Mathematics Practice Problem Worksheet
How to Use This Worksheet Effectively
This worksheet provides a powerful mix of practice problems across several core math areas. Use it to prepare for tests, standardized exams, or math competitions. To maximize your learning, don't just solve the problems—train with them.
- Print or write neatly: Treat this like a real test. Work on paper, show all steps, and circle your final answer.
- Time yourself: Set a timer (e.g., 25–30 minutes per section) to improve focus and speed.
- Check your work: Review your solutions after each section, marking problems as correct and confident, correct but unsure, or incorrect.
- Use ScholarComp: Rebuild weak skills with targeted practice sets and solutions to create more problems based on your errors.
- Repeat weekly: Return to similar types of problems and observe your improvement in speed and accuracy.
Section A: Arithmetic and Number Sense
Warm up your brain here, focusing on accuracy and mental math.
- Integer Operations Compute each of the following. Show your work. Evaluate: 37 − 85 Evaluate: −24 + 57 Evaluate: (−18) − (−35) Evaluate: 6 × (−9) Evaluate: (−96) ÷ 12
- Fractions and Decimals Simplify all fractions. Add: 3/4 + 5/6 Subtract: 7/8 − 1/3 Multiply: 5/9 × 27/10 Divide: 11/12 ÷ 2/3 Convert: 0.375 to a fraction in simplest form. Convert: 7/20 to a decimal.
- Percent Problems Translate each situation into a mathematical expression. What is 18% of 250? 45 is 60% of what number? A video game originally costs $80 and is on sale for 25% off. What is the sale price? A student scored 72 out of 90. What percent is this?
Section B: Algebra Foundations
Sharpen your equation-solving and expression skills here.
- Evaluating Expressions Let x = −2 and y = 5. Evaluate the following: 3x + 4yx² − 2y2xy − 5x(x − y)²
- Solving One-Step and Two-Step Equations Solve for the unknown variable. Show each step. x + 7 = 194y − 5 = 233a = −27b/5 + 6 = 28 − 2k = −4
- Multi-Step Linear Equations Solve each equation after simplifying both sides. 5x − 3 = 2x + 124(2y − 1) = 3(y + 5)7 − 2(3a − 4) = 153(2k + 5) − 4k = 18
- Intro to Inequalities Solve each inequality and graph the solution on a number line. x − 4 > 93y + 2 ≤ 17−2k > 105 − a ≥ 1
Section C: Ratios, Proportions, and Word Problems
These questions connect math to real-life situations.
- Ratios and Rates If a recipe uses a sugar-to-flour ratio of 2:5 and you use 15 cups of flour, how many cups of sugar do you need? The ratio of boys to girls in a math club is 3:4. If there are 21 boys, how many girls? A car travels 180 miles in 3 hours. What is its speed? A printer can print 120 pages in 8 minutes. How many pages in 20 minutes?
- Proportions Solve each proportion and show cross multiplication. 3/x = 12/207/9 = y/275/8 = 15/za/6 = 4/9
- Word Problems with Equations Translate each story into an equation then solve. Maria has 8 more than twice as many stickers as John. Together they have 50 stickers. How many does each have? A movie theater sells adult tickets for $9 and children for $6. How many adult tickets were bought if $117 was spent on 15 tickets? A number decreased by 12 equals half of the original number. What is it? Three consecutive integers have a sum of 117. What are they?
Section D: Geometry Basics
Work with perimeter, area, volume, and angles here.
- Perimeter and Area A rectangle has a length of 12 cm and a width of 7 cm. Find its perimeter and area. A square has an area of 81 cm². What is the length of each side and its perimeter? A right triangle has legs of 5 cm and 12 cm. What is its area? A parallelogram has a base of 10 cm and a height of 6 cm. Find its area.
- Circles Use π ≈ 3.14 unless instructed otherwise. A circle has a radius of 4 cm. Find its circumference and area. A circular garden has a diameter of 10 m. What is its circumference? The area of a circle is 50.24 cm². Find the radius using π = 3.14.
- Volume A rectangular prism has a length of 6 cm, a width of 4 cm, and height of 3 cm. Find its volume. A cube has a volume of 125 cm³. What is the length of each side? A cylinder has a radius of 3 cm and a height of 10 cm. Find its volume using π = 3.14.
- Angles and Triangles Two angles are complementary. One measures 37°. What is the measure of the other? Two angles are supplementary. One measures 128°. What is the other angle? The three angles of a triangle measure 2x, 3x, and 5x. Find x and each angle's measure. In a right triangle, one acute angle is 35°. What is the measure of the other acute angle?
Section E: Problem-Solving and Challenge Questions
These problems resemble math competition questions. Work slowly and think strategically.
- Multi-Step Arithmetic and Logic A number is increased by 25% and then decreased by 20%. The final result is 60. What was the original number? If 4 pens and 3 notebooks cost $23, and 2 pens and 5 notebooks cost $27, find the cost of one pen and one notebook. The sum of three consecutive even integers is 96. What are the integers? A farmer has chickens and cows. There are 35 heads and 98 legs. How many of each?
- Geometry and Ratios The sides of a triangle are in the ratio 3:4:5 and its perimeter is 96 cm. Find the length of each side. A rectangle has the same perimeter as a square. The rectangle is 10 cm by 18 cm. What is the area of the square? A map uses a scale of 1 cm : 50 km. Two cities are 7.6 cm apart on the map. How far apart are they in kilometers? A right triangle has a hypotenuse of 13 and one leg of 5. Find the length of the other leg.
- Algebraic Thinking Twice a number plus 9 equals 5 less than three times the number. What is it? When a number is divided by 7, the quotient is 8 and the remainder is 5. What is the number? Five years ago, Alex was four times as old as Sam. In five years, Alex will be twice as old as Sam. How old are they now? A vending machine sells snacks for $1.50 each. It has only dollar coins, quarters, and dimes, totaling $24. If there are 40 coins in total and 10 are dimes, how many dollars and quarters are there?
Self-Check: Reflection and Next Steps
Finished the worksheet? Great! Here’s how to turn practice into growth.
- Sort your questions: Circle the ones you solved confidently and correctly. Checkmark ones you got right but felt unsure about. Star the ones you missed or didn't know how to start.
- Identify patterns: Are your starred problems mostly in geometry, fractions, or word problems? That's your current “training zone.”
- Redo, don’t just review: For each missed problem, try again from scratch. Can you solve it cleanly now?
- Create your own similar problem: Change the numbers for at least three challenging questions and write a new version. Solve your new version to reinforce understanding.
Using ScholarComp and Other Tools for Extra Practice
For a steady stream of practice problems that match your needs, online tools can help.
- With ScholarComp: Convert this worksheet into a digital practice set by typing in the problem types you found hardest. Generate similar problems and practice them in timed sets. Review step-by-step solutions to understand each step.
- With other platforms: Use free resources like Khan Academy to reinforce specific skills such as fractions, algebra, or geometry with videos and practice questions.
- Build a practice routine:3 days per week: 20–30 minutes of mixed problems like this worksheet. 1 day per week: Focus on your weakest topic. Every few weeks: Return to parts of this worksheet and compare your scores and speed.
Tips for Parents and Coaches
If you’re helping a student through this worksheet, you don't need to be a math expert to be valuable.
- Focus on effort and process: Ask questions like “How did you start this?” or “Can you explain your steps?”
- Use small goals: Suggest that your student complete five problems from each section rather than the entire worksheet at once.
- Encourage corrections: Praise students for fixing mistakes. Correcting errors is powerful practice.
- Track progress: Keep a simple chart of: Number of problems attempted Number correct on the first try Topics that are improving
- Leverage ScholarComp: Generate custom follow-up worksheets for specific topics where your student struggles.
Wrapping Up
This worksheet provides a robust mix of arithmetic, algebra, geometry, ratios, and challenge problems—the same skills that appear in school tests and math competitions. The real power comes from how you use it. Will you time yourself, track mistakes, and revisit it next week?
Treat this not as a one-time task but as part of a training plan. With consistent practice, reflection, and tools like ScholarComp, your math skills can develop rapidly. Ready to tackle your next questions?
