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 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.
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 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.
Group T5B — metric system and decibels
All of the questions in group T5B are math questions, so you have a 100% chance of getting exactly one math question from this group. It will be in one of these subject areas:
- Eight questions in this group test your ability to convert numbers within the metric system. In most cases, if you know the definitions of the metric prefixes, you can answer without doing any actual arithmetic. For example, "How many volts are equal to one microvolt?" The definition of "micro-" is one millionth, so the correct answer is, "One one-millionth of a volt."
- Three questions in this group test your ability to work with decibels. However, these also require little or no arithmetic. For example, "What is the approximate amount of change, measured in decibels (dB), of a power increase from 5 watts to 10 watts?" You should learn the fact that a 3 dB increase is a doubling of power. Since 10 is double 5, you can select the correct answer of "3 dB" without doing any arithmetic.
Group T5B questions
Group T5C — Power
Group T5C has 3 math questions and 8 non-math questions, so you have a 27% 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.
Group T5C questions
Group T5D — Ohm's law
Group T5D has 9 math questions and 3 non-math questions, so you have a 75% 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.
Here's where the definition of "non-math question" becomes fuzzy. For example, I don't consider this to be a math question, because it does not require you to do any calculation. This is just a memorization question. "What formula is used to calculate voltage in a circuit?" The answer is, "Voltage (E) equals current (I) multiplied by resistance (R)."
Group T5D questions
T9A — Antenna length
Group T9A has 2 math questions and 9 non-math questions, so you have a 18% 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.
Group T9A questions
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 3.
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.
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 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.
Group G5B questions
Group G5C — Components in series and parallel, transformer windings
Group G5C has 10 math questions and 5 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.
Group G5C questions
Group G8B — Frequency deviation
Group G8B has 2 math questions and 10 non-math questions, so you have a 17% chance of getting a math question from this group. The questions relate to the frequency deviation of FM signals.
Group G8B questions
Group G9A — Standing wave ratios
Group G9A has 5 math questions and 8 non-math questions, so you have a 38% 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.
Group G9A questions
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.
Group G9B questions
Extra exam
There are only 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 3-5.
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.
Group E4B — Accuracy of frequency counter
Group E4B has 3 math questions and 12 non-math questions, so you have a 20% chance of getting a math question from this group. The calculation questions relate to the accuracy of a frequency counter
Group E4B questions
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 one math question is about intermodulation interference frequency.
Group E4D questions
Group E5A — Resonance and half-power bandwidth
Group E5A has 8 math questions and 9 non-math questions, so you have a 47% chance of getting a math question from this group. This group has four questions where you calculate resonant frequency of an RLC circuit, and four questions where you calculate half-power bandwidth.
Group E5A questions
Group E5B — Time constants and phase angles
Group E5B has 9 math questions and 4 non-math questions, so you have a 69% chance of getting a math question from this group. This group has four questions about time constants and five about phase angles.
Group E5B questions
Group E5C — Impedances in rectangular and polar coordinates
Group E5C has 17 math questions and 6 non-math questions, so you have a 74% chance of getting a math question from this group. These questions all relate to impedances of circuits in rectangular or polar coordinates.
Group E5C questions
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 questions all relate to power factors.
Group E5D questions
Group E6D — Winding toroidal inductors
Group E6D has 2 math questions and 14 non-math questions, so you have a 13% chance of getting a math question from this group. The math questions both related to winding toroidal inductors.
Group E6D questions
Group E8B — Modulation index and deviation ratio
Group E8B has 4 math questions and 8 non-math questions, so you have a 33% chance of getting a math question from this group. The math questions relate to the modulation index and deviation ratio of FM signals.
Group E8B questions
Group E8D — Power
Group E8D has 5 math questions and 11 non-math questions, so you have a 31% chance of getting a math question from this group. The math questions are similar to the ones in groups T5C and G5B.
Group E8D questions
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.
Group E9F questions
Group E9H — Decibels
Group E9H has 3 math questions and 9 non-math questions, so you have a 25% chance of getting a math question from this group. The three math questions test your ability to combine gains and losses measured in decibels, then determine the resulting effective radiated power of the system.
Group E9H questions
Doing the math
To summarize:
- Your Technician exam will probably only have 2 math questions.
- Your General exam will probably only have 3 math questions.
- Your Extra exam will probably only have 3-5 math questions.
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.
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