IBEW MATH · 10 Active Recall Flashcards

Math & Algebra — Active Recall Cards

2026 IBEW/NJATC/JATC Exam Aligned · No Calculator · 83 Seconds Per Question · Professional Plan

IBEW-MATH-01 · Order of Operations (PEMDAS)
MediumWeight: 12–15%
CONCEPT — FRONT OF CARD

PEMDAS — The Sequence Every Calculation Depends On

Apply operations in this exact order: Parentheses · Exponents · Multiplication & Division (left to right) · Addition & Subtraction (left to right). Violating this order produces a wrong answer even if individual calculations are correct. The exam builds its hardest traps around candidates who add before multiplying.

R3 MEMORY TIP

Please Excuse My Dear Aunt Sally. M/D and A/S are evaluated LEFT TO RIGHT — whichever comes first in the expression. This is where most points are lost.

DISTRACTOR NOTE

Most common trap: adding before multiplying because addition appears first in the expression. 3 + 4 x 2 = 11 NOT 14. The exam places 14 as a distractor answer.

SAMPLE QUESTIONS — BACK OF CARD (5 QUESTIONS WITH FULL ANSWERS)
Q1 OF 5
Evaluate: 4 + 3 x 5 - 2
Q2 OF 5
Simplify: 2 x (3 + 4)^2 / 7
Q3 OF 5
What is 18 / 3 x 2 + 1?
Q4 OF 5
Evaluate: 5 x 3 - (8-2)^2 + 10
Q5 OF 5
Simplify: 2 + 3 x 4 - 1
IBEW-MATH-02 · Linear Equations
MediumWeight: 20–24%
CONCEPT — FRONT OF CARD

Solving Linear Equations — Isolate x on One Side

A linear equation has one unknown variable raised to the first power. Goal: isolate the variable by performing identical operations to both sides. Work backwards: undo addition/subtraction first, then multiplication/division. For equations with fractions: multiply both sides by the LCD to clear fractions before solving.

R3 MEMORY TIP

Whatever you do to ONE side, do to the OTHER. Work backwards from the variable: undo addition/subtraction first, then multiplication/division. Fractions? Multiply by LCD first.

DISTRACTOR NOTE

Most common trap: stopping one step early and selecting the intermediate value. The exam places the partially-solved answer as a distractor.

SAMPLE QUESTIONS — BACK OF CARD (5 QUESTIONS WITH FULL ANSWERS)
Q1 OF 5
Solve: 3x + 7 = 22
Q2 OF 5
Solve: 5x - 3 = 2x + 9
Q3 OF 5
Solve: x/6 = x/2 - 4/3
Q4 OF 5
Solve: 5(x - 3) = 20
Q5 OF 5
Solve: 4x + 3 = 2x + 11
IBEW-MATH-03 · Number Series & Patterns
Medium-HardWeight: 15–21%
CONCEPT — FRONT OF CARD

Number Series — Identify the Pattern Before Answering

Four main IBEW series types: (1) Arithmetic — constant difference. (2) Geometric — constant ratio. (3) Alternating — two interleaved sequences. (4) Growing differences — differences themselves follow a pattern. Always write out the differences between consecutive terms on scratch paper.

R3 MEMORY TIP

CHECK THE DIFFERENCES FIRST. If differences are constant: arithmetic. If differences are multiplying: geometric. If irregular: look for two interleaved sequences.

DISTRACTOR NOTE

Most common trap: assuming arithmetic when the series is geometric. In 2,4,8,16 the differences are 2,4,8 (growing) not constant.

SAMPLE QUESTIONS — BACK OF CARD (5 QUESTIONS WITH FULL ANSWERS)
Q1 OF 5
What comes next? 3, 7, 11, 15, __
Q2 OF 5
What comes next? 2, 6, 18, 54, __
Q3 OF 5
What comes next? 1, 4, 2, 5, 3, 6, 4, __
Q4 OF 5
What comes next? 100, 50, 25, 12.5, __
Q5 OF 5
Find the next term: 2, 3, 5, 8, 12, 17, __
IBEW-MATH-04 · Fractions, Decimals & Percentages
Easy-MediumWeight: 12–18%
CONCEPT — FRONT OF CARD

The Conversion Triangle — Fractions, Decimals, and Percents

Fraction to decimal: divide numerator by denominator. Decimal to percent: multiply by 100. Percent to decimal: divide by 100. Adding fractions: find LCD, convert, then add numerators only. Multiplying fractions: numerator x numerator OVER denominator x denominator — no LCD needed.

R3 MEMORY TIP

Percent means PER HUNDRED. Adding fractions: LCD first, always. Multiplying fractions: straight across. Know: 1/4=0.25=25%, 1/2=0.5=50%, 3/4=0.75=75%, 1/3=0.333=33.3%, 1/8=0.125=12.5%.

DISTRACTOR NOTE

Most common trap: adding fractions by adding numerators AND denominators. 1/3+1/4 does NOT equal 2/7. Must find LCD=12, get 4/12+3/12=7/12.

SAMPLE QUESTIONS — BACK OF CARD (5 QUESTIONS WITH FULL ANSWERS)
Q1 OF 5
What is 3/4 + 1/6?
Q2 OF 5
Express 0.375 as a fraction in lowest terms.
Q3 OF 5
What is 15% of 240?
Q4 OF 5
A wire is 3/8 inch thick. Express as a decimal.
Q5 OF 5
What percent of 80 is 20?
IBEW-MATH-05 · Functions & Linear Graphs
Medium-HardWeight: 12–18%
CONCEPT — FRONT OF CARD

y = mx + b — Slope, Intercept, and the Line Equation

Linear function: y = mx + b. m = slope (rise over run). b = y-intercept. Slope from two points: m = (y2-y1)/(x2-x1). Positive slope rises left to right. Negative slope falls left to right. Zero slope = horizontal. Undefined = vertical. To write equation: find m from two points, then substitute one point to solve for b.

R3 MEMORY TIP

SLOPE = Rise over Run = (y2-y1)/(x2-x1). Always: Y change on TOP, X change on bottom. To find b: plug slope and one known point into y=mx+b and solve.

DISTRACTOR NOTE

Most common trap: reversing numerator and denominator — using (x2-x1)/(y2-y1) instead of (y2-y1)/(x2-x1). Rise is always on top.

SAMPLE QUESTIONS — BACK OF CARD (5 QUESTIONS WITH FULL ANSWERS)
Q1 OF 5
What is the slope through (2,5) and (6,13)?
Q2 OF 5
If f(x)=3x-4, what is f(7)?
Q3 OF 5
What is the y-intercept of y=-2x+5?
Q4 OF 5
Which has negative slope? A.y=2x+1 B.y=-3x+4 C.y=x-2 D.y=4
Q5 OF 5
Write equation of a line with slope 3 through (1,7).
IBEW-MATH-06 · Ratios & Proportions
Easy-MediumWeight: 9–12%
CONCEPT — FRONT OF CARD

Cross-Multiply to Solve — Same Units on Same Side

A proportion states two ratios are equal: a/b=c/d. To solve for an unknown: cross-multiply (ad=bc) then divide. Set up the proportion so the SAME UNITS are in the same position on both sides.

R3 MEMORY TIP

Cross-multiply = multiply DIAGONALS of the proportion. If a/b=c/d, then ad=bc. Units must match positions.

DISTRACTOR NOTE

Most common trap: setting up the proportion with inconsistent unit alignment. Also: inverse proportion problems where candidates apply direct proportion.

SAMPLE QUESTIONS — BACK OF CARD (5 QUESTIONS WITH FULL ANSWERS)
Q1 OF 5
If 5 resistors cost $8, how much do 15 cost?
Q2 OF 5
Map scale: 1 inch=50 miles. Cities 3.5 inches apart. Distance in miles?
Q3 OF 5
Ratio of electricians to apprentices is 2:5. If 14 electricians, how many apprentices?
Q4 OF 5
Machine makes 240 parts in 6 hours. How many in 9 hours?
Q5 OF 5
A 36-foot wire is cut in ratio 4:5. Length of shorter piece?
IBEW-MATH-07 · Powers, Roots & Exponents
MediumWeight: 9–12%
CONCEPT — FRONT OF CARD

Exponent Rules and Square Roots — No Calculator Required

Key rules: x^a x x^b = x^(a+b) (multiply same base: ADD exponents). x^a / x^b = x^(a-b) (divide same base: SUBTRACT). (x^a)^b = x^(ab) (power of a power: MULTIPLY). x^0=1. x^(-n)=1/x^n. Perfect squares to memorize: 1,4,9,16,25,36,49,64,81,100,121,144,169,196,225.

R3 MEMORY TIP

MULTIPLY bases = ADD exponents. DIVIDE bases = SUBTRACT exponents. POWER of a power = MULTIPLY exponents. Perfect squares: 12x12=144, 13x13=169, 14x14=196, 15x15=225.

DISTRACTOR NOTE

Most common trap: multiplying exponents when you should add them. x^3 x x^4 = x^7 (ADD), NOT x^12 (MULTIPLY).

SAMPLE QUESTIONS — BACK OF CARD (5 QUESTIONS WITH FULL ANSWERS)
Q1 OF 5
Simplify: x^3 x x^5
Q2 OF 5
Evaluate: 3^4
Q3 OF 5
Simplify: sqrt(144)
Q4 OF 5
Simplify: (x^2)^4
Q5 OF 5
What is 5^0?
IBEW-MATH-08 · Quadratic Expressions & Factoring
HardWeight: 6–9%
CONCEPT — FRONT OF CARD

Factoring Quadratics — Find Two Numbers That Multiply AND Add

To factor x^2+bx+c into (x+p)(x+q): find p and q such that p x q = c AND p + q = b. Difference of squares: x^2-a^2=(x+a)(x-a). FOIL for expanding: First, Outer, Inner, Last.

R3 MEMORY TIP

FOIL to expand. 'Find two numbers' to factor. Difference of squares pattern: x^2-25=(x+5)(x-5). Always verify by FOIL-ing your answer back out.

DISTRACTOR NOTE

Most common trap: getting signs wrong on factors. Verify BOTH conditions: numbers must MULTIPLY to c AND ADD to b.

SAMPLE QUESTIONS — BACK OF CARD (5 QUESTIONS WITH FULL ANSWERS)
Q1 OF 5
Factor: x^2+7x+12
Q2 OF 5
Expand: (x+5)(x-5)
Q3 OF 5
Factor: x^2-9
Q4 OF 5
Expand using FOIL: (2x+3)(x-4)
Q5 OF 5
Solve: x^2-5x+6=0
IBEW-MATH-09 · Systems of Equations
HardWeight: 6–9%
CONCEPT — FRONT OF CARD

Two Equations, Two Unknowns — Elimination or Substitution

Method 1 — Elimination: Multiply equations to make coefficients match, then add or subtract to eliminate one variable. Method 2 — Substitution: Solve one equation for one variable, substitute into the other. Always find BOTH variables and verify in BOTH original equations.

R3 MEMORY TIP

ELIMINATION = line up and cancel. Add when signs are opposite. Subtract when signs are same. After finding one variable, ALWAYS substitute back to find the second.

DISTRACTOR NOTE

Most common trap: solving for one variable and forgetting to find the second. The exam asks for BOTH values and places single-variable answers as distractors.

SAMPLE QUESTIONS — BACK OF CARD (5 QUESTIONS WITH FULL ANSWERS)
Q1 OF 5
Solve: x+y=10 and x-y=4
Q2 OF 5
Solve: 2x+y=11 and x-y=1
Q3 OF 5
Solve by substitution: y=2x and x+y=12
Q4 OF 5
Solve: 3x+2y=16 and x+2y=8
Q5 OF 5
If 2x+3y=18 and x=3, what is y?
IBEW-MATH-10 · Geometry & Measurement
MediumWeight: 3–6%
CONCEPT — FRONT OF CARD

Area, Perimeter & the Pythagorean Theorem — Electricians Use These Daily

Rectangle: Area=L x W. Perimeter=2(L+W). Triangle area=(base x height)/2. Circle area=pi x r^2 (use pi=3.14). Circle circumference=2 x pi x r. Pythagorean theorem: a^2+b^2=c^2. Common triples: 3-4-5, 5-12-13, 6-8-10, 8-15-17.

R3 MEMORY TIP

Area = INSIDE (multiply dimensions, square units). Perimeter = AROUND (add all sides, linear units). c is ALWAYS the hypotenuse. Memorize 3-4-5 and its multiples: 6-8-10, 9-12-15.

DISTRACTOR NOTE

Most common trap: using area formula when perimeter is asked, or vice versa. Also: giving c^2 as the answer instead of c when using the Pythagorean theorem.

SAMPLE QUESTIONS — BACK OF CARD (5 QUESTIONS WITH FULL ANSWERS)
Q1 OF 5
A panel is 24 inches wide and 36 inches tall. What is its area?
Q2 OF 5
Conduit runs around perimeter of 15ft x 12ft room. Feet of conduit needed?
Q3 OF 5
Wire runs 6ft along wall then 8ft up to ceiling, connected diagonally. Length of diagonal wire?
Q4 OF 5
Triangle with base 10 inches and height 6 inches. What is the area?
Q5 OF 5
Circular junction box radius 4 inches. Area? (pi=3.14)

Ready to test yourself under timed conditions?

Start 60-Question Practice →