response should match 7 and make sense in the original problem.

Answer: 7

4. Evaluate 3^2.

Show solution
  1. Final Review: First identify exactly what the question is asking: Evaluate 3^2.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. 3^2 = 3 x 3.
  4. 3 x 3 = 9.
  5. Check the result by substituting or estimating: the response should match 9 and make sense in the original problem.

Answer: 9

5. Solve x - 6 = 10.

Show solution
  1. Final Review: First identify exactly what the question is asking: Solve x - 6 = 10.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Add 6 to both sides.
  4. 10 + 6 = 16.
  5. Check the result by substituting or estimating: the response should match 16 and make sense in the original problem.

Answer: 16

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