Electrical Aptitude Mastery & Math Refresher
Daily Goal: 8/8 Cards โข Rotation: Algebra & Functions
Rebuild the muscle memory at your own pace. Change the numbers and watch every step play out, no calculator and no judgment.
Select an expression or enter your own to see every operation evaluated strictly by precedence rules.
Adjust Slope (m) and Y-Intercept (b) to visually inspect how the line shifts and where intercepts land.
The IBEW test frequently features sequences whose step sizes grow linearly. Input any sequence to find the rule and next 2 terms.
๐ก Memory trick: when the gaps between numbers aren't the same, find the gaps between the gaps. Once THOSE are steady, you've found the pattern.
Find two numbers p and q such that p + q = B and p ร q = C.
Move the sliders and watch direction, speed and force change. The same three rules cover most mechanical reasoning questions.
The PEMDAS solver is free to try. Unlock every step-through tool, every flashcard, and the full Concept Guide in all four trade modules for $12 (12 months).
Get Full Access ($12) Already paid? Redeem your code โA rusty-brain-friendly cheat sheet: the rules, plus a memory trick for each one, so you don't need to have used this math recently for it to click.
Section 1: Algebra & Functions: 33 Questions in 46 Minutes (~83 seconds/question). NO calculators allowed.
Section 2: Reading Comprehension: 36 Questions in 51 Minutes (~85 seconds/question).
Scoring: Stanine Scale 1 to 9. A qualifying score of 4 or higher is required for interview qualification. There is no penalty for guessing, so never leave a bubble blank!
๐ก Memory trick: "Please Excuse My Dear Aunt Sally": the first letters spell out the order above. Say it in your head before every problem until it becomes automatic again.
Trap Alert: Multiplication does NOT automatically come before Division! Solve Multiplication and Division in the order they appear from left to right: 12 รท 3 ร 2 = 4 ร 2 = 8 (NOT 12 รท 6 = 2).
Must find the Least Common Denominator (LCD). Example: 1/3 + 2/5 = 5/15 + 6/15 = 11/15.
Keep the first fraction, change รท to ร, flip the second fraction: (3/4) รท (2/3) = (3/4) ร (3/2) = 9/8.
๐ก Memory trick: Say "Keep, Change, Flip" out loud as you write each step. If you can say it, you can't forget which fraction gets flipped.
Slope Formula: m = (yโ - yโ) / (xโ - xโ) (Rise over Run).
Slope-Intercept Form: y = mx + b (where m = slope, b = y-intercept where x=0).
Finding Intercepts:
๐ก Memory trick: "Rise over run": rise (up/down, y) always goes on top, run (left/right, x) always goes on the bottom. Say it in that order every time.
aยฒ - bยฒ = (a - b)(a + b) (e.g., xยฒ - 36 = (x - 6)(x + 6)).
For xยฒ + Bx + C, find two numbers that multiply to C and add to B.
First, Outside, Inside, Last.
๐ก Memory trick: For factoring, it's a guess-and-check puzzle, not a formula. Try a couple of number pairs before worrying you're doing it wrong. For difference of squares, two perfect squares split by a minus sign are always "twins with a sign swap": (a - b)(a + b).
Meshed gears turn in opposite directions. Number them from the driver: odd gears match gear 1, even gears are opposite. Teeth ร rpm is the same for every gear, so a smaller gear spins faster. Size never changes direction.
Farther from the fulcrum means less force. If you push from farther out than the load sits, your answer must be smaller than the load.
Count the rope segments holding up the moving block, then divide the load by that number. A single fixed pulley only changes the direction of pull. The trade-off: you pull that many feet of rope for each foot of lift.
Open belt: same direction. Crossed belt (an X between the pulleys): opposite direction.
Water pressure depends on depth only, not on how wide the tank is (about 0.43 psi per foot of water). Hydraulics: pressure = force รท area, and it is the same everywhere in the fluid, so a piston 10 times bigger pushes 10 times harder.
Same height, longer ramp, less force. The work is the same; it is spread over more distance.
๐ก Memory trick: almost every mechanical question is a trade: less force always costs more distance. If an answer gives you less force AND less distance, it is wrong.
Quick ways to rule a pattern OUT: it has a 2ร2 block of squares, it has 5 or more squares in a row, or, in a row of 4, the two extra squares sit on the same side. A pattern that fails any of these can't fold into a cube. Passing them doesn't prove it works, so picture the last one or two options folding up.
Pick one distinctive part (a corner or a sticking-out square) and track it as you turn the option. A rotation keeps the shape's "handedness." A mirror image is the left-hand twin and never lines up without flipping.
Count column by column, not face by face. Every visible top has cubes underneath it, because nothing floats.
Cutting a square from each corner shortens every side twice (once at each end). The cut size becomes the height.
Straight cut across a round pipe: circle. Slanted cut: oval (ellipse). Straight cut across a square duct: square; slanted: rectangle.
๐ก Memory trick: eliminate before you imagine. Two quick rules usually knock out two or three options, and you only have to picture the last one or two.
Grade (fall): fall = run in feet ร fall per foot. 1/4" per foot is "divide by 4"; 1/8" per foot is "divide by 8". Under the model plumbing code, horizontal drains 2-1/2" and smaller need at least 1/4" per foot, 3" to 6" need at least 1/8" per foot.
45ยฐ offset: travel = offset ร 1.414. Going the other way, offset = travel ร 0.707. Travel is always the longer number.
Tape fractions: convert everything to eighths (or sixteenths), add the tops, carry any extra whole inch.
๐ก Memory trick: "1.414 goes long." If your travel comes out shorter than the offset, you used 0.707.
Circumference (stretch-out): ฯ ร diameter, about 3.14 ร d. A little over three diameters.
Duct surface: perimeter ร length. Convert inches to feet (รท 12) first.
Square inches to square feet: รท 144 (a square foot is 12 ร 12).
Airflow: CFM = area in sq ft ร velocity in feet per minute.
๐ก Memory trick: "go around, then go along" for duct metal, and "144, not 12" for square feet.
Roping: with 2:1 roping the ropes travel twice as far (and twice as fast) as the car, and each rope carries half the load.
Counterweight: typically the car's own weight plus 40 to 50% of its rated load, so the machine only lifts the difference.
Percentages: find 10% by sliding the decimal one place, then build the rest (40% = 4 ร 10%).
Travel time: distance รท speed in feet per minute gives minutes; ร 60 for seconds.
๐ก Memory trick: check the units the answer asks for (seconds vs. minutes, lb vs. psi) before you pick.
1. Read the Questions First: Skim the questions to know what key facts or terms to hunt for in technical paragraphs.
2. Grounded Evidence Only: Never select an answer based on external assumptions. The correct choice must be supported strictly by text inside the passage.
3. Eliminate Extreme Language: Beware of answers containing words like always, never, all, impossible unless specifically confirmed in the text.
๐ก Memory trick: Treat every question like a scavenger hunt, not a memory test. The answer is hiding in the passage in almost the same words as the question. Your job is just to find it, not to already know it.
This test is one step on a much longer road. Once you're a licensed Journeyman Electrician, these are some of the paths people build from there:
๐ก Keep going: Every flashcard you master here is a small deposit toward all of these doors being open to you later. Nobody who's rusty on fractions today stays rusty forever. You're not behind, you're just early.
Boost retention with structured 25-minute study intervals (Pomodoro method).