ASVAB Mathematics Knowledge (MK) Practice Test (2026) covers ASVAB Mathematics Knowledge (MK) practice test in a four-choice format with a “Show Answer” toggle for review. Each item includes the correct answer, a concise explanation, and official citations where applicable so you can verify what the test is targeting. Use it to practice algebra basics, geometry fundamentals, exponents, and applied problem-solving.
FAQ
Where can I take an ASVAB Mathematics Knowledge (MK) practice test?
Use a practice set that matches real wording and keeps you answering before you peek. After each question, open “Show Answer,” compare your reasoning to the explanation, and retake missed concepts later to confirm retention.
What should an ASVAB Mathematics Knowledge (MK) study guide cover?
A solid guide focuses on the core terms, common situations, and definitions that show up repeatedly. Pair reading with practice runs, and use explanations to learn why wrong options are wrong, not just which option is right.
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Use your browser’s print-to-PDF feature on this page to save a clean copy for offline work. Keep the on-page explanations available so you can verify steps and confirm why the correct option is correct.
What should I know for ASVAB Mathematics Knowledge (MK) on the ASVAB?
Focus on the recurring concepts that appear in many forms, not one-off trivia. Learn the key terms, practice mixed sets, and use explanations to build a quick recognition habit so you don’t overthink simple items.
What should I know for ASVAB Mathematics Knowledge (MK) on the ASVAB (part 2)?
Focus on the recurring concepts that appear in many forms, not one-off trivia. Learn the key terms, practice mixed sets, and use explanations to build a quick recognition habit so you don’t overthink simple items.
ASVAB Mathematics Knowledge (MK) Practice Test
Q201. Simplify: 63 × 64
Correct Answer: C
Explanation: When multiplying powers with the same base, add exponents: 3+4=7.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: exponent product rule; simplifying expressions; order of operations.
Explanation: When multiplying powers with the same base, add exponents: 3+4=7.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: exponent product rule; simplifying expressions; order of operations.
Q202. Simplify: 35 / 32
Correct Answer: A
Explanation: When dividing powers with the same base, subtract exponents: 5−2=3.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: exponent quotient rule; subtraction; simplifying expressions.
Explanation: When dividing powers with the same base, subtract exponents: 5−2=3.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: exponent quotient rule; subtraction; simplifying expressions.
Q203. Simplify: (23)4
Correct Answer: D
Explanation: Power of a power multiplies exponents: (2^3)^4 = 2^(3×4) = 2^12.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: power of a power rule; multiplication; exponent laws.
Explanation: Power of a power multiplies exponents: (2^3)^4 = 2^(3×4) = 2^12.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: power of a power rule; multiplication; exponent laws.
Q204. Rewrite without negative exponents: 5-3
Correct Answer: A
Explanation: A negative exponent means reciprocal: 5^-3 = 1/5^3.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: negative exponents; reciprocals; exponent laws.
Explanation: A negative exponent means reciprocal: 5^-3 = 1/5^3.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: negative exponents; reciprocals; exponent laws.
Q205. Simplify: (106)(10-2)
Correct Answer: C
Explanation: Add exponents for same base: 6 + (−2) = 4.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: exponent product rule; integers; simplifying expressions.
Explanation: Add exponents for same base: 6 + (−2) = 4.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: exponent product rule; integers; simplifying expressions.
Q206. Multiply and write in scientific notation: (3×105)(4×103)
Correct Answer: A
Explanation: Multiply coefficients: 3×4=12 and add exponents: 10^(5+3)=10^8. Then normalize 12×10^8 = 1.2×10^9.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: scientific notation; exponent addition; place-value normalization.
Explanation: Multiply coefficients: 3×4=12 and add exponents: 10^(5+3)=10^8. Then normalize 12×10^8 = 1.2×10^9.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: scientific notation; exponent addition; place-value normalization.
Q207. Divide and write in scientific notation: (8×107)/(2×103)
Correct Answer: D
Explanation: Divide coefficients: 8/2=4 and subtract exponents: 10^(7−3)=10^4, so 4×10^4.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: scientific notation; exponent subtraction; division.
Explanation: Divide coefficients: 8/2=4 and subtract exponents: 10^(7−3)=10^4, so 4×10^4.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: scientific notation; exponent subtraction; division.
Q208. Write 0.000072 in scientific notation.
Correct Answer: A
Explanation: Move the decimal 5 places right to get 7.2, so the exponent is −5: 7.2×10^-5.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: scientific notation; place value; powers of ten.
Explanation: Move the decimal 5 places right to get 7.2, so the exponent is −5: 7.2×10^-5.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: scientific notation; place value; powers of ten.
Q209. Write 5.63×106 as a standard number.
Correct Answer: B
Explanation: 10^6 moves the decimal 6 places right: 5.63 becomes 5,630,000.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: scientific notation; place value; multiplying by powers of ten.
Explanation: 10^6 moves the decimal 6 places right: 5.63 becomes 5,630,000.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: scientific notation; place value; multiplying by powers of ten.
Q210. Simplify: 91/2
Correct Answer: A
Explanation: An exponent of 1/2 means square root: 9^(1/2)=√9=3.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: rational exponents; square roots; exponent-root equivalence.
Explanation: An exponent of 1/2 means square root: 9^(1/2)=√9=3.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: rational exponents; square roots; exponent-root equivalence.
Q211. √72 simplified is:
Correct Answer: D
Explanation: 72 = 36×2, so √72 = √36√2 = 6√2.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: simplifying radicals; factoring perfect squares; properties of square roots.
Explanation: 72 = 36×2, so √72 = √36√2 = 6√2.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: simplifying radicals; factoring perfect squares; properties of square roots.
Q212. √200 simplified is:
Correct Answer: A
Explanation: 200 = 100×2, so √200 = 10√2.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: simplifying radicals; perfect-square factors; multiplication under radicals.
Explanation: 200 = 100×2, so √200 = 10√2.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: simplifying radicals; perfect-square factors; multiplication under radicals.
Q213. Simplify: √(50) / √(2)
Correct Answer: C
Explanation: √50/√2 = √(50/2) = √25.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: radical quotient rule; simplifying radicals; division.
Explanation: √50/√2 = √(50/2) = √25.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: radical quotient rule; simplifying radicals; division.
Q214. Rationalize the denominator: 7/√3
Correct Answer: A
Explanation: Multiply numerator and denominator by √3: 7/√3 → 7√3/3.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: rationalizing denominators; multiplying by 1; simplifying radicals.
Explanation: Multiply numerator and denominator by √3: 7/√3 → 7√3/3.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: rationalizing denominators; multiplying by 1; simplifying radicals.
Q215. Rationalize the denominator: 5/(2√6)
Correct Answer: D
Explanation: Multiply by √6/√6: 5/(2√6) = 5√6/(2×6)=5√6/12.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: rationalizing denominators; fraction simplification; multiplying by conjugate (simple form).
Explanation: Multiply by √6/√6: 5/(2√6) = 5√6/(2×6)=5√6/12.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: rationalizing denominators; fraction simplification; multiplying by conjugate (simple form).
Q216. Simplify: (3√8)
Correct Answer: A
Explanation: √8=√(4×2)=2√2, so 3√8=3(2√2)=6√2.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: simplifying radicals; distributive property; factoring perfect squares.
Explanation: √8=√(4×2)=2√2, so 3√8=3(2√2)=6√2.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: simplifying radicals; distributive property; factoring perfect squares.
Q217. Simplify: √45
Correct Answer: C
Explanation: 45=9×5, so √45=√9√5=3√5.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: simplifying radicals; perfect-square factors; multiplication.
Explanation: 45=9×5, so √45=√9√5=3√5.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: simplifying radicals; perfect-square factors; multiplication.
Q218. Simplify: √27
Correct Answer: A
Explanation: 27=9×3, so √27=3√3.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: simplifying radicals; factoring; square root properties.
Explanation: 27=9×3, so √27=3√3.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: simplifying radicals; factoring; square root properties.
Q219. Simplify: 163/4
Correct Answer: D
Explanation: 16^(3/4) = (√[4]{16})^3. Since √[4]{16}=2, result is 2^3=8.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: rational exponents; roots; exponent rules.
Explanation: 16^(3/4) = (√[4]{16})^3. Since √[4]{16}=2, result is 2^3=8.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: rational exponents; roots; exponent rules.
Q220. Simplify: 811/4
Correct Answer: A
Explanation: 81^(1/4)=√[4]{81}. Since 3^4=81, the value is 3.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: rational exponents; inverse operations; perfect powers.
Explanation: 81^(1/4)=√[4]{81}. Since 3^4=81, the value is 3.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: rational exponents; inverse operations; perfect powers.
Q221. Evaluate: log10(1000)
Correct Answer: C
Explanation: log10(1000)=3 because 10^3=1000.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: logarithms as inverses; powers of ten; evaluation.
Explanation: log10(1000)=3 because 10^3=1000.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: logarithms as inverses; powers of ten; evaluation.
Q222. Evaluate: log2(32)
Correct Answer: A
Explanation: log2(32)=5 because 2^5=32.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: logarithms; exponents; inverse operations.
Explanation: log2(32)=5 because 2^5=32.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: logarithms; exponents; inverse operations.
Q223. Evaluate: log3(81)
Correct Answer: D
Explanation: log3(81)=4 because 3^4=81.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: logarithms; perfect powers; evaluation.
Explanation: log3(81)=4 because 3^4=81.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: logarithms; perfect powers; evaluation.
Q224. Solve for x: 5x = 125
Correct Answer: A
Explanation: 125 is 5^3, so x=3.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: exponential equations; recognizing powers; inverse operations.
Explanation: 125 is 5^3, so x=3.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: exponential equations; recognizing powers; inverse operations.
Q225. Solve for x: 2x = 1/8
Correct Answer: C
Explanation: 1/8 = 2^-3, so x=-3.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: negative exponents; exponential equations; reciprocals.
Explanation: 1/8 = 2^-3, so x=-3.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: negative exponents; exponential equations; reciprocals.
Q226. Simplify: log10(106)
Correct Answer: A
Explanation: log10(10^6)=6 by the inverse relationship between log base 10 and powers of 10.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: logarithms; inverse functions; exponent laws.
Explanation: log10(10^6)=6 by the inverse relationship between log base 10 and powers of 10.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: logarithms; inverse functions; exponent laws.
Q227. Simplify: log2(16/2)
Correct Answer: D
Explanation: 16/2=8, and log2(8)=3 because 2^3=8.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: logarithms; quotient simplification; evaluation.
Explanation: 16/2=8, and log2(8)=3 because 2^3=8.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: logarithms; quotient simplification; evaluation.
Q228. Simplify: log3(27) + log3(3)
Correct Answer: A
Explanation: log3(27)=3 and log3(3)=1, so the sum is 4.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: logarithms; evaluation; addition.
Explanation: log3(27)=3 and log3(3)=1, so the sum is 4.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: logarithms; evaluation; addition.
Q229. If log10(x)=2, what is x?
Correct Answer: C
Explanation: log10(x)=2 means 10^2=x, so x=100.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: logarithms; inverse operations; powers of ten.
Explanation: log10(x)=2 means 10^2=x, so x=100.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: logarithms; inverse operations; powers of ten.
Q230. If log4(x)=3, what is x?
Correct Answer: A
Explanation: log4(x)=3 means 4^3=x, so x=64.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: logarithms; exponents; inverse operations.
Explanation: log4(x)=3 means 4^3=x, so x=64.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: logarithms; exponents; inverse operations.
Q231. Factor: x² + 7x + 12
Correct Answer: D
Explanation: Find two numbers that multiply to 12 and add to 7: 3 and 4.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: factoring quadratics; integer pairs; distributive property.
Explanation: Find two numbers that multiply to 12 and add to 7: 3 and 4.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: factoring quadratics; integer pairs; distributive property.
Q232. Factor: x² – x – 20
Correct Answer: A
Explanation: Numbers that multiply to -20 and add to -1 are -5 and 4.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: factoring quadratics; signed numbers; checking by multiplication.
Explanation: Numbers that multiply to -20 and add to -1 are -5 and 4.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: factoring quadratics; signed numbers; checking by multiplication.
Q233. Solve: x² – 9 = 0
Correct Answer: C
Explanation: x^2=9 so x=±3.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: difference of squares; solving equations; square roots.
Explanation: x^2=9 so x=±3.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: difference of squares; solving equations; square roots.
Q234. For x² + 6x + 5 = 0, what is the sum of the solutions?
Correct Answer: A
Explanation: For x^2+bx+c=0, sum of roots is -b. Here b=6, so sum=-6.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: Vieta’s formulas; coefficients; algebraic reasoning.
Explanation: For x^2+bx+c=0, sum of roots is -b. Here b=6, so sum=-6.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: Vieta’s formulas; coefficients; algebraic reasoning.
Q235. For x² – 4x – 21 = 0, what is the product of the solutions?
Correct Answer: D
Explanation: For x^2+bx+c=0, product of roots is c. Here c=-21.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: Vieta’s formulas; product of roots; coefficients.
Explanation: For x^2+bx+c=0, product of roots is c. Here c=-21.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: Vieta’s formulas; product of roots; coefficients.
Q236. Complete the square: x² + 10x + 9
Correct Answer: A
Explanation: x^2+10x = (x+5)^2-25, so x^2+10x+9 = (x+5)^2-16.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: completing the square; algebraic manipulation; perfect-square trinomials.
Explanation: x^2+10x = (x+5)^2-25, so x^2+10x+9 = (x+5)^2-16.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: completing the square; algebraic manipulation; perfect-square trinomials.
Q237. How many real solutions does x² + 4x + 10 = 0 have?
Correct Answer: C
Explanation: Discriminant b^2-4ac = 16-40 = -24 < 0, so no real solutions.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: discriminant; quadratic formula; real vs complex roots.
Explanation: Discriminant b^2-4ac = 16-40 = -24 < 0, so no real solutions.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: discriminant; quadratic formula; real vs complex roots.
Q238. How many real solutions does x² – 8x + 16 = 0 have?
Correct Answer: A
Explanation: Discriminant b^2-4ac = 64-64=0, so one real repeated root.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: discriminant; perfect squares; root multiplicity.
Explanation: Discriminant b^2-4ac = 64-64=0, so one real repeated root.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: discriminant; perfect squares; root multiplicity.
Q239. Solve: x² + 2x – 15 = 0
Correct Answer: D
Explanation: Factor to (x+5)(x-3)=0, so x=-5 or x=3.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: factoring; zero-product property; solving equations.
Explanation: Factor to (x+5)(x-3)=0, so x=-5 or x=3.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: factoring; zero-product property; solving equations.
Q240. Solve: x² – 12x + 35 = 0
Correct Answer: A
Explanation: Factor to (x-5)(x-7)=0, so x=5 or x=7.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: factoring; zero-product property; integer roots.
Explanation: Factor to (x-5)(x-7)=0, so x=5 or x=7.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: factoring; zero-product property; integer roots.
Q241. If f(x)=3x-7, what is f(5)?
Correct Answer: C
Explanation: Substitute x=5: f(5)=3(5)-7=15-7=8.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: function evaluation; substitution; order of operations.
Explanation: Substitute x=5: f(5)=3(5)-7=15-7=8.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: function evaluation; substitution; order of operations.
Q242. If g(x)=x²-4x, what is g(-3)?
Correct Answer: A
Explanation: g(-3)=(-3)^2-4(-3)=9+12=21.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: function evaluation; squaring negatives; distributive property.
Explanation: g(-3)=(-3)^2-4(-3)=9+12=21.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: function evaluation; squaring negatives; distributive property.
Q243. What is the slope of the line through (2, -1) and (8, 5)?
Correct Answer: D
Explanation: Slope m=(5-(-1))/(8-2)=6/6=1.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: slope formula; subtraction; fractions.
Explanation: Slope m=(5-(-1))/(8-2)=6/6=1.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: slope formula; subtraction; fractions.
Q244. What is the slope of the line through (-4, 3) and (2, -9)?
Correct Answer: A
Explanation: m=(-9-3)/(2-(-4))=-12/6=-2.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: slope from two points; integer division; coordinate geometry.
Explanation: m=(-9-3)/(2-(-4))=-12/6=-2.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: slope from two points; integer division; coordinate geometry.
Q245. What is the midpoint of (1, 7) and (9, -1)?
Correct Answer: C
Explanation: Midpoint=((1+9)/2,(7+(-1))/2)=(5,3).
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: midpoint formula; averaging; coordinate geometry.
Explanation: Midpoint=((1+9)/2,(7+(-1))/2)=(5,3).
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: midpoint formula; averaging; coordinate geometry.
Q246. What is the distance between (0, 0) and (6, 8)?
Correct Answer: A
Explanation: Distance=√(6^2+8^2)=√(36+64)=√100=10.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: distance formula; Pythagorean theorem; square roots.
Explanation: Distance=√(6^2+8^2)=√(36+64)=√100=10.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: distance formula; Pythagorean theorem; square roots.
Q247. If h(x)=2(x-4)+3, simplify h(x).
Correct Answer: D
Explanation: Distribute: 2(x-4)=2x-8, then add 3 to get 2x-5.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: distributive property; combining like terms; linear functions.
Explanation: Distribute: 2(x-4)=2x-8, then add 3 to get 2x-5.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: distributive property; combining like terms; linear functions.
Q248. For y=-3x+12, what is the x-intercept?
Correct Answer: A
Explanation: At x-intercept, y=0: 0=-3x+12 → 3x=12 → x=4.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: intercepts; solving linear equations; substitution.
Explanation: At x-intercept, y=0: 0=-3x+12 → 3x=12 → x=4.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: intercepts; solving linear equations; substitution.
Q249. For y=2x+1, what is y when x=-2?
Correct Answer: C
Explanation: Plug in x=-2: y=2(-2)+1=-4+1=-3.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: function evaluation; substitution; arithmetic.
Explanation: Plug in x=-2: y=2(-2)+1=-4+1=-3.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: function evaluation; substitution; arithmetic.
Q250. What is the equation of a line with slope 2 passing through (0, -3)?
Correct Answer: A
Explanation: Use y=mx+b. With x=0 gives y=b=-3, so y=2x-3.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: slope-intercept form; identifying intercept; linear equations.
Explanation: Use y=mx+b. With x=0 gives y=b=-3, so y=2x-3.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: slope-intercept form; identifying intercept; linear equations.
Q251. A triangle has angles 48° and 67°. What is the third angle?
Correct Answer: D
Explanation: Triangle angles sum to 180°. 180-(48+67)=65°.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: triangle angle sum; subtraction; angle relationships.
Explanation: Triangle angles sum to 180°. 180-(48+67)=65°.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: triangle angle sum; subtraction; angle relationships.
Q252. A circle has radius 7. What is its circumference in terms of π?
Correct Answer: A
Explanation: Circumference C=2πr=2π(7)=14π.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: circle circumference; formulas; multiplication.
Explanation: Circumference C=2πr=2π(7)=14π.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: circle circumference; formulas; multiplication.
Q253. A circle has radius 6. What is its area in terms of π?
Correct Answer: B
Explanation: Area A=πr^2=π(6^2)=36π.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: circle area; exponentiation; formulas.
Explanation: Area A=πr^2=π(6^2)=36π.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: circle area; exponentiation; formulas.
Q254. A rectangle is 9 by 4. What is its area?
Correct Answer: A
Explanation: Area = length×width = 9×4 = 36.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: area of a rectangle; multiplication; units.
Explanation: Area = length×width = 9×4 = 36.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: area of a rectangle; multiplication; units.
Q255. A rectangular prism measures 5 by 3 by 8. What is its volume?
Correct Answer: D
Explanation: Volume=l×w×h=5×3×8=120.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: volume; multiplication; geometry formulas.
Explanation: Volume=l×w×h=5×3×8=120.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: volume; multiplication; geometry formulas.
Q256. Two similar figures have a scale factor of 3:1 (larger to smaller). Areas scale by what factor?
Correct Answer: A
Explanation: Area scale factor is the square of side scale factor: 3^2=9.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: similarity; area scaling; exponentiation.
Explanation: Area scale factor is the square of side scale factor: 3^2=9.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: similarity; area scaling; exponentiation.
Q257. A right triangle has legs 9 and 12. What is the hypotenuse?
Correct Answer: B
Explanation: c=√(9^2+12^2)=√(81+144)=√225=15.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: Pythagorean theorem; square roots; right triangles.
Explanation: c=√(9^2+12^2)=√(81+144)=√225=15.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: Pythagorean theorem; square roots; right triangles.
Q258. What is the sum of interior angles of a 9-sided polygon?
Correct Answer: A
Explanation: Sum=(n-2)×180=(9-2)×180=1260°.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: polygon angle sum; formulas; multiplication.
Explanation: Sum=(n-2)×180=(9-2)×180=1260°.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: polygon angle sum; formulas; multiplication.
Q259. A line has a 35° angle with a transversal. What is the adjacent supplementary angle?
Correct Answer: D
Explanation: Supplementary angles sum to 180°: 180-35=145°.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: supplementary angles; linear pairs; subtraction.
Explanation: Supplementary angles sum to 180°: 180-35=145°.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: supplementary angles; linear pairs; subtraction.
Q260. A square has perimeter 48. What is one side length?
Correct Answer: A
Explanation: Perimeter=4s, so s=48/4=12.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: perimeter of square; division; formulas.
Explanation: Perimeter=4s, so s=48/4=12.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: perimeter of square; division; formulas.
Q261. In a right triangle, opposite=9 and hypotenuse=15. What is sin(θ)?
Correct Answer: B
Explanation: sin(θ)=opposite/hypotenuse=9/15, which simplifies to 3/5.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: right-triangle trig; ratios; fraction simplification.
Explanation: sin(θ)=opposite/hypotenuse=9/15, which simplifies to 3/5.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: right-triangle trig; ratios; fraction simplification.
Q262. In a right triangle, adjacent=12 and hypotenuse=13. What is cos(θ)?
Correct Answer: A
Explanation: cos(θ)=adjacent/hypotenuse=12/13.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: right-triangle trig; ratio definitions; simplifying fractions.
Explanation: cos(θ)=adjacent/hypotenuse=12/13.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: right-triangle trig; ratio definitions; simplifying fractions.
Q263. In a right triangle, opposite=5 and adjacent=12. What is tan(θ)?
Correct Answer: D
Explanation: tan(θ)=opposite/adjacent=5/12.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: right-triangle trig; ratios; division.
Explanation: tan(θ)=opposite/adjacent=5/12.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: right-triangle trig; ratios; division.
Q264. What is sin(30°)?
Correct Answer: A
Explanation: From a 30-60-90 triangle, sin(30°)=1/2.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: special angles; 30-60-90 triangle; trig values.
Explanation: From a 30-60-90 triangle, sin(30°)=1/2.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: special angles; 30-60-90 triangle; trig values.
Q265. What is sin(45°)?
Correct Answer: B
Explanation: From a 45-45-90 triangle, sin(45°)=√2/2.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: special angles; 45-45-90 triangle; trig values.
Explanation: From a 45-45-90 triangle, sin(45°)=√2/2.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: special angles; 45-45-90 triangle; trig values.
Q266. What is sin(60°)?
Correct Answer: A
Explanation: From a 30-60-90 triangle, sin(60°)=√3/2.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: special angles; 30-60-90 triangle; trig values.
Explanation: From a 30-60-90 triangle, sin(60°)=√3/2.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: special angles; 30-60-90 triangle; trig values.
Q267. If cos(θ)=3/5 and θ is acute, what is sin(θ)?
Correct Answer: D
Explanation: Use sin^2+cos^2=1: sin=√(1-(3/5)^2)=√(1-9/25)=√(16/25)=4/5 (positive for acute).
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: Pythagorean identity; square roots; sign by quadrant.
Explanation: Use sin^2+cos^2=1: sin=√(1-(3/5)^2)=√(1-9/25)=√(16/25)=4/5 (positive for acute).
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: Pythagorean identity; square roots; sign by quadrant.
Q268. If sin(θ)=5/13 and θ is acute, what is cos(θ)?
Correct Answer: A
Explanation: cos=√(1-sin^2)=√(1-25/169)=√(144/169)=12/13 (acute → positive).
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: Pythagorean identity; fraction arithmetic; square roots.
Explanation: cos=√(1-sin^2)=√(1-25/169)=√(144/169)=12/13 (acute → positive).
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: Pythagorean identity; fraction arithmetic; square roots.
Q269. A right triangle has hypotenuse 25 and one leg 7. What is the other leg?
Correct Answer: B
Explanation: Use c^2=a^2+b^2: b=√(25^2-7^2)=√(625-49)=√576=24.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: Pythagorean theorem; subtraction; square roots.
Explanation: Use c^2=a^2+b^2: b=√(25^2-7^2)=√(625-49)=√576=24.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: Pythagorean theorem; subtraction; square roots.
Q270. A right triangle has legs 8 and 15. What is the hypotenuse?
Correct Answer: A
Explanation: c=√(8^2+15^2)=√(64+225)=√289=17.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: Pythagorean theorem; square roots; integer triples.
Explanation: c=√(8^2+15^2)=√(64+225)=√289=17.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: Pythagorean theorem; square roots; integer triples.
Q271. A bag has 4 red, 3 blue, and 5 green marbles. What is P(not blue)?
Correct Answer: D
Explanation: Not blue means red or green: 4+5=9 out of 12. 9/12 simplifies to 3/4.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: basic probability; counting outcomes; simplifying fractions.
Explanation: Not blue means red or green: 4+5=9 out of 12. 9/12 simplifies to 3/4.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: basic probability; counting outcomes; simplifying fractions.
Q272. A fair die is rolled. What is the probability of rolling an even number?
Correct Answer: C
Explanation: Even outcomes are {2,4,6}: 3 favorable out of 6 total, so 3/6=1/2.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: probability; favorable/total; fraction simplification.
Explanation: Even outcomes are {2,4,6}: 3 favorable out of 6 total, so 3/6=1/2.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: probability; favorable/total; fraction simplification.
Q273. A coin is flipped 2 times. What is the probability of getting exactly 2 heads?
Correct Answer: B
Explanation: Outcomes are HH, HT, TH, TT (4 equally likely). Only HH works: 1/4.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: probability; sample space; multiplication principle.
Explanation: Outcomes are HH, HT, TH, TT (4 equally likely). Only HH works: 1/4.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: probability; sample space; multiplication principle.
Q274. What is the mean of 6, 9, 12, 15, 18?
Correct Answer: C
Explanation: Sum=6+9+12+15+18=60. Mean=60/5=12.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: mean; arithmetic; division.
Explanation: Sum=6+9+12+15+18=60. Mean=60/5=12.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: mean; arithmetic; division.
Q275. What is the median of 2, 7, 9, 10, 14, 18, 21?
Correct Answer: D
Explanation: With 7 values, the median is the 4th value when ordered, which is 10.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: median; ordering; position counting.
Explanation: With 7 values, the median is the 4th value when ordered, which is 10.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: median; ordering; position counting.
Q276. A set has values 4, 4, 5, 6, 6, 6, 9. What is the mode?
Correct Answer: A
Explanation: Mode is the most frequent value. 6 appears three times, more than any other.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: mode; frequency; interpreting data.
Explanation: Mode is the most frequent value. 6 appears three times, more than any other.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: mode; frequency; interpreting data.
Q277. If the mean of 5 numbers is 14, what is their total sum?
Correct Answer: B
Explanation: Mean = sum/5, so sum = 14×5 = 70.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: mean; inverse operations; multiplication.
Explanation: Mean = sum/5, so sum = 14×5 = 70.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: mean; inverse operations; multiplication.
Q278. If a data set has median 8, what does that tell you?
Correct Answer: A
Explanation: Median is the middle value; it splits ordered data so half are at or below it and half at or above it.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: median concept; ordering; data interpretation.
Explanation: Median is the middle value; it splits ordered data so half are at or below it and half at or above it.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: median concept; ordering; data interpretation.
Q279. A spinner has 8 equal sections labeled 1–8. What is P(landing on a prime)?
Correct Answer: D
Explanation: Primes among 1–8 are 2,3,5,7: 4 favorable out of 8 total, so 4/8=1/2.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: probability; identifying primes; simplifying fractions.
Explanation: Primes among 1–8 are 2,3,5,7: 4 favorable out of 8 total, so 4/8=1/2.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: probability; identifying primes; simplifying fractions.
Q280. Two fair dice are rolled. What is the probability the sum is 7?
Correct Answer: A
Explanation: There are 36 outcomes. Sum 7 occurs in 6 ways: (1,6)(2,5)(3,4)(4,3)(5,2)(6,1). 6/36=1/6.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: probability; counting outcomes; fractions.
Explanation: There are 36 outcomes. Sum 7 occurs in 6 ways: (1,6)(2,5)(3,4)(4,3)(5,2)(6,1). 6/36=1/6.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: probability; counting outcomes; fractions.
Q281. Solve for x: 3/5 = x/20
Correct Answer: B
Explanation: Cross-multiply: 3×20=5x → 60=5x → x=12.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: proportions; cross-multiplication; division.
Explanation: Cross-multiply: 3×20=5x → 60=5x → x=12.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: proportions; cross-multiplication; division.
Q282. An arithmetic sequence starts at 7 and has common difference 4. What is the 10th term?
Correct Answer: C
Explanation: a_n=a1+(n-1)d=7+9×4=7+36=43.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: arithmetic sequences; nth-term formula; substitution.
Explanation: a_n=a1+(n-1)d=7+9×4=7+36=43.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: arithmetic sequences; nth-term formula; substitution.
Q283. A geometric sequence has a1=3 and r=2. What is a5?
Correct Answer: D
Explanation: a5=3×2^4=3×16=48.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: geometric sequences; exponents; multiplication.
Explanation: a5=3×2^4=3×16=48.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: geometric sequences; exponents; multiplication.
Q284. Solve: 5x – 12 = 3x + 8
Correct Answer: C
Explanation: Subtract 3x: 2x-12=8. Add 12: 2x=20 → x=10.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: solving linear equations; combining like terms; inverse operations.
Explanation: Subtract 3x: 2x-12=8. Add 12: 2x=20 → x=10.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: solving linear equations; combining like terms; inverse operations.
Q285. Solve the inequality: 4x + 3 ≤ 19
Correct Answer: B
Explanation: Subtract 3: 4x≤16. Divide by 4 (positive): x≤4.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: linear inequalities; inverse operations; division.
Explanation: Subtract 3: 4x≤16. Divide by 4 (positive): x≤4.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: linear inequalities; inverse operations; division.
Q286. Solve: |x – 6| ≤ 3
Correct Answer: C
Explanation: |x-6|≤3 means x is within 3 of 6: 6-3 ≤ x ≤ 6+3 → 3≤x≤9.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: absolute value inequalities; intervals; number line distance.
Explanation: |x-6|≤3 means x is within 3 of 6: 6-3 ≤ x ≤ 6+3 → 3≤x≤9.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: absolute value inequalities; intervals; number line distance.
Q287. Solve: (x-2)(x+5) > 0
Correct Answer: D
Explanation: A product is positive when both factors have the same sign. That happens outside the roots -5 and 2.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: quadratic inequalities; sign analysis; factoring.
Explanation: A product is positive when both factors have the same sign. That happens outside the roots -5 and 2.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: quadratic inequalities; sign analysis; factoring.
Q288. A quantity increases by 20% then decreases by 10%. What is the net multiplier?
Correct Answer: C
Explanation: Successive multipliers: (1+0.20)(1-0.10)=1.2×0.9=1.08.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: percent change; multiplicative reasoning; order of operations.
Explanation: Successive multipliers: (1+0.20)(1-0.10)=1.2×0.9=1.08.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: percent change; multiplicative reasoning; order of operations.
Q289. If 60% of a number is 42, what is the number?
Correct Answer: B
Explanation: 0.60N=42 → N=42/0.60=70.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: percent equations; solving proportions; division.
Explanation: 0.60N=42 → N=42/0.60=70.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: percent equations; solving proportions; division.
Q290. Evaluate: | -8 – 5 |
Correct Answer: C
Explanation: Inside first: -8-5=-13, then | -13 | = 13.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: absolute value; subtraction; order of operations.
Explanation: Inside first: -8-5=-13, then | -13 | = 13.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: absolute value; subtraction; order of operations.
Q291. Simplify: (3 + 4i) + (5 – 2i)
Correct Answer: D
Explanation: Add real parts: 3+5=8 and imaginary parts: 4i+(-2i)=2i, giving 8+2i.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: complex addition; combining like terms; signed arithmetic.
Explanation: Add real parts: 3+5=8 and imaginary parts: 4i+(-2i)=2i, giving 8+2i.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: complex addition; combining like terms; signed arithmetic.
Q292. Simplify: (2 – 3i) + (-6 + i)
Correct Answer: C
Explanation: Real: 2+(-6)=-4. Imaginary: -3i+i=-2i. Result -4-2i.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: complex addition; integer arithmetic; combining like terms.
Explanation: Real: 2+(-6)=-4. Imaginary: -3i+i=-2i. Result -4-2i.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: complex addition; integer arithmetic; combining like terms.
Q293. Simplify: (1 + 2i)(3 – i)
Correct Answer: B
Explanation: FOIL: 1×3=3, 1×(-i)=-i, 2i×3=6i, 2i×(-i)=-2i^2=+2. Combine: (3+2)+( -i+6i)=5+5i.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: complex multiplication; distributive property; i² = -1.
Explanation: FOIL: 1×3=3, 1×(-i)=-i, 2i×3=6i, 2i×(-i)=-2i^2=+2. Combine: (3+2)+( -i+6i)=5+5i.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: complex multiplication; distributive property; i² = -1.
Q294. Rationalize: 9/(3√2)
Correct Answer: C
Explanation: First simplify 9/(3√2)=3/√2. Multiply by √2/√2 to get 3√2/2.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: rationalizing denominators; simplifying fractions; multiplying by 1.
Explanation: First simplify 9/(3√2)=3/√2. Multiply by √2/√2 to get 3√2/2.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: rationalizing denominators; simplifying fractions; multiplying by 1.
Q295. Find det([[2, 5], [3, -1]]).
Correct Answer: D
Explanation: For [[a,b],[c,d]], det=ad-bc. Here 2(-1)-5(3)=-2-15=-17.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: 2×2 determinants; multiplication; subtraction.
Explanation: For [[a,b],[c,d]], det=ad-bc. Here 2(-1)-5(3)=-2-15=-17.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: 2×2 determinants; multiplication; subtraction.
Q296. Find det([[-4, 2], [7, 3]]).
Correct Answer: C
Explanation: det=ad-bc=(-4)(3) – (2)(7) = -12-14 = -26.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: determinants; integer arithmetic; subtraction.
Explanation: det=ad-bc=(-4)(3) – (2)(7) = -12-14 = -26.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: determinants; integer arithmetic; subtraction.
Q297. Solve: x² – 16 = 0
Correct Answer: B
Explanation: x^2=16 so x=±4.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: difference of squares; square roots; solving equations.
Explanation: x^2=16 so x=±4.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: difference of squares; square roots; solving equations.
Q298. Simplify: (x² – 25)/(x – 5) for x ≠ 5
Correct Answer: C
Explanation: x^2-25=(x-5)(x+5). Cancel (x-5) to get x+5.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: factoring; simplifying rational expressions; domain restrictions.
Explanation: x^2-25=(x-5)(x+5). Cancel (x-5) to get x+5.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: factoring; simplifying rational expressions; domain restrictions.
Q299. Evaluate: log2(1/32)
Correct Answer: D
Explanation: 1/32 = 2^-5, so log2(1/32) = -5.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: logarithms; negative exponents; inverse operations.
Explanation: 1/32 = 2^-5, so log2(1/32) = -5.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: logarithms; negative exponents; inverse operations.
Q300. How many combinations are there when choosing 3 items from 8 (order does not matter)?
Correct Answer: C
Explanation: C(8,3)=8!/(3!5!) = (8×7×6)/(3×2×1)=56.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: combinations; factorials; simplifying fractions.
Explanation: C(8,3)=8!/(3!5!) = (8×7×6)/(3×2×1)=56.
Citation: ASVAB content domain — Mathematics Knowledge; underlying principles: combinations; factorials; simplifying fractions.
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