SWLCAT Aptitude Test Study Guide 2026
How to Pass the Math & Reading Sections — A Complete, Confidence-Building Prep Guide
Written by a 10-Year Journeyman Lineman
Detailed breakdowns · Step-by-step worked examples · Full study plan · Test-day strategies
A Note Before You Start
If you’re reading this, you’re already doing more than most people who walk into this test. The SWLCAT trips up applicants not because it’s impossibly hard — it’s because most people don’t know what to expect or how to prepare. This guide fixes that.
By the time you finish reading, you’ll know exactly what’s on the test, how to solve every type of problem, and how to walk in calm, ready, and confident. Take it one section at a time. Do the practice problems with a pencil in hand. You’ve got this.
What Is the SWLCAT Aptitude Test?
The SWLCAT (Southwest Line Constructors Aptitude Test) is the entry-level aptitude exam required by the IBEW/JATC apprenticeship programs in the Southwest region. It is the same test widely known as the NJATC Aptitude Test.
What it tests:
• Mathematical ability
• Reading comprehension
• Reasoning skills
Test format:
• 2 sections: Math and Reading Comprehension
• Approximately 69–100 questions depending on version
• Time-limited (typically 46–97 minutes total)
• No calculator allowed
• Multiple choice
What score do you need?
A score of 4 out of 9 (roughly the 4th stanine) is the general minimum to move forward, but higher scores improve your ranking on the applicant list. The higher you score, the better your placement chances. Aim for 7 or above.
Important: You cannot use a calculator. Every problem must be solved mentally or by hand. This is why daily no-calculator practice is non-negotiable.
Section 1: Math
This is where most applicants struggle. The math is not advanced — it covers algebra, number patterns, and basic arithmetic — but it requires speed and accuracy without a calculator. Master these five categories and you will be prepared.
Category 1: Number Series
What it is: You are given a sequence of numbers with a hidden pattern. Your job is to find the next number.
How to approach it:
1. Write out the differences between each consecutive pair of numbers.
2. Look for a repeating pattern in those differences.
3. Apply the pattern to find the next number.
Example 1 — Alternating pattern:
Sequence: 110, 112, 107, 109, 104, ?
Step 1 — Find the differences:
• 112 − 110 = +2
• 107 − 112 = −5
• 109 − 107 = +2
• 104 − 109 = −5
Step 2 — Identify the pattern:
The differences alternate: +2, −5, +2, −5…
Step 3 — Apply the pattern:
The last difference was −5, so the next must be +2.
104 + 2 = 106
✅ Answer: 106
Example 2 — Increasing pattern:
Sequence: 3, 6, 10, 15, 21, ?
Step 1 — Find the differences:
• 6 − 3 = +3
• 10 − 6 = +4
• 15 − 10 = +5
• 21 − 15 = +6
Step 2 — Identify the pattern:
The differences increase by 1 each time: +3, +4, +5, +6…
Step 3 — Apply the pattern:
The next difference should be +7.
21 + 7 = 28
✅ Answer: 28
Example 3 — Multiplying pattern:
Sequence: 2, 6, 18, 54, ?
Step 1 — Find the relationship:
• 6 ÷ 2 = 3
• 18 ÷ 6 = 3
• 54 ÷ 18 = 3
Step 2 — Identify the pattern:
Each number is multiplied by 3.
Step 3 — Apply the pattern:
54 × 3 = 162
✅ Answer: 162
Practice Problems — Number Series:
Try these on your own before checking the answers.
1. 5, 10, 8, 16, 14, 28, 26, ?
2. 100, 95, 85, 70, 50, ?
3. 1, 4, 9, 16, 25, ?
Answers:
1. 52 (pattern: ×2, −2, ×2, −2…)
2. 25 (differences: −5, −10, −15, −20, −25)
3. 36 (perfect squares: 1², 2², 3², 4², 5², 6²)
Category 2: Algebra
What it is: You are given a formula with variables and specific values. Plug in the values and solve using order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).
Golden rule: Always work inside parentheses FIRST. Then multiply or divide. Then add or subtract.
Example 1:
If A = B + 3(4 − C) and B = 5, C = 2, what is A?
Step 1 — Substitute the known values:
A = 5 + 3(4 − 2)
Step 2 — Solve inside the parentheses first:
4 − 2 = 2
A = 5 + 3(2)
Step 3 — Multiply:
3 × 2 = 6
A = 5 + 6
Step 4 — Add:
A = 11
✅ Answer: 11
Example 2:
If Y = 2X² − 4 and X = 3, what is Y?
Step 1 — Substitute:
Y = 2(3)² − 4
Step 2 — Exponent first:
3² = 9
Y = 2(9) − 4
Step 3 — Multiply:
2 × 9 = 18
Y = 18 − 4
Step 4 — Subtract:
Y = 14
✅ Answer: 14
Example 3 — Solving for a variable:
Solve for x: 2x + 5 = 17
Step 1 — Subtract 5 from both sides:
2x = 17 − 5
2x = 12
Step 2 — Divide both sides by 2:
x = 12 ÷ 2
x = 6
✅ Answer: 6
Example 4 — Two-step equation:
Solve for x: 3x − 4 = 14
Step 1 — Add 4 to both sides:
3x = 14 + 4
3x = 18
Step 2 — Divide both sides by 3:
x = 18 ÷ 3
x = 6
✅ Answer: 6
Practice Problems — Algebra:
1. If A = 3B − 2C and B = 4, C = 3, what is A?
2. Solve for x: 5x + 3 = 28
3. If P = 2(L + W) and L = 8, W = 5, what is P?
Answers:
1. A = 3(4) − 2(3) = 12 − 6 = 6
2. 5x = 25, x = 5
3. P = 2(8 + 5) = 2(13) = 26
Category 3: Word Problems (Work Rate)
What it is: Two machines, workers, or pumps working together to complete a job. You need to find how long it takes them combined.
The formula:
• Find each person/machine’s rate (how much of the job they complete per hour).
• Rate = 1 job ÷ hours to complete alone
• Add the rates together.
• Divide 1 by the combined rate to get total time.
Example 1:
Pump A fills a tank in 6 hours. Pump B fills it in 4 hours. How long will both pumps working together take to fill the tank?
Step 1 — Find each pump’s rate per hour:
• Pump A: 1/6 of the tank per hour
• Pump B: 1/4 of the tank per hour
Step 2 — Add the rates:
1/6 + 1/4
To add fractions, find a common denominator (12):
• 1/6 = 2/12
• 1/4 = 3/12
• 2/12 + 3/12 = 5/12
Combined rate: 5/12 of the tank per hour
Step 3 — Find the total time:
Time = 1 ÷ (5/12) = 12/5 = 2.4 hours
Step 4 — Convert to hours and minutes (if needed):
0.4 hours × 60 minutes = 24 minutes
= 2 hours and 24 minutes
✅ Answer: 2 hours and 24 minutes
Example 2:
Worker A can complete a job in 8 hours. Worker B can complete the same job in 12 hours. How long will they take working together?
Step 1 — Rates:
• Worker A: 1/8 per hour
• Worker B: 1/12 per hour
Step 2 — Add rates (common denominator is 24):
• 1/8 = 3/24
• 1/12 = 2/24
• 3/24 + 2/24 = 5/24
Step 3 — Total time:
Time = 1 ÷ (5/24) = 24/5 = 4.8 hours
Convert: 0.8 × 60 = 48 minutes = 4 hours 48 minutes
✅ Answer: 4 hours and 48 minutes
Practice Problems — Work Rate:
1. Machine A completes a job in 3 hours. Machine B completes the same job in 6 hours. How long do they take together?
2. Pipe A fills a pool in 5 hours. Pipe B fills the same pool in 10 hours. How long together?
Answers:
1. Rates: 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2. Time = 1 ÷ (1/2) = 2 hours
2. Rates: 1/5 + 1/10 = 2/10 + 1/10 = 3/10. Time = 10/3 = 3 hours 20 minutes
Category 4: Percentages
What it is: Finding a percentage of a number, or finding what percentage one number is of another.
Key formulas:
• X% of a number: multiply the number by (X ÷ 100)
• What % is A of B: divide A by B, then multiply by 100
Example 1:
What is 30% of 240?
Step 1 — Convert the percentage to a decimal:
30% = 30 ÷ 100 = 0.30
Step 2 — Multiply:
0.30 × 240 = 72
✅ Answer: 72
Example 2:
A wire that was 80 feet long is now 92 feet. What is the percentage increase?
Step 1 — Find the difference:
92 − 80 = 12
Step 2 — Divide by the original:
12 ÷ 80 = 0.15
Step 3 — Convert to percent:
0.15 × 100 = 15%
✅ Answer: 15% increase
Practice Problems — Percentages:
1. What is 45% of 200?
2. A crew of 25 people has 5 apprentices. What percentage are apprentices?
3. A part costs $60 and increases by 20%. What is the new price?
Answers:
1. 0.45 × 200 = 90
2. 5 ÷ 25 × 100 = 20%
3. 0.20 × 60 = 12. New price = 60 + 12 = $72
Category 5: Ratios and Proportions
What it is: Comparing two quantities or scaling a relationship.
Key approach: Set up two equal fractions (a proportion) and cross-multiply to solve for the unknown.
Example 1:
A wire uses 3 feet of insulation for every 10 feet of cable. How much insulation is needed for 70 feet of cable?
Step 1 — Set up the proportion:
3/10 = x/70
Step 2 — Cross multiply:
10x = 3 × 70
10x = 210
Step 3 — Solve:
x = 210 ÷ 10 = 21 feet
✅ Answer: 21 feet
Example 2:
A mixture requires a 2:5 ratio of chemical A to chemical B. If you use 8 gallons of chemical A, how much chemical B do you need?
Step 1 — Set up the proportion:
2/5 = 8/x
Step 2 — Cross multiply:
2x = 5 × 8
2x = 40
Step 3 — Solve:
x = 40 ÷ 2 = 20 gallons
✅ Answer: 20 gallons
Category 6: Basic Geometry
What it is: Calculating area and perimeter of basic shapes. You don’t need advanced geometry — just the core formulas.
Formulas to memorize:
Formulas to Memorize — SWLCAT Math
ORDER OF OPERATIONS (PEMDAS)
Parentheses → Exponents → Multiply/Divide → Add/Subtract
ALGEBRA
Solve for x: get x alone by doing the opposite operation on both sides
Example: 2x + 5 = 17 → 2x = 12 → x = 6
WORK RATE
Rate = 1 ÷ hours to complete alone
Add rates together, then divide 1 by the total rate
Example: 1/6 + 1/4 = 5/12 → Time = 12/5 = 2.4 hours
PERCENTAGES
X% of a number = multiply by (X ÷ 100)
Example: 30% of 240 = 0.30 × 240 = 72
Percent change = (difference ÷ original) × 100
RATIOS & PROPORTIONS
Set up two equal fractions, cross multiply, solve for the unknown
Example: 3/10 = x/70 → 10x = 210 → x = 21
GEOMETRY — AREA
Rectangle: Length × Width
Triangle: 1/2 × Base × Height
Circle: 3.14 × radius × radius
GEOMETRY — PERIMETER / CIRCUMFERENCE
Rectangle: 2 × (Length + Width)
Circle: 2 × 3.14 × radius
NUMBER SERIES
Write out the difference between each number
Look for a repeating or growing pattern
Apply that pattern to find the next number
(Use π ≈ 3.14)
Example 1 — Rectangle:
A rectangular work area is 12 feet long and 8 feet wide. What is the area?
Area = Length × Width
Area = 12 × 8 = 96 square feet
✅ Answer: 96 sq ft
Example 2 — Triangle:
A triangular piece of land has a base of 10 feet and a height of 6 feet. What is the area?
Area = ½ × Base × Height
Area = ½ × 10 × 6
Area = ½ × 60 = 30 square feet
✅ Answer: 30 sq ft
Example 3 — Circle:
A circular conduit opening has a radius of 5 inches. What is the area?
Area = π × r²
Area = 3.14 × 5²
Area = 3.14 × 25 = 78.5 square inches
✅ Answer: 78.5 sq in
Practice Problems — Geometry:
1. What is the area of a rectangle that is 15 feet by 9 feet?
2. A triangle has a base of 14 feet and a height of 10 feet. What is the area?
3. A circle has a radius of 7 inches. What is the circumference?
Answers:
1. 15 × 9 = 135 sq ft
2. ½ × 14 × 10 = 70 sq ft
3. 2 × 3.14 × 7 = 43.96 inches
Section 2: Reading Comprehension
What it is: You will read short passages — typically 150–300 words — and answer multiple choice questions about what you just read. Topics are often workplace-related, technical, or instructional.
What they’re testing:
• Did you understand the main idea?
• Can you identify specific details?
• Can you draw logical conclusions from the text?
The 5-Step Reading Strategy
Step 1 — Read the questions FIRST.
Before you read the passage, skim the questions. This tells you exactly what to look for. You’re reading with a purpose, not just absorbing words.
Step 2 — Read the passage actively.
As you read, underline or mentally note:
• The main topic (usually in the first sentence or two)
• Any numbers, dates, or specific facts
• Any cause-and-effect relationships
• Any words like “however,” “therefore,” “but,” “because” — these signal important shifts
Step 3 — Answer from the text, not from your memory.
Every correct answer is supported by something written in the passage. If you’re relying on outside knowledge, you’re guessing. Go back to the text.
Step 4 — Eliminate wrong answers.
Cross out answers that:
• Contradict the passage
• Are too extreme (“always,” “never,” “all”)
• Are not mentioned at all
This leaves you with 1–2 choices, making your decision much easier.
Step 5 — Watch out for “almost right” answers.
The test writers are good at creating answer choices that sound right but contain one wrong word. Read carefully.
Reading Comprehension — Practice Passage
Read the following passage and answer the questions below.
“Electrical linemen are responsible for the installation, maintenance, and repair of high-voltage power lines and related equipment. The work requires both technical knowledge and physical fitness, as linemen frequently climb utility poles and work at heights. Safety training is a core part of the apprenticeship program, and all apprentices must pass a series of assessments before working unsupervised on energized lines. Journeyman linemen often mentor apprentices on the job, passing down techniques and safety habits developed over years of field experience. The demand for skilled linemen continues to grow as aging infrastructure requires replacement and renewable energy projects expand across the country.”
Question 1: What is the main idea of this passage?
• A) Electrical linemen earn high wages
• B) Linemen do technical, physical work and are in growing demand
• C) Apprentices must pass tests
• D) Renewable energy is growing
Best answer: B — It covers the broadest theme of the passage.
Question 2: According to the passage, what must apprentices do before working on energized lines unsupervised?
• A) Complete 4 years of school
• B) Pass a series of assessments
• C) Work alongside a journeyman for 2 years
• D) Obtain a state license
Best answer: B — Directly stated in the passage.
Question 3: What does the word “mentor” mean as used in the passage?
• A) Supervise and discipline
• B) Test and evaluate
• C) Guide and teach
• D) Replace and promote
Best answer: C — Context clues: “passing down techniques and safety habits.”
4–6 Week Study Plan
This plan is designed for someone working or busy. It’s realistic, effective, and builds from fundamentals to full test simulations.
Weeks 1–2: Build Your Foundation
Goal: Understand every math concept in this guide. Don’t rush — accuracy first.
• Day 1–2: Review Number Series. Do 15 problems per day.
• Day 3–4: Review Algebra and equations. Do 15 problems per day.
• Day 5–6: Review Word Problems (work rate). Do 10 problems per day.
• Day 7: Review Percentages and Ratios. Do 20 mixed problems.
• Repeat each week.
Reading: Read one short article or manual each day (news, technical writing, any nonfiction). After reading, summarize the main idea in one sentence and identify 2 specific details.
Time per day: 30–45 minutes minimum.
Weeks 3–4: Timed Practice Tests
Goal: Build speed and test-taking stamina.
• Take one full timed practice test every 3–4 days.
• Time yourself strictly — no pausing.
• After each test, go through every wrong answer and write out WHY you got it wrong.
• Keep a “mistake log”: a notebook where you track which problem types you miss most.
Time per day: 45–60 minutes.
Weeks 5–6: Target Weak Areas and Taper
Goal: Fix your specific weak spots. Build confidence.
• Use your mistake log to identify your 2–3 weakest areas.
• Spend focused time on just those areas.
• Take 1–2 final full practice tests in test conditions (no phone, timer running, pencil and scratch paper only).
• Final 3 days before the test: light review only. No cramming. Rest your brain.
Best Study Resources
Free Resources
• Khan Academy — khanacademy.org
• Search: “Algebra basics,” “Arithmetic,” “Number patterns”
• Free, self-paced, and excellent for fundamentals
• YouTube
• Search: “NJATC aptitude test prep,” “IBEW aptitude test math”
• Many former apprentices and journeymen post walkthrough videos
• This guide — Work through every example and practice problem with pencil and paper.
Paid Resources (Highly Recommended)
• JobTestPrep — jobtestprep.com
• Offers full NJATC practice test packages with detailed answer explanations
• Worth the cost if you want the most realistic test simulation
• iPrep — iprep.com
• Similar to JobTestPrep, solid practice material
• Good if you want variety in your practice tests
Recommendation: Start with free resources. If you’re still struggling after 2 weeks, invest in a paid package. Many people pass with free resources alone.
Test-Day Checklist
Use this the night before and morning of your test.
The Night Before
• Lay out your photo ID and any required paperwork
• Pack extra pencils and scratch paper if allowed
• Know exactly where the testing location is — confirm the address
• Set your alarm with extra time to spare
• Do a light 20-minute review — no heavy studying
• Get to bed at a reasonable hour
Morning of the Test
• Eat a real breakfast — your brain needs fuel
• Avoid excessive caffeine (jittery is not the same as focused)
• Arrive 10–15 minutes early
• Bring your ID and required documents
• Leave your phone in the car or turned off
During the Test
• Read every question fully before looking at answer choices
• Show your work on scratch paper — don’t do math in your head
• Skip questions you’re stuck on and come back to them
• If you have time left, go back and check your work
• Don’t change answers unless you have a specific reason — first instincts are often right
• Breathe. Pace yourself. You are prepared.
Common Mistakes to Avoid
1. Skipping steps in math.
Write everything out. Even if you think you can do it in your head, write it. This catches small errors that cost you points.
2. Second-guessing yourself constantly.
Pick your answer, move on. Changing answers back and forth wastes time and leads to more errors.
3. Ignoring number series.
This section is very learnable. Most patterns are simple once you practice them. Don’t skip this category.
4. Reading comprehension rushing.
People rush through reading because they’re nervous about the math. Don’t. Slow down, read the questions first, and go back to the text for every answer.
5. Not practicing without a calculator.
If you study with a calculator and test without one, you will panic on test day. Every single practice session must be done by hand.
6. Cramming the night before.
Cramming the night before a test like this does very little. Your performance on test day depends on weeks of consistent practice, not one all-nighter.
A Final Word
The people who fail this test mostly fail for one reason: they didn’t prepare. You are already not that person. The fact that you’re reading a study guide means you’re serious about getting in.
The math is manageable. The reading is straightforward. The test is designed to find people who can learn, follow instructions, and apply logic — and that’s you.
Stay consistent over the next few weeks. Work through these problems by hand every day. Take the timed practice tests. Fix your weak spots. Then walk in on test day knowing you did the work.
The apprenticeship on the other side of this test is worth it. Let’s get you in.
— Cyrus Simmons, 10-Year Journeyman Lineman
Questions? Drop them in the comments below. Which section are you struggling with most?
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