ASVAB math practice: Math Knowledge

Three angles of a quadrilateral measure 85°, 95° and 110°. What is the fourth angle?

1. 110°
   110° is 180° − 70°, the supplement of the missing angle.
2. 250°
   250° uses 540°, the angle sum of a pentagon, instead of 360°.
3. 70°
   The angles of a quadrilateral sum to 360°, so the fourth is 360° − (85° + 95° + 110°) = 70°.
4. 90°
   90° assumes the missing angle is a right angle; nothing in the question says so.

ID 813222 · Report a problem

√36 + √64 = ?

1. 14
   Take each root first: √36 = 6 and √64 = 8, so the sum is 14.
2. 48
   48 multiplies the roots, 6 × 8, instead of adding them.
3. 10
   10 adds under one root, √(36 + 64) = √100; √a + √b is not √(a + b).
4. 50
   50 halves 36 + 64 = 100 instead of taking square roots.

ID 857050 · Report a problem

(2x³y⁴)(3xy²)² = ?

1. 18x⁵y⁸
   First (3xy²)² = 9x²y⁴; then 2 × 9 = 18, x³⁺² = x⁵ and y⁴⁺⁴ = y⁸, giving 18x⁵y⁸.
2. 6x⁴y⁶
   6x⁴y⁶ ignores the square and multiplies the two factors as written.
3. 6x⁵y⁸
   6x⁵y⁸ squares the variables but not the coefficient 3; 3² = 9.
4. 18x⁶y¹⁶
   18x⁶y¹⁶ multiplies the exponents of like bases instead of adding them.

ID 857285 · Report a problem

√200 lies between which two consecutive whole numbers?

1. 20 and 21
   20 and 21 brackets √400, not √200.
2. 13 and 14
   13 and 14 stops one square too early; 14² = 196 is still below 200.
3. 14 and 15
   14² = 196 and 15² = 225, and 200 lies between them, so √200 is between 14 and 15.
4. 99 and 100
   99 and 100 halves 200 instead of taking its square root.

ID 857287 · Report a problem

(1/2) ÷ (3/4) = ?

1. 3/2
   3/2 is the reciprocal of the answer; it divides 3/4 by 1/2.
2. 3/8
   3/8 multiplies straight across, 1/2 × 3/4, without flipping the divisor.
3. 2/3
   Multiply by the reciprocal of the divisor: 1/2 × 4/3 = 4/6 = 2/3.
4. 8/3
   8/3 flips both fractions, 2/1 × 4/3.

ID 857290 · Report a problem

(2/3)⁻² = ?

1. 9/4
   A negative exponent means the reciprocal: (2/3)⁻² = (3/2)² = 9/4.
2. 4/9
   4/9 squares 2/3 but forgets to take the reciprocal.
3. −4/3
   −4/3 multiplies the base by −2, treating the exponent as a factor.
4. −4/9
   −4/9 squares the base and makes the result negative; a negative exponent does not change the sign.

ID 857395 · Report a problem

How many prime numbers are between 30 and 50?

1. 6
   6 counts 49 as prime, but 49 = 7 × 7.
2. 5
   The odd numbers 33, 35, 39, 45, 49 all have factors (3 × 11, 5 × 7, 3 × 13, 3² × 5, 7²), leaving 31, 37, 41, 43, 47: five primes.
3. 7
   7 counts both 49 = 7 × 7 and 39 = 3 × 13 as primes.
4. 10
   10 counts every odd number from 31 to 49; being odd does not make a number prime.

ID 858205 · Report a problem

Using F = (9/5)C + 32, what is 90°C in degrees Fahrenheit?

1. 82°F
   82°F multiplies by 5/9, the factor from the reverse formula, then adds 32 (50 + 32).
2. 194°F
   (9/5) × 90 = 162, and 162 + 32 = 194°F.
3. 162°F
   162°F multiplies by 9/5 but forgets to add 32.
4. 122°F
   122°F adds 32 to 90 without the 9/5 factor.

ID 858237 · Report a problem

Which is closest to (0.49 × 802) ÷ 19.8?

1. 0.2
   0.2 shifts the decimal point two places, treating the product as about 4.
2. 20
   Round to friendly numbers: 0.5 × 800 = 400, and 400 ÷ 20 = 20.
3. 200
   200 shifts the decimal point the other way, dividing 400 by 2 instead of by 20.
4. 2
   2 shifts the decimal point one place, reading 0.49 as about 0.05.

ID 858470 · Report a problem

Which of the following is the smallest?

1. 3/8
   3/8 = 0.375, which is larger than 0.36.
2. 37%
   37% = 0.37, which is larger than 0.36.
3. √0.16
   √0.16 = 0.4 (because 0.4² = 0.16); reading it as 0.04 makes it look the smallest.
4. 0.36
   As decimals the options are 0.36, 0.375, 0.37 and 0.4, so 0.36 is the smallest.

ID 858484 · Report a problem

What is 2/5 of 3/4 of 120?

1. 36
   "Of" means multiply: 3/4 × 120 = 90, then 2/5 × 90 = 36.
2. 90
   90 is 3/4 of 120; the 2/5 step is missing.
3. 138
   138 adds the fractions (2/5 + 3/4 = 23/20) and takes 23/20 of 120 instead of multiplying.
4. 48
   48 is 2/5 of 120; the 3/4 has been skipped.

ID 858515 · Report a problem

Calculate (6 × 10⁴)(3 × 10⁻²) and write the result in scientific notation.

1. 1.8 × 10⁻⁸
   1.8 × 10⁻⁸ multiplies the exponents (4 × −2) instead of adding them.
2. 1.8 × 10²
   1.8 × 10² turns 18 into 1.8 but forgets to raise the exponent by one.
3. 9 × 10²
   9 × 10² adds the coefficients 6 + 3 instead of multiplying them.
4. 1.8 × 10³
   Multiply the coefficients (6 × 3 = 18) and add the exponents (4 − 2 = 2): 18 × 10² = 1.8 × 10³.

ID 970046 · Report a problem

What is the volume of a cylinder with radius 3 and height 7?

1. 252π
   252π uses the diameter 6 in place of the radius 3.
2. 63π
   V = πr²h = π × 3² × 7 = 63π.
3. 21π
   21π forgets to square the radius (π × 3 × 7).
4. 42π
   42π is 2πrh, the area of the curved side, not the volume.

ID 1821340 · Report a problem

√144 + √25 ÷ √(1/4) = ?

1. 32
   32 forgets the root of 1/4 and divides by 1/4: 12 + 20.
2. 14.5
   14.5 multiplies 5 by 1/2 instead of dividing (12 + 2.5).
3. 34
   34 adds first, (12 + 5) ÷ 1/2, breaking the order of operations.
4. 22
   The roots are 12, 5 and 1/2; division comes before addition, so 12 + 5 ÷ 1/2 = 12 + 10 = 22.

ID 813005 · Report a problem

If y = 3x − 7, which expression gives x in terms of y?

1. 3y + 7
   3y + 7 multiplies by 3 where it should divide; x is multiplied by 3 in the equation.
2. y/3 + 7
   y/3 + 7 divides only y by 3; the 7 must be added before dividing, so it is divided too.
3. (y − 7)/3
   (y − 7)/3 undoes the −7 with the wrong sign; to cancel −7, add 7.
4. (y + 7)/3
   Add 7 to both sides (y + 7 = 3x), then divide by 3: x = (y + 7)/3.

ID 813661 · Report a problem

If x < 0, which of the following must be positive?

1. x²
   A negative number times itself is positive, so x² > 0 for every x < 0.
2. x³
   x³ is an odd power, which keeps the negative sign.
3. 2x
   2x is twice a negative number, so it is still negative.
4. −x²
   −x² is the negative of the positive number x², so it is negative; it is not (−x)².

ID 857685 · Report a problem

|3 − 8| − |−4| =

1. −9
   −9 drops both absolute values: −5 − 4.
2. 9
   9 drops the bars on |−4| and subtracts a negative: 5 − (−4).
3. 1
   Work inside the bars first: |3 − 8| = |−5| = 5 and |−4| = 4, so 5 − 4 = 1.
4. −1
   −1 keeps 3 − 8 as −5 but turns |−4| into +4: −5 + 4.

ID 1897935 · Report a problem

Which of the following is a factor of x² − 5x − 14?

1. x − 14
   x − 14 uses the constant term as a root; 14² − 5 × 14 − 14 = 112, not 0.
2. x − 7
   x² − 5x − 14 = (x − 7)(x + 2), because −7 × 2 = −14 and −7 + 2 = −5; so x − 7 is a factor.
3. x + 7
   x + 7 has the sign of the 7 reversed; (x + 7)(x − 2) = x² + 5x − 14.
4. x − 2
   x − 2 has the sign of the 2 reversed; (x − 7)(x − 2) = x² − 9x + 14.

ID 9410005 · Report a problem