Rebuild the basics
Fractions, decimals, percentages, signed numbers, order of operations, and one-step equations.
APPRENTICESHIP ENTRANCE PREP
FREE STUDY GUIDE
Get ready for the
union aptitude test.
Build speed and confidence in algebra, functions, number patterns, and reading comprehension—the skills commonly tested when applying for an electrical apprenticeship.
FOUR-WEEK PLAN
Train the exact skills you need
Study five days each week. Spend about 30–45 minutes on math and 20 minutes on reading. Keep a notebook of every question you miss.
Algebra & formulas
Multi-step equations, substitution, ratios, proportions, exponents, and rearranging formulas.
Functions & reading
Tables, patterns, function rules, graphs, main ideas, details, vocabulary, and inference.
Timed mixed practice
Work without distractions, skip difficult questions temporarily, then review every mistake.
Algebra & functions
Focus on accuracy first. Speed follows repetition.
Number skills
- Positive and negative numbers
- Fractions, decimals, and percentages
- Ratios and proportions
- Order of operations
Equations
- Combine like terms
- Use the distributive property
- Isolate the variable
- Check by substitution
Functions
- Evaluate a function rule
- Read input-output tables
- Identify number patterns
- Compare linear relationships
Powers & formulas
- Exponent rules
- Square roots
- Scientific notation
- Rearrange a formula for one variable
The equation method
- Simplify each side.
- Move variable terms to one side.
- Move constants to the other side.
- Divide by the variable’s coefficient.
- Substitute your answer into the original equation.
Reading comprehension
The correct answer must be supported by the passage—not by outside knowledge.
Main idea
Ask what the entire passage is mostly trying to explain, prove, or describe.
Supporting detail
Return to the exact sentence or paragraph connected to the question.
Inference
Choose what logically follows from the text without adding assumptions.
Words in context
Replace the word with each choice and decide which meaning fits the sentence.
The reading method
- Read the question carefully.
- Identify the key idea or detail it asks about.
- Return to the relevant lines.
- Eliminate choices that add, exaggerate, or contradict information.
- Select the answer best supported by the passage.
ORIGINAL PRACTICE SET
Practice before you check
Solve each problem on paper, then open it to see the answer and method. These are original study questions—not questions copied from an actual entrance exam.
1. Solve: 5x + 7 = 32
Answer: x = 5. Subtract 7 from both sides: 5x = 25. Divide by 5.
2. Solve: 3(x − 4) = 21
Answer: x = 11. Divide by 3 to get x − 4 = 7, then add 4.
3. Solve: −6x + 3 = 22 − 9x
Answer: x = 19⁄3. Add 9x to both sides: 3x + 3 = 22. Subtract 3, then divide by 3.
4. If f(x) = 4x − 3, what is f(6)?
Answer: 21. Substitute 6 for x: 4(6) − 3 = 24 − 3.
5. Complete the pattern: 4, 9, 14, 19, ___
Answer: 24. Each term increases by 5.
6. What is 3⁄4 of 64?
Answer: 48. Divide 64 by 4, then multiply by 3.
7. A crew installs 18 fixtures in 3 hours at a steady rate. How many in 7 hours?
Answer: 42 fixtures. The rate is 6 fixtures per hour; 6 × 7 = 42.
8. Rearrange V = IR to solve for R.
Answer: R = V⁄I. Divide both sides by I.
9. Which value is greatest: 0.62, 5⁄8, 61%, or 0.6?
Answer: 5⁄8. Convert to decimals: 0.625, 0.62, 0.61, and 0.60.
10. Solve: 2x + 5 > 17
Answer: x > 6. Subtract 5, then divide by 2.
READING PASSAGE
Before beginning a conduit run, an installer studies the drawings and walks the planned route. This preparation reveals obstructions, changes in elevation, and other trades occupying the same space. A few minutes spent planning can reduce unnecessary bends, wasted material, and installation time. Planning does not eliminate every field change, but it gives the installer a clearer starting point.
11. What is the passage’s main idea?
Answer: Planning a conduit route before installation can prevent problems and improve efficiency.
12. Which benefit is directly stated?
Answer: Planning can reduce unnecessary bends, wasted material, and installation time.
13. What can reasonably be inferred?
Answer: Drawings alone may not reveal every condition found in the field.
14. In the passage, “obstructions” most nearly means what?
Answer: Objects or conditions that block the planned route.
15. Which statement would the author most likely agree with?
Answer: Preparation improves the starting plan even when later changes may still be necessary.
TEST-DAY STRATEGY
Keep moving
- Read every sign and operation carefully.
- Estimate first so unreasonable answers stand out.
- Skip a time-consuming question and return later.
- Use the passage—not personal opinion—for reading answers.
- Leave time to revisit flagged questions.
AFTER THE TEST
Prepare for the interview
If your local includes an interview, be ready to explain why you want the trade, how you handle difficult work, what reliability means to you, and examples of teamwork, safety, persistence, and learning from mistakes.
Practice out loud
- Why do you want to become a union electrician?
- Tell us about a time you completed a difficult task.
- How have you handled conflict on a team?
- What does being dependable look like?
- How will you manage work, class, and studying?