Pre-Algebra Midterm Exam
A free Pre-Algebra lesson from the “Algebra Readiness” unit, with a worked example and practice problems including step-by-step solutions.
The midterm covers Units 1-4: integers, factors and multiples, fractions, ratios, rates, percents, decimals, scientific notation, roots, the real number system, proportions, unit conversions, order of operations, expressions, equations, and inequalities. Problems are mixed and unlabeled, just like a real exam.
What you'll learn
- Demonstrate mastery of the first half of Pre-Algebra (Units 1-4)
- Apply number sense, decimals, proportional reasoning, and algebra-readiness skills without topic labels
- Build test-taking stamina with a 25-question mixed assessment
Worked example
Problem. A 40 dollar shirt is 30% off. What is the sale price?
- Find 30% of 40: 0.30 x 40 = 12.
- Subtract the discount from the original price.
- 40 - 12 = 28, so the sale price is 28 dollars.
Answer: 28
Practice problems
1. Compute -6 + 10.
Show solution
- Midterm Review: First identify exactly what the question is asking: Compute -6 + 10.
- For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
- The signs are different.
- 10 - 6 = 4, and the positive number is farther from zero.
- Check the result by substituting or estimating: the response should match 4 and make sense in the original problem.
Answer: 4
2. Compute 3/5 + 1/5.
Show solution
- Midterm Review: First identify exactly what the question is asking: Compute 3/5 + 1/5.
- For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
- Same denominator: add the numerators.
- 3 + 1 = 4, so the answer is 4/5.
- Check the result by substituting or estimating: the response should match 4/5 and make sense in the original problem.
Answer: 4/5
3. Find 20% of 50.
Show solution
- Midterm Review: First identify exactly what the question is asking: Find 20% of 50.
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- 20% is 0.20.
- 0.20 x 50 = 10.
- Check the result by substituting or estimating: the response should match 10 and make sense in the original problem.
Answer: 10
4. Evaluate 2 + 3 x 4.
Show solution
- Midterm Review: First identify exactly what the question is asking: Evaluate 2 + 3 x 4.
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- Multiply first: 3 x 4 = 12.
- 2 + 12 = 14.
- Check the result by substituting or estimating: the response should match 14 and make sense in the original problem.
Answer: 14
5. Solve x + 8 = 15.
Show solution
- Midterm Review: First identify exactly what the question is asking: Solve x + 8 = 15.
- Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
- Subtract 8 from both sides.
- 15 - 8 = 7.
- Check the result by substituting or estimating: the response should match 7 and make sense in the original problem.
Answer: 7
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