ASTB-E · Officer Aptitude Rating (OAR)
Math Skills
Math Skills is the ASTB-E subtest in which you solve math problems, in words or in symbols, and pick the correct answer among four.
- Items
- 30
- Time
- 40 minutes
- Format
- Computer-adaptive
- Answer options
- 4
- Calculator
- Not allowed, formulas provided
- Counts toward
- OAR
Screens of the trainer
The subtest
Measures
The subtest measures how well you solve a short math problem, from arithmetic through algebra, geometry and probability. Its score counts toward the Officer Aptitude Rating (OAR).
Applicants to Officer Candidate School take the OAR alone; pilot and flight officer applicants take the full battery.
Format
The subtest is computer-adaptive: a right answer is followed by a harder item, a wrong one by an easier item. No item can be skipped, and an answer, once given, cannot be changed.
The 30 items run in 40 minutes, and the subtest can end before the time is up once enough answers are in.
No calculator is allowed, and the formulas an item needs are provided. Scrap paper is supplied.
Scoring
The items are scaled for difficulty, so the score is comparable between test-takers who saw different items.
Math Skills, Reading Comprehension and Mechanical Comprehension together produce the OAR score.
Item types
Word problems and computation
Items mix word problems and pure computation. They run from fractions and averages through algebra, geometry, number properties and probability, and reach logarithms at the hard end.
A computation item gives an expression to evaluate or simplify, or an equation to solve. A word problem gives rates, money, counts or chances and asks for one figure.
Free practice test
Item 1 of 5
The value of 7 + 36 ÷ 6 × 3 − 5 is
Show the answer
Answer: 20
Division and multiplication are done left to right: 36 ÷ 6 = 6, then 6 × 3 = 18. Addition and subtraction follow: 7 + 18 − 5 = 20.
Item 2 of 5
A club divides 90 tickets among three groups in the ratio 2 to 3 to 5. How many tickets does the largest group receive?
Show the answer
Answer: 45
The ratio makes 2 + 3 + 5 = 10 equal parts, so one part is 90 ÷ 10 = 9 tickets. The largest group takes 5 parts: 5 × 9 = 45 tickets.
Item 3 of 5
If (2x − 3)² = 49, the two values of x are
Show the answer
Answer: x = 5 or x = −2
A quantity whose square is 49 is either 7 or −7, so 2x − 3 = 7 or 2x − 3 = −7. The first gives 2x = 10 and x = 5; the second gives 2x = −4 and x = −2.
Item 4 of 5
A spinner has 8 equal sections, 3 of them shaded. The spinner is spun twice. What is the probability that the two spins land on sections of the same kind, that is both shaded or both unshaded?
Show the answer
Answer: 17/32
Two shaded spins have probability 3/8 × 3/8 = 9/64 and two unshaded spins 5/8 × 5/8 = 25/64. The two cases cannot both happen, so they add: 9/64 + 25/64 = 34/64 = 17/32.
Item 5 of 5
log₈ 2 =
Show the answer
Answer: 1/3
The question asks what power of 8 gives 2. Since 8 = 2³, the cube root of 8 is 2, and a cube root is the one-third power, so log₈ 2 = 1/3.
The Frontline Forge trainer
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Feedback after each answer
Training mode shows the correct answer and its calculation after each answer, and the clock pauses while you read. Previous and Next move among the questions you have answered.
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The real format
Test mode runs 30 items with four options in 40 minutes and locks each answer: no going back, as on the real subtest. Each attempt draws its 30 items from a bank of 630 covering arithmetic, algebra, geometry, probability, statistics and logarithms, with the formula in the stem when an item needs one.
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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.