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Officer Candidate / Aptitude tests (AFOQT) Quantitative and Mathematical Aptitude Flashcards
50 question-and-answer cards covering Quantitative and Mathematical Aptitude as it is examined in Officer Candidate / Aptitude tests (AFOQT). 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Quantitative and Mathematical Aptitude deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
What is the quadratic formula for ax² + bx + c = 0?
x = [−b ± √(b² − 4ac)] ÷ (2a).
Give the difference of squares and the FOIL expansion of (a+b)².
a² − b² = (a+b)(a−b); (a+b)² = a² + 2ab + b².
How do you solve a two-step linear equation like 3x + 5 = 20?
Undo addition/subtraction first (subtract 5 → 3x = 15), then undo multiplication/division (divide by 3 → x = 5).
What is the formula for the area and circumference of a circle?
Area = πr²; Circumference = 2πr (or πd).
State the Pythagorean theorem.
In a right triangle, a² + b² = c², where c is the hypotenuse (side opposite the right angle).
What is the sum of the interior angles of a triangle and of any quadrilateral?
Triangle = 180°; quadrilateral = 360°.
Give the area formulas for a triangle, rectangle, and trapezoid.
Triangle = ½ × base × height; Rectangle = length × width; Trapezoid = ½(b₁ + b₂) × height.
What is the formula for the volume of a rectangular box (prism) and a cylinder?
Box = length × width × height; Cylinder = πr²h.
What are the two special right-triangle side ratios?
45-45-90: 1 : 1 : √2. 30-60-90: 1 : √3 : 2 (short leg : long leg : hypotenuse).
What is the difference between prime and composite numbers?
A prime has exactly two factors (1 and itself); a composite has more than two factors. 1 is neither.
What are the divisibility rules for 3 and 9?
Divisible by 3 if the digit sum is divisible by 3; divisible by 9 if the digit sum is divisible by 9.
What is the difference between LCM and GCF?
GCF (greatest common factor) is the largest number dividing all given numbers; LCM (least common multiple) is the smallest number all given numbers divide into.
What rules govern the sign of a product or quotient with negative numbers?
Same signs → positive result; different signs → negative result. An even count of negatives gives positive; odd gives negative.
What is an integer, and how do even and odd combine under addition?
Integers are whole numbers and their negatives (no fractions). Even ± even = even; odd ± odd = even; even ± odd = odd.
What is the distance formula between points (x₁,y₁) and (x₂,y₂)?
d = √[(x₂−x₁)² + (y₂−y₁)²].
What is the slope formula and the slope-intercept form of a line?
Slope m = (y₂−y₁)/(x₂−x₁); slope-intercept form is y = mx + b, where b is the y-intercept.
What is the midpoint formula for two points?
Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2).
Give the basic SOH-CAH-TOA trig ratios.
sin = opposite/hypotenuse; cos = adjacent/hypotenuse; tan = opposite/adjacent.
How do slopes of parallel and perpendicular lines relate?
Parallel lines have equal slopes; perpendicular lines have slopes that are negative reciprocals (product = −1).
When reading a chart or graph, what should you check first before interpreting any data point?
The title, axis labels, units, and scale (including whether the axis starts at zero).
On a pie chart, how do you convert a percentage slice into an actual quantity?
Multiply the slice's percentage (as a decimal) by the chart's total value.
What is the difference between a bar graph and a line graph's typical use?
Bar graphs compare discrete categories; line graphs show trends or change in a value over time.
What is a fast estimation strategy for multiplication problems on a timed test?
Round each factor to a convenient number, multiply, then adjust; use it to eliminate answer choices that are far off.
On a timed aptitude test where wrong answers aren't penalized, what is the best tactic for a question you can't solve?
Make an educated guess (after eliminating choices) rather than leaving it blank, and don't waste time—move on.
What this deck covers
The Quantitative and Mathematical Aptitude deck follows the Officer Candidate / Aptitude tests (AFOQT) Quantitative and Mathematical Aptitude syllabus — 3 chapters and 11 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 16.7 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 83 characters, which is long enough to carry the reasoning and short enough to say out loud.
A deck like this earns its keep on the second and third pass. Read the syllabus first so you know the shape of the subject, then use the cards to find the specific facts that have not stuck.
Quantitative and Mathematical Aptitude flashcards FAQ
How many Quantitative and Mathematical Aptitude flashcards are in this Officer Candidate / Aptitude tests (AFOQT) deck?
50 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these Officer Candidate / Aptitude tests (AFOQT) flashcards free?
Yes. The preview here is free to read with no signup, and the full 50-card deck is free inside the Examius app.
What do the Quantitative and Mathematical Aptitude cards cover?
They follow the Officer Candidate / Aptitude tests (AFOQT) Quantitative and Mathematical Aptitude syllabus — 3 chapters and 11 topics — so the questions track what is actually examinable.
How should I use these flashcards?
Read the syllabus first so you know the shape of the subject, then drill the deck. Examius schedules each card with spaced repetition, so cards you keep missing come back sooner and ones you know drift further apart.