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Pre-Algebra Readiness Test

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 readiness test is a course-level mixed assessment. It samples number sense, decimals, fractions, rates, percents, scientific notation, expressions, equations, inequalities, graphing foundations, angle relationships, geometry, statistics, probability, 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 taxi charges 4 dollars plus 3 dollars per mile. What is the cost for 8 miles?

  1. The fixed charge is 4 dollars.
  2. The mileage charge is 3 x 8 = 24 dollars.
  3. Add them: 4 + 24 = 28.
  4. Connect the calculation back to Pre-Algebra Readiness Test so the method, not just the arithmetic, is clear.

Answer: 28

Practice problems

1. Compute -8 + 13.

Show solution
  1. Course Review: First identify exactly what the question is asking: Compute -8 + 13.
  2. For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
  3. Different signs: 13 - 8 = 5.
  4. The positive number has the larger distance.
  5. Check the result by substituting or estimating: the response should match 5 and make sense in the original problem.

Answer: 5

2. Compute 3/4 - 1/8.

Show solution
  1. Course Review: First identify exactly what the question is asking: Compute 3/4 - 1/8.
  2. For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
  3. Rewrite 3/4 as 6/8.
  4. 6/8 - 1/8 = 5/8.
  5. Check the result by substituting or estimating: the response should match 5/8 and make sense in the original problem.

Answer: 5/8

3. Find 40% of 75.

Show solution
  1. Course Review: First identify exactly what the question is asking: Find 40% of 75.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. 40% is 0.40.
  4. 0.40 x 75 = 30.
  5. Check the result by substituting or estimating: the response should match 30 and make sense in the original problem.

Answer: 30

4. A runner travels 24 miles in 3 hours. What is the unit rate?

Show solution
  1. Course Review: First identify exactly what the question is asking: A runner travels 24 miles in 3 hours. What is the unit rate?
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Divide miles by hours.
  4. 24/3 = 8.
  5. Check the result by substituting or estimating: the response should match 8 and make sense in the original problem.

Answer: 8

5. Evaluate 5 + 2(9 - 4).

Show solution
  1. Course Review: First identify exactly what the question is asking: Evaluate 5 + 2(9 - 4).
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Parentheses first: 9 - 4 = 5.
  4. 2 x 5 = 10.
  5. 5 + 10 = 15.
  6. Check the result by substituting or estimating: the response should match 15 and make sense in the original problem.

Answer: 15

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