Test Name Here
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.