# 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 5 groups in the Technician question pool which contain math questions. Therefore, it is theoretically possible that your exam could have as many as 5 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 T4A: Power supply rating

Group T4A has 1 math question and 11 non-math questions, so you have a 8% chance of getting a math question from this group. It will be about power supply rating.

### Technician Exam Group T5B: Metric conversions

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. 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.

There are also some questions about decibels, but you can answer all of them without calculation as long as you remember the definition of bel (a factor of 10), and that 3 dB is approximately a factor of 2.

### Technician Exam Group T5C: DC power calculations

Group T5C has 3 math questions and 10 non-math questions, so you have a 23% 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

Group T5D has 9 math questions and 5 non-math questions, so you have a 64% 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: – Antenna length calculation

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 1/2-wavelength and 1/4-wavelength antennas for a specified frequency.

## General exam

There are only 5 groups in the General question pool which contain math questions. Therefore, it is theoretically possible that your exam could have as many as 5 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 G5B — Power and decibels

Group G5B has 9 math questions and 5 non-math questions, so you have a 64% chance of getting a math question from this group. Most students memorize some of these math answers, 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 9 math questions and 5 non-math questions, so you have a 64% 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 2 questions involving transformers.

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

Group G8B has 2 math questions and 11 non-math questions, so you have a 15% 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 2 math questions and 9 non-math questions, so you have a 18% 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, testing that you know and can use the formula to calculate the lengths of 1/2-wavelength and 1/4-wavelength antennas for a specified frequency.

## Extra exam

There are 11 groups in the Extra question pool which contain math questions. Therefore, it is theoretically possible that your exam could have as many as 11 math questions. However, the probability is that your exam will only have 2 or 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 — Forward and reflected power

Group E4B has 1 math question and 10 non-math questions, so you have a 9% chance of getting a math question from this group. The 1 question relates to forward versus reflected power.

### Extra Group E4C — Image response

Group E4C has 1 math question and 14 non-math questions, so you have a 7% 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 11 non-math questions, so you have a 8% 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 12 non-math questions, so you have a 25% 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 8 non-math questions, so you have a 33% 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 1 math question and 11 non-math questions, so you have a 8% 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 8 non-math questions, so you have a 47% chance of getting a math question from this group. The math questions all relate to power factors.

### 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 4 math questions and 9 non-math questions, so you have a 31% 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 10 non-math questions, so you have a 23% 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 2 or 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!