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OAR and ASTB-E · Math Skills Test

The Math Skills Test on the OAR and ASTB-E

Updated Nov 6, 2026facts checked Nov 6, 2026

MST is the math subtest of the OAR and of the full ASTB-E: arithmetic, algebra and some geometry, much of it as word problems. The math is school-level; the conditions are not.

OAR practice test OAR guide

What MST asks for

NAMI describes MST as solving equations and applying arithmetic, algebra, geometry and data analysis. In practice that means rates and distances, ratios, percents, averages, exponents and roots, simple probability, and areas and angles.

The skills themselves are taught once on this site, on Arithmetic Reasoning for word problems and Math Knowledge for algebra and geometry. This page covers how MST serves them.

MST conditions

  • Calculator: no calculator; the formulas you need are given and scratch paper is provided.
  • Delivery: adaptive, one item at a time, no skipping or going back.
  • Length: not fixed, because the subtest is adaptive.
  • Choices: 4 choices on MST and RCT; 3 on MCT.
  • Counts toward: the OAR on both tests and, by formulas NAMI does not publish, the aviation ratings on the full ASTB-E.

15 MST practice questions

0 of 15 answeredPick a letter: the reasoning for every choice opens under it.
Q1 of 15 · Math Skills Test (MST)

A fair coin is tossed 4 times. What is the probability of getting exactly 3 heads?

  1. 3/8 = 6/16 is the probability of exactly two heads.
  2. 1/16 counts only one arrangement, such as HHHT, out of 16.
  3. 1/8 = (1/2)³ covers three tosses and ignores the fourth toss and the 4 positions of the tail.
  4. There are 24 = 16 equally likely sequences, and 4 have exactly three heads (the tail can be in any of 4 places): 4/16 = 1/4.

ID 857399Report a problem

Q2 of 15 · Math Skills Test (MST)

A depot splits 5,400 MREs equally among 6 units. Each unit has 50 soldiers, and each soldier eats 3 MREs a day. How many days will a unit's MREs last?

  1. Each unit gets 5,400 ÷ 6 = 900 MREs and uses 50 × 3 = 150 a day, so they last 900 ÷ 150 = 6 days.
  2. 36 divides the whole depot's 5,400 MREs by one unit's daily use of 150.
  3. 18 divides 900 by the 50 soldiers and forgets that each eats 3 MREs a day.
  4. 900 is one unit's share of MREs, not the number of days.

ID 716329Report a problem

Q3 of 15 · Math Skills Test (MST)

An aircraft has a ground speed of 320 knots while flying with a 40-knot tailwind. What is its airspeed?

  1. 360 knots adds the tailwind again; 320 knots already includes it.
  2. A tailwind adds to airspeed, so airspeed = ground speed − tailwind = 320 − 40 = 280 knots.
  3. 240 knots subtracts the 40-knot wind twice.
  4. 320 knots is the ground speed; the tailwind is part of it.

ID 812994Report a problem

Q4 of 15 · Math Skills Test (MST)

An aircraft with an airspeed of 210 knots flies 720 nautical miles into a 30-knot headwind and returns with the same wind as a tailwind. How long is the round trip?

  1. 8 hours uses the 180-knot headwind speed for both legs.
  2. 6 hours uses the 240-knot tailwind speed for both legs.
  3. 6 hours 51 minutes (1,440 ÷ 210) assumes the wind cancels out; more time is spent in the headwind, so it does not.
  4. Out at 210 − 30 = 180 knots takes 720 ÷ 180 = 4 hours; back at 240 knots takes 3 hours; 7 hours in all.

ID 813003Report a problem

Q5 of 15 · Math Skills Test (MST)

An aircraft's fuel flow rises by 20% during a climb and then by a further 25% when power is added. By what percent has the fuel flow increased over the original?

  1. 45% adds 20% + 25%; the 25% is taken of the higher flow, so the increases multiply.
  2. 25% is only the second increase, which applies to the already higher flow.
  3. 20% is only the first increase; the second 25% comes on top of it.
  4. Successive increases multiply: 1.20 × 1.25 = 1.50, a 50% increase over the original.

ID 813013Report a problem

Q6 of 15 · Math Skills Test (MST)

The sequence 3, 7, 11, 15, … increases by the same amount each time. What is its 10th term?

  1. The nth term is 3 + (n − 1) × 4, so the 10th term is 3 + 9 × 4 = 39.
  2. 43 = 3 + 10 × 4 takes 10 steps; from the 1st to the 10th term there are 9.
  3. 36 = 9 × 4 is the total increase from the first term; the starting 3 is missing.
  4. 40 = 10 × 4 forgets the first term and uses 10 steps.

ID 813132Report a problem

Q7 of 15 · Math Skills Test (MST)

The probability that a pilot traps on any single carrier approach is .9, independently of other approaches. What is the probability of at least one trap in two approaches?

  1. At least one trap is the complement of missing both: 1 − (.1 × .1) = .99.
  2. .90 ignores the second approach.
  3. .81 = .9 × .9 is the chance of trapping on both approaches.
  4. .18 = 2 × .9 × .1 is the chance of exactly one trap.

ID 813324Report a problem

Q8 of 15 · Math Skills Test (MST)

The radius of a cylindrical fuel tank is doubled while its height stays the same. By what factor does its volume change?

  1. 2 treats the volume as proportional to the radius; it depends on r².
  2. 16 = 4² squares the factor a second time.
  3. V = πr²h, so doubling r multiplies the volume by 2² = 4.
  4. 8 = 2³ is the factor when every dimension doubles; the height stays the same.

ID 813325Report a problem

Q9 of 15 · Math Skills Test (MST)

A ship is on course 300°. A buoy is sighted at a relative bearing of 090° (measured clockwise from the bow). What is the true bearing of the buoy?

  1. 120° is the reciprocal of the course (300° − 180°).
  2. 210° subtracts the relative bearing from the course; relative bearings are added.
  3. True bearing = course + relative bearing = 300° + 090° = 390°, and 390° − 360° = 030°.
  4. 090° is the relative bearing; the ship's course has not been added.

ID 813329Report a problem

Q10 of 15 · Math Skills Test (MST)

If 5/8 of a number, increased by 15, equals 55, what is the number?

  1. (5/8)x + 15 = 55, so (5/8)x = 40 and x = 40 × 8/5 = 64.
  2. 70 is the value of (5/8)x after adding 15 to 55 instead of subtracting; it is not divided by 5/8 either.
  3. 112 adds 15 instead of subtracting it: (5/8)x = 70.
  4. 88 skips subtracting 15 and solves (5/8)x = 55.

ID 813644Report a problem

Q11 of 15 · Math Skills Test (MST)

(3/4)³ × (4/3)² = ?

  1. 4/3 subtracts the exponents the wrong way round, 2 − 3.
  2. Because 4/3 is the reciprocal of 3/4, (4/3)² = (3/4)−2, and the product is (3/4)3 − 2 = 3/4.
  3. 16/9 is (4/3)² alone; the (3/4)³ factor has been ignored.
  4. 1 assumes reciprocals cancel completely, but the powers 3 and 2 differ.

ID 857540Report a problem

Q12 of 15 · Math Skills Test (MST)

(4³ × 2²) ÷ (8² × 2−1) = ?

  1. 2 treats dividing by 2−1 as dividing by 2; dividing by 2−1 multiplies by 2.
  2. 4 writes 4³ as 25, adding the exponents 2 + 3 instead of multiplying them.
  3. In base 2, 4³ = 26 and 8² = 26, so the value is 26 + 2 − 6 + 1 = 2³ = 8.
  4. 16 writes 8² as 25, adding the exponents 3 + 2 instead of multiplying them.

ID 857679Report a problem

Q13 of 15 · Math Skills Test (MST)

∛(−64) + √81 = ?

  1. 1 uses −8, the square root of 64 with a minus sign, instead of the cube root −4.
  2. −1 takes the fourth root of 81 (3) instead of the square root: −4 + 3.
  3. The cube root of a negative number is negative: ∛(−64) = −4, and √81 = 9, so −4 + 9 = 5.
  4. 13 drops the sign of the cube root: 4 + 9.

ID 857737Report a problem

Q14 of 15 · Math Skills Test (MST)

In a right triangle, angle A is acute and sin A = 3/5. What is cos A?

  1. 5/4 is the cosine turned upside down (the secant).
  2. sin A = 3/5 gives opposite 3 and hypotenuse 5, so the adjacent side is √(25 − 9) = 4 and cos A = 4/5.
  3. 3/4 is opposite over adjacent, which is tan A.
  4. 5/3 is the sine turned upside down (the cosecant).

ID 970050Report a problem

Q15 of 15 · Math Skills Test (MST)

Simplify: (6a²b) ÷ (9ab³)

  1. 2ab²/3 puts the leftover b² in the numerator; it belongs in the denominator.
  2. Divide the coefficients and subtract exponents: 6/9 = 2/3, a²/a = a, b/b³ = 1/b², so 2a/(3b²).
  3. 3a/(2b²) inverts the coefficient; 6/9 = 2/3.
  4. 2a/(3b) leaves only one b in the denominator; b/b³ = 1/b².

ID 858217Report a problem

Your tally shows here once every question above has an answer.

Common MST traps

  • Given formulas, unknown use. The sheet gives you the formula, not which one the problem needs. Name the quantity asked for before you pick one.
  • Percent of what? A rise or fall is measured against the original amount, so name the 100% figure before you multiply.
  • Two kinds of mile. A nautical mile is longer than a statute mile; a problem in knots works in nautical miles.
  • Averages with zeros. A game or day with nothing in it still counts in the average (NAMI sample MST-7).
  • Long division of decimals. Without a calculator, clear the decimal first: 4.2 ÷ 0.07 is 420 ÷ 7.
  • Rules of exponents. Multiply powers of the same base by adding exponents, never by multiplying them.

MST compared with other math subtests

The Air Force's AFOQT math is fixed and timed rather than adaptive, and the Army's SIFT has its own adaptive math section on the SIFT practice test. The same arithmetic shows up on all three; what changes is the pacing.

MST sets on your phone

Practice on your phone

OAR questions with the reasoning for every choice, in a study app (see both stores).

App StoreGoogle Play

Beside MST on the OAR

MST questions

Can you use a calculator on the ASTB-E math section?

No. The conditions above list what you get instead.

Is the OAR math section the same as on the full ASTB-E?

Yes. MST is one subtest that both tests share, and an OAR sitting is the first three subtests of the battery.

What level of math is on MST?

High-school arithmetic, algebra and basic geometry, mostly as word problems. NAMI's harder items include exponents and logarithms.