2026 IBEW/NJATC/JATC Exam Aligned · No Calculator · 83 Seconds Per Question · Professional Plan
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.
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.
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.
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.
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.
Most common trap: stopping one step early and selecting the intermediate value. The exam places the partially-solved answer as a distractor.
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.
CHECK THE DIFFERENCES FIRST. If differences are constant: arithmetic. If differences are multiplying: geometric. If irregular: look for two interleaved sequences.
Most common trap: assuming arithmetic when the series is geometric. In 2,4,8,16 the differences are 2,4,8 (growing) not constant.
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.
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%.
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.
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.
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.
Most common trap: reversing numerator and denominator — using (x2-x1)/(y2-y1) instead of (y2-y1)/(x2-x1). Rise is always on top.
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.
Cross-multiply = multiply DIAGONALS of the proportion. If a/b=c/d, then ad=bc. Units must match positions.
Most common trap: setting up the proportion with inconsistent unit alignment. Also: inverse proportion problems where candidates apply direct proportion.
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.
MULTIPLY bases = ADD exponents. DIVIDE bases = SUBTRACT exponents. POWER of a power = MULTIPLY exponents. Perfect squares: 12x12=144, 13x13=169, 14x14=196, 15x15=225.
Most common trap: multiplying exponents when you should add them. x^3 x x^4 = x^7 (ADD), NOT x^12 (MULTIPLY).
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.
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.
Most common trap: getting signs wrong on factors. Verify BOTH conditions: numbers must MULTIPLY to c AND ADD to b.
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.
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.
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.
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.
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.
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.
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