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.
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.
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.
Technician Group T5B — metric system and decibels
Group T5B has 11 math questions and 2 non-math questions, so you have a 85% chance of getting a math question from this group. It will be in one of these subject areas:
- 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.
- 3 questions in this group test your ability to work with decibels. You don't really need much arithmetic to answer these. 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
Technician Group T5C — Power
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.
Group T5C questions
Technician 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.
Group T5D questions
Technician T9A — Antenna length
Group T9A has 2 math questions and 12 non-math questions, so you have a 14% 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 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 2-3.
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.
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.
Group G4D questions
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.
Group G5B questions
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.
Group G5C questions
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.
Group G8B questions
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.
Group G9A questions
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.
Group G9B questions
Extra exam
There are 13 groups in the Extra question pool which contain math questions. Therefore, it is theoretically possible that your exam could have as many as 13 math questions. However, the probability is that your exam will only have 2-4.
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.
Group E4B questions
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.
Group E4C questions
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.
Group E4D questions
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.
Group E5A questions
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.
Group E5B questions
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.
Group E5C questions
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.
Group E5D questions
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.
Group E6D questions
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.
Group E7G questions
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.
Group E8B questions
Extra Group E8C — Necessary bandwidths
Group E8C has 2 math questions and 9 non-math questions, so you have a 18% chance of getting a math question from this group. The 2 math questions relate to necessary bandwidth of digital signals.
Group E8C questions
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.
Group E9A questions
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.
Group E9F questions
Doing the math
To summarize:
- Your Technician exam will probably only have 2 math questions.
- Your General exam will probably only have 2-3 math questions.
- Your Extra exam will probably only have 2-4 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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