# How Much Math is on the Amateur Radio Exams

#### by John Cunningham, W1AI

Passing the ham radio exams requires less math that most people think. This article explores the question of how much math you can expect to see on each exam.

In order to predict the number of math questions on the actual exam, you must understand how the exams are generated:

- The question pools are divided into groups.

- There are the same number of groups in the question pool as there are questions on the exam.

- The actual exams are generated by taking one question from each group.

So we can determine the maximum number of math questions on the exam by counting the number groups that contain any math questions. However, since many groups contain a mixture of math and non-math questions, the actual number of math questions on your exam will probably be less than this theoretical maximum.

We define a "math question" as one that requires some calculation to derive the correct answer. So a question asking you what the formula is for calculating something is not considered to be a math question, since you do not need to do any calculations. The question of how many volts are in a kilovolt is a memorization question, not a math question, since it merely requires you to remember that "kilo" means one thousand.

Use the "Calcs only" option on the **View courses** screen to list the questions on each exam which require calculations.

## Technician exam

There are only 4 groups in the Technician question pool which contain math questions. Therefore, it is theoretically possible that your exam could have as many as 4 math questions. However, the probability is that your exam will only have 1 or 2.

Since you can miss 9 questions and still pass, as long as you learn the other materials well, you can miss all the math questions and still pass.

### Technician Exam Group T5B: Math for electronics: conversion of electrical units; decibels; the metric system

Group T5B has 8 math questions and 5 non-math questions, so you have a 62% chance of getting a math question from this group. It will be in one of these subject areas:

- All 8 questions in this group test your ability to convert numbers within the metric system. These calculations really only require you to move the decimal place. The challenge is to know which way and how far to move it.

- You can answer all of the questions about decibels without doing any calculations. You just need to remember the a bel is a factor of 10, and 3 dB is (approximately) a factor of 2.

### Technician Exam Group T5C: Electronic principles: capacitance; inductance; current flow in circuits; alternating current; definition of RF; definition of polarity; DC power calculations; impedance

Group T5C has 3 math questions and 11 non-math questions, so you have a 21% chance of getting a math question from this group. The math questions in this group test that you know and can use the formulas to calculate power in a DC circuit.

### Technician Exam Group T5D: – Ohm’s Law: formulas and usage; components in series and parallel

Group T5D has 9 math questions and 7 non-math questions, so you have a 56% chance of getting a math question from this group. The math questions in this group test that you know and can use the various forms of Ohm's Law formulas. Note that we consider questions asking you to know the formulas to be memorization questions, not math questions.

### Technician Exam group T9A: – Antennas: vertical and horizontal polarization; concept of gain; common portable and mobile antennas; relationships between resonant length and frequency; concept of dipole antennas

Group T9A has 2 math questions and 10 non-math questions, so you have a 17% chance of getting a math question from this group. The math questions test that you know and can use the formula to calculate the lengths of 1/4-wavelength and 1/2-wavelength antennas for a specified frequency.

## General exam

There are only 6 groups in the General question pool which contain math questions. Therefore, it is theoretically possible that your exam could have as many as 6 math questions. However, the probability is that your exam will only have 2.

Since you can miss 9 questions and still pass, as long as you learn the other materials well, you can miss all the math questions and still pass.

### General Group G4D — Speech processors; S meters; sideband operation near band edges

Group G4D has 1 math question and 10 non-math questions, so you have a 9% chance of getting a math question from this group.

The one math question only requires you to know that 20 dB is equal to a 100 times increase in power. Most students will just memorize this answer.

### General Group G5B — Power and decibels

Group G5B has 8 math questions and 5 non-math questions, so you have a 62% chance of getting a math question from this group. Most students will memorize some of these math questions, like converting between 120 V RMS, 170 V peak, and 340 V peak-to-peak, rather than remembering the formulas and actually doing the calculation.

### General Group G5C — Components in series and parallel, transformer windings

Group G5C has 12 math questions and 6 non-math questions, so you have a 67% chance of getting a math question from this group. Most of the math questions relate to combining resistors, inductors, and capacitors in series or in parallel, but there are a few harder ones involving transformer windings.

### General Group G8B — FM frequency deviation and bandwidth

Group G8B has 2 math questions and 8 non-math questions, so you have a 20% chance of getting a math question from this group. The questions relate to the frequency deviation and bandwidth of FM signals.

### General Group G9A — Standing wave ratios

Group G9A has 5 math questions and 10 non-math questions, so you have a 33% chance of getting a math question from this group. The questions relate to the expected standing wave ratio from mismatches between feed lines and antennas.

### General Group G9B — Antenna length

Group G9B has 3 math questions and 9 non-math questions, so you have a 25% chance of getting a math question from this group. The questions are similar those in group T9A, test that you know and can use the formula to calculate the lengths of 1/4-wavelength and 1/2-wavelength antennas for a specified frequency.

## Extra exam

There are 12 groups in the Extra question pool which contain math questions. Therefore, it is theoretically possible that your exam could have as many as 12 math questions. However, the probability is that your exam will only have 3.

Since you can miss 13 questions and still pass, as long as you learn the other materials well, you can miss all the math questions and still pass.

### Extra Group E4B — Accuracy of frequency counter, directional wattmeter

Group E4B has 4 math questions and 13 non-math questions, so you have a 24% chance of getting a math question from this group. 3 math questions relate to the accuracy of a frequency counter, and 1 involves forward versus reflected power.

### Extra Group E4C — Image response

Group E4C has 1 math questions and 16 non-math questions, so you have a 6% chance of getting a math question from this group. The 1 math question involves image response frequency.

### Extra Group E4D — Intermodulation

Group E4D has 1 math question and 13 non-math questions, so you have a 7% chance of getting a math question from this group. The 1 math question is about intermodulation interference frequency.

### Extra Group E5A — Resonant frequency and half-power bandwidth

Group E5A has 4 math questions and 13 non-math questions, so you have a 24% chance of getting a math question from this group. This group has 2 math questions where you calculate resonant frequency of an RLC circuit, and 2 math questions where you calculate half-power bandwidth.

### Extra Group E5B — Time constants and phase angles

Group E5B has 4 math questions and 9 non-math questions, so you have a 31% chance of getting a math question from this group. This group has 1 math question about time constants and 3 about phase angles.

### Extra Group E5C — Impedances in rectangular and polar coordinates

Group E5C has 2 math questions and 15 non-math questions, so you have a 12% chance of getting a math question from this group. The 2 math questions all relate to plotting the impedance of RLC circuits.

### Extra Group E5D — Power factor

Group E5D has 7 math questions and 11 non-math questions, so you have a 39% chance of getting a math question from this group. The math questions all relate to power factors.

### Extra Group E6D — Winding toroidal inductors

Group E6D has 2 math questions and 15 non-math questions, so you have a 12% chance of getting a math question from this group. The 2 math questions both relate to winding toroidal inductors.

### Extra Group E7G — Operational amplifiers

Group E7G has 4 math questions and 8 non-math questions, so you have a 33% chance of getting a math question from this group. The 4 math questions relate to operational amplifiers.

### Extra Group E8B — Modulation index and deviation ratio

Group E8B has 4 math questions and 7 non-math questions, so you have a 36% chance of getting a math question from this group. The 4 math questions relate to the modulation index and deviation ratio of FM signals.

### Extra Group E9A — Antenna gain

Group E9A has 5 math questions and 13 non-math questions, so you have a 28% chance of getting a math question from this group. The 5 math questions related to antenna gain.

### Extra Group E9F — Velocity factor

Group E9F has 3 math questions and 13 non-math questions, so you have a 19% chance of getting a math question from this group. The math questions relate to velocity factor on transmission lines.

## Doing the math

To summarize:

- Your Technician exam will probably only have 1 or 2 math questions. You can miss 9 questions and still pass.

- Your General exam will probably only have 2 math questions. You can miss 9 questions and still pass.

- Your Extra exam will probably only have 3 math questions. You can miss 13 questions and still pass.

Now that you understand how little math there is on the exams, you can see why people who hate math can **Skip all calculations for now** and still easily pass the exams!