Common Math Problems in General Class Exam

The General Class exam includes more mathematical concepts than Technician. That does not mean it is a “math-heavy” test in the schoolwork sense. Most problems are short, practical, and highly repeatable once you understand the formula families behind them. This guide will help you recognize those families and practice them in a way that actually sticks.

Essential Formulas

Ohm’s Law Triangle

The foundation of many electrical calculations:

    E
   ---
  I x R

E = I x R  (Voltage = Current x Resistance)
I = E / R  (Current = Voltage / Resistance)
R = E / I  (Resistance = Voltage / Current)

Power Formulas

P = E x I          (Power = Voltage x Current)
P = I² x R         (Power = Current² x Resistance)
P = E² / R         (Power = Voltage² / Resistance)

Decibels (dB)

Decibels express power ratios:

dB	Power Ratio	Meaning
+3 dB	2x	Double the power
+6 dB	4x	Quadruple the power
+10 dB	10x	Ten times the power
-3 dB	0.5x	Half the power
-10 dB	0.1x	One-tenth the power

Quick tip: Every 3 dB is roughly a doubling or halving of power.

Common Problem Types

Problem Type 1: Power Calculations

Example: What is the power in a circuit with 12V and 2A current?

P = E x I
P = 12V x 2A
P = 24 Watts

Problem Type 2: Resistance Calculations

Example: A 120V circuit draws 0.5A. What is the resistance?

R = E / I
R = 120V / 0.5A
R = 240 Ohms

Problem Type 3: Wavelength and Frequency

Formula: Wavelength (m) = 300 / Frequency (MHz)

Example: What is the wavelength of a 7.2 MHz signal?

lambda = 300 / 7.2
lambda = 41.67 meters

Problem Type 4: Antenna Length

Half-wave dipole: Length (feet) = 468 / Frequency (MHz)

Example: What length for a 20-meter dipole (14.2 MHz)?

Length = 468 / 14.2
Length = 32.96 feet ≈ 33 feet

Problem Type 5: Impedance Matching

SWR (Standing Wave Ratio) indicates impedance match quality:

SWR	Match Quality
1:1	Perfect
1.5:1	Excellent
2:1	Good
3:1	Acceptable
>3:1	Poor

Reactance Formulas

Capacitive Reactance

Xc = 1 / (2pi x f x C)

Where:

Xc = Capacitive reactance (Ohms)
f = Frequency (Hz)
C = Capacitance (Farads)

Inductive Reactance

XL = 2pi x f x L

Where:

XL = Inductive reactance (Ohms)
f = Frequency (Hz)
L = Inductance (Henrys)

How Math Questions Usually Appear on the General Exam

Most General math questions are not long derivations. They test whether you can:

choose the right formula
keep units straight
estimate whether your answer makes sense

This is why it helps to study math inside the Electrical Principles topic hub and the General G5 category instead of memorizing formulas as isolated trivia.

For example:

G5B03 is a straight power problem
G5C07 tests matching and ratio reasoning
G5A11 reinforces the language behind reactance

When you can move between those question types without panic, you are in good shape.

Calculator-Free Shortcuts Worth Memorizing

On exam day, simple mental shortcuts save time:

If resistance doubles while voltage stays fixed, current is cut in half
A +3 dB change means about double the power
A -3 dB change means about half the power
Higher frequency means shorter wavelength
A dipole for a higher-frequency band is physically shorter

These checkpoints help you eliminate obviously wrong answers before you finish the calculation.

Study Strategy for Math Questions

1. Memorize Core Formulas

Focus on these first:

Ohm’s Law (E = I x R)
Power (P = E x I)
Wavelength (lambda = 300 / f)

2. Practice with Real Numbers

Use General category practice to see how the formulas appear in actual exam wording.

3. Learn the Shortcuts

For dB: memorize the 3 dB = 2x rule
For wavelength: 300 / MHz
For dipole length: 468 / MHz

4. Use Estimation

On the exam, you can often eliminate wrong answers by estimating:

If the answer should be around 50, eliminate 5 and 500
If a transformer is stepping from high impedance to low impedance, the ratio should move in that direction
If a result is physically unrealistic, your formula choice is probably wrong

A Better Practice Routine for Formula Retention

If math is one of your weak spots, do not save it for one giant cram session. A stronger plan is:

spend 10 minutes on one formula family per day
work 3 to 5 questions from the matching subcategory immediately after
review those same questions two or three days later
add one mock exam every few days to test recall under pressure

This works especially well for:

If you are upgrading from Technician, pair this guide with Upgrade from Technician to General Class so the formulas stay connected to your larger study plan.

Common Mistakes to Avoid

Unit confusion: Make sure voltage is in Volts and current in Amps
Frequency units: Convert kHz to MHz if needed
Rounding errors: The exam often expects approximate but sensible values
Formula mix-up: Double-check which relationship applies
Memorizing without meaning: If you cannot explain what reactance or impedance describes, the formula will not stick

Questions to Practice Right Now

If you want a compact, high-value drill set, start with:

Then pair those with:

Practice Makes Perfect

The best way to master these calculations is repeated, focused practice:

General Class Questions - Practice all topics
Mock Exam - Simulate test conditions
Wrong Answers Review - Focus on problem areas
Favorites - Save formulas or question styles you want to revisit

With consistent practice, these formulas become much less intimidating. Good luck.