AFOQT · Pilot, CSO and ABM composites
Math Knowledge
Math Knowledge is the AFOQT subtest in which you solve short math problems and pick the correct answer among five.
- Items
- 25
- Time
- 22 minutes
- Answer options
- 5
- Composites
- Pilot, CSO, ABM, Academic Aptitude, Quantitative
- Guessing penalty
- None
- Calculator
- None
Screens of the trainer
The subtest
Measures
The subtest measures knowledge of mathematical terms and principles.
It counts toward five composites, more than any other subtest: Pilot, CSO, ABM, Academic Aptitude and Quantitative.
Format
The pace is just under 53 seconds per item.
No calculator is allowed.
Scoring
The score is the number of correct answers. A wrong answer loses no points, so a guess costs nothing.
The composites it feeds are reported as percentiles from 1 to 99.
Item types
Expressions, equations and properties
Each item is a short math problem: an expression to evaluate, an equation or a system to solve, an expression to factor, or a property of a figure stated in words.
Items include fractions, signed numbers and the order of operations, systems of linear equations, factoring, and the properties of a triangle.
Free practice test
Item 1 of 5
If x = −1/4, then 8x² + 4x =
Show the answer
Answer: −1/2
x² = 1/16, so 8x² = 1/2.
4x = 4(−1/4) = −1.
1/2 + (−1) = −1/2.
Item 2 of 5
If y = 2x − 5 and 3x + 2y = 11, then (x, y) =
Show the answer
Answer: (3, 1)
Substitute y = 2x − 5: 3x + 2(2x − 5) = 11.
7x − 10 = 11, so x = 3.
y = 2(3) − 5 = 1.
Item 3 of 5
Two adjacent angles share a vertex and a side, and their two non-shared sides form a straight line. Which statement about this linear pair is correct?
Show the answer
Answer: The two angles are always supplementary.
The two angles together form a straight angle, 180 degrees.
Two angles that sum to 180 degrees are supplementary.
They are congruent only when both measure 90 degrees.
Item 4 of 5
Factor: x² + 8x + 15
Show the answer
Answer: (x + 3)(x + 5)
3 × 5 = 15 and 3 + 5 = 8.
So x² + 8x + 15 = (x + 3)(x + 5).
Item 5 of 5
(2a³)² × (a²)⁻³ =
Show the answer
Answer: 4
(2a³)² = 4a⁶ and (a²)⁻³ = a⁻⁶.
4a⁶ × a⁻⁶ = 4a⁰ = 4.
The Frontline Forge trainer
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Feedback after each answer
Training mode shows the correct answer and its explanation after each answer. The clock pauses while you read.
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The real format
Test mode runs 25 items in 22 minutes, the count and time of the real subtest, then reviews every item with its explanation. Each attempt draws its 25 items from a bank of 600 items covering arithmetic, algebra with quadratics and simple functions, geometry without figures, primes and divisibility, and exponents.
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Ranked against other test-takers
Each score is ranked against the scores of other test-takers. The Statistics page plots the ranking of every attempt, so you see whether you are beating more test-takers than before.