Most trade apprenticeship tests cover basic maths: fractions, decimals, percentages, ratios, unit conversions, area, volume and simple algebra, with occasional geometry such as the Pythagorean theorem. The level is typically middle-school to early high-school, and the format varies by programme, so confirm what yours tests. Local examples in our guides show the range: Ironworkers Local 721 describes Grade 10 equivalency, Local 467 (UA) lists whole numbers, fractions, decimals, integers, rational numbers, exponents and algebra essentials, and some locals use no written test at all.
1. Fractions
Add or subtract with a common denominator, multiply tops and bottoms, and divide by flipping the second fraction. Example: 3/4 + 2/3 = 9/12 + 8/12 = 17/12 = 1 5/12. Practise with OpenStax fractions.
2. Decimals and Converting to Fractions
Use place value and simplify. Example: 0.375 = 375/1000 = 3/8, so a 3/8-inch bit is 0.375 inch. See decimals.
3. Percentages
Convert to a decimal and multiply. Example: 15% of 240 = 0.15 × 240 = 36. Waste allowances and material overage use this. See percents.
4. Ratios and Proportions
Add the parts, divide the total by that number, then multiply for each part. Example: a 1:2:3 mix totalling 60 cubic feet has 6 parts of 10, so 10, 20 and 30.
5. Unit Conversions
| From | To | Rule |
|---|---|---|
| Feet | Inches | × 12 |
| Yards | Feet | × 3 |
| Cubic feet | Cubic yards | ÷ 27 |
| Square feet | Square yards | ÷ 9 |
Example: 2.5 feet × 12 = 30 inches.
6. Reading a Tape Measure
Most US tapes mark inches down to 1/16. Count the small marks past the last whole inch and simplify: 6 marks is 6/16, or 3/8.
7. Perimeter, Area and Volume
- Rectangle area: length × width. Triangle area: ½ × base × height.
- Circle area: π × radius² (use 3.14 unless told otherwise). Circumference: 2 × π × radius.
- Box volume: length × width × height.
Examples: a 12 ft by 15 ft room has 180 square feet. A slab 10 ft by 4 ft by 0.5 ft is 20 cubic feet, and 20 ÷ 27 is about 0.74 cubic yards. A pad with a 3 ft radius has an area of about 3.14 × 9 = 28.3 square feet. See geometry.
8. The Pythagorean Theorem
For a right triangle, a² + b² = c². Example: legs of 6 ft and 8 ft give 36 + 64 = 100, so 10 ft. A 3-4-5 triangle follows the same pattern.
9. Order of Operations
Brackets, exponents, multiplication and division left to right, then addition and subtraction left to right. Example: 8 + 4 × 3 = 8 + 12 = 20, not 36.
10. Simple Algebra
Do the same operation to both sides. Example: 3x + 5 = 20, so 3x = 15 and x = 5.
11. Rates and Word Problems
Identify what is asked, pull out the numbers and choose the formula. Example: 120 feet of pipe in 4 hours is 30 feet per hour, so 150 feet takes 5 hours.
All examples are original practice problems, not real exam questions.
How to Study Fast
- Find out what is tested and ask for a test outline or sample.
- Master fractions and unit conversions first, since they appear everywhere.
- Memorise the key formulas, and ask whether a formula sheet is provided.
- Practise word problems for 15 to 20 minutes a day.
- Show your steps and check the units.
- Take timed practice once you know the real time limit.
- Review mistakes and keep a list of the question types you miss.
Official programme information is on Apprenticeship.gov. Never pay anyone for a guaranteed apprenticeship spot, and verify all fees with the programme. See also mechanical reasoning and retake rules.
Frequently Asked Questions
Can I use a calculator on the apprenticeship test?
It depends on the programme. Ask in advance and practise without one in case.
What level of math is it?
Usually middle-school to early high-school math. Local 721, for example, describes Grade 10 equivalency.
What if I am bad at math?
Most people improve with regular practice on fractions, conversions and word problems.
Do I need to memorise formulas?
Often yes. Ask whether your programme provides a formula sheet.
How long should I study?
Plan a few weeks of consistent practice, starting with your weakest topics.
Is there a test at every programme?
No. Some programmes list no aptitude test, so check first.
Which topics matter most?
Fractions, percentages, unit conversions, area, volume and basic algebra.
Where can I practise?
Use OpenStax Prealgebra and your programme's own samples.
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More Job Guides
Related guides:
- Mechanical Reasoning Questions Explained — levers, gears, hydraulics
- Can You Retake the Apprenticeship Aptitude Test? — retake rules
- Ironworker Aptitude Test: Format, Math and Practice — ironwork entry
- Sheet Metal Aptitude Test: Sections, Tips, Study Plan — sheet metal entry
This article is a general guide and not legal, financial or immigration advice. Reviewed on 16 October 2026 against official sources. Rules, fees and requirements change, so follow the official instructions for your own case.
