69 questions (33 math + 36 reading) · ~97 minutes · NO calculator · scored 1–9 · 4 clears the bar at most locals
Order of Operations
PEMDAS — Parentheses, Exponents, Multiply/Divide (left to right), Add/Subtract (left to right)
- Multiply and divide are the same step — do them left to right, in the order they appear. Same for add/subtract.
- Work the innermost parentheses first if there are several layers.
- An exponent applies only to what's directly under it — not to a whole sum unless it's in parentheses.
6 + 4 × (9 − 3)² ÷ 2
= 6 + 4 × 6² ÷ 2 = 6 + 4 × 36 ÷ 2 = 6 + 144 ÷ 2 = 6 + 72 = 78
Trap — doing addition or subtraction before finishing all the multiply/divide steps, just because it appears first when reading left to right.
Fractions
- Add/subtract: common denominator first, then add or subtract the numerators only.
- Multiply: straight across — top × top, bottom × bottom. No common denominator needed.
- Divide: flip the second fraction and multiply.
- Always reduce. Unreduced answers are planted distractors.
- Decimal → sixteenths: multiply by 16. .4375 × 16 = 7 → 7/16. (Eighths/sixteenths conversions come up constantly in the trade — conduit bends, box fill, wire sizing.)
- Fraction → decimal: it's division. Top ÷ bottom, by hand.
1/16=.0625 1/8=.125 3/16=.1875 1/4=.25
5/16=.3125 3/8=.375 7/16=.4375 1/2=.5
9/16=.5625 5/8=.625 11/16=.6875 3/4=.75
13/16=.8125 7/8=.875 15/16=.9375
Ratios & Proportions
- "1 to 4" means 5 total parts, not 4 — the most common miss on the whole math section.
- Proportions: a/b = c/d → cross-multiply → a×d = b×c.
- Scale & wire-run problems are proportions in disguise: "a conduit drops 3 inches every 8 feet — how much over 20 feet?" → 3/8 = x/20 → x = 7.5 inches.
- Rate problems: reduce to one worker, one hour first, then scale up. Don't jump crew size to crew size.
- Percent: move the decimal two places left, then multiply. 25% of 160 → .25 × 160 = 40.
Exponents
xᵃ × xᵇ = x⁽ᵃ⁺ᵇ⁾ xᵃ ÷ xᵇ = x⁽ᵃ⁻ᵇ⁾ (xᵃ)ᵇ = x⁽ᵃˣᵇ⁾
- Same base, multiply: add the exponents.
- Same base, divide: subtract the exponents.
- Power of a power: multiply the exponents.
- Anything to the 0 power is 1. (Except 0⁰, which the test won't ask about.)
- Negative exponent flips it to the bottom of a fraction: x⁻ᵃ = 1/xᵃ.
(2³)² × 2¹ = 2⁶ × 2¹ = 64 × 2 = 128
Solving Linear Equations
- Distribute and clear parentheses first.
- Combine like terms on each side.
- Move variable terms to one side, plain numbers to the other — whatever you do to one side, do to the other.
- Divide both sides by the coefficient of x last.
- Always check by plugging your answer back into the original equation.
4x + 7 = 31 → 4x = 24 → x = 6
3(x − 2) = 21 → 3x − 6 = 21 → 3x = 27 → x = 9
Evaluating Functions
- f(x) is a machine: plug the number in for x, follow the rule, get one output.
- Do exponents before multiplication, same as always — order of operations still applies inside a function.
- Reading a function from a table works the same way: find the input row, read the output column.
f(x) = 2x² − 3. Find f(4).
2(4)² − 3 = 2(16) − 3 = 32 − 3 = 29
Word Problems
- The whole trick is translating sentences into an equation. Circle the numbers, underline what's being asked, then solve.
- Most errors here are setup errors, not arithmetic errors — write down what's given before touching numbers.
Ohm's Law shape: V = I × R.
120 volts across 15 ohms — find the current.
120 = I × 15 → I = 120 ÷ 15 = 8 amps
Base fee + rate: a job bills $500 base + $45/hour. Total bill was $860 — how many hours?
500 + 45h = 860 → 45h = 360 → h = 8 hours
Reading Comprehension
- About 36 questions in 51 minutes — roughly 85 seconds each. Pace is part of the test.
- Read the questions before the passage so you know what you're hunting for.
- Main idea: the answer covers the whole passage. Wrong answers are true details that only cover one paragraph or one sentence.
- Detail: the answer is stated in the passage. Go find the line — don't answer from outside knowledge, even if it's true in real life.
- Inference: what the passage implies but never says outright. Stay close to the text — don't reason two steps beyond what's there.
- Vocabulary in context: answer from how the word is used in that sentence, not its dictionary definition.
- Answer choices with "always," "never," or "all" are usually wrong.
- Eliminate the clearly-wrong choices before picking — two-option guesses beat four-option guesses.