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FAST Math Grade 6 study materials
FAST Math Grade 6 study resources

FAST Math Grade 6 practice questions

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Question 1Rational numbers and operations

Which symbol correctly compares the rational numbers to make a true statement: -3 ___ -7?

  1. <
  2. =
  3. > Correct answer.
  4. cannot be determined

Explanation

On a number line, numbers farther to the right are greater. Since -3 is to the right of -7, -3 is greater than -7, so -3 > -7. With negatives, the number closer to zero is larger.

Question 2Rational numbers and operations

Which list shows the numbers ordered from least to greatest: 0.5, -2, 3/4, -1?

  1. -1, -2, 0.5, 3/4
  2. -2, -1, 0.5, 3/4 Correct answer.
  3. 3/4, 0.5, -1, -2
  4. -2, -1, 3/4, 0.5

Explanation

Negative numbers are less than positive numbers, and -2 is less than -1. Then 0.5 = 0.50 and 3/4 = 0.75, so 0.5 comes before 3/4. The correct order is -2, -1, 0.5, 3/4.

Question 3Rational numbers and operations

What is the value of |-12|?

  1. -12
  2. 0
  3. 24
  4. 12 Correct answer.

Explanation

Absolute value is the distance a number is from zero on the number line, and distance is always non-negative. The number -12 is 12 units from zero, so |-12| = 12.

Question 4Rational numbers and operations

A diver is at -30 feet and a hawk is at 18 feet relative to sea level. Which animal is farther from sea level?

  1. The hawk, because 18 is positive
  2. The diver, because |-30| = 30 is greater than |18| = 18 Correct answer.
  3. They are the same distance from sea level
  4. The diver, because -30 is less than 18

Explanation

Distance from sea level is the absolute value of each position. |-30| = 30 and |18| = 18, and 30 > 18, so the diver is farther from sea level. Comparing absolute values tells us distance regardless of sign.

Question 5Rational numbers and operations

What is the product of 3.4 and 2.5?

  1. 85
  2. 8.5 Correct answer.
  3. 0.85
  4. 8.9

Explanation

Multiply 34 x 25 = 850, then place the decimal point. There are two decimal places total (one in each factor), so the answer is 8.50, which equals 8.5.

Question 6Ratios, expressions and equations

A bag has 12 red marbles and 18 blue marbles. What is the ratio of red marbles to blue marbles in simplest form?

  1. 12:18
  2. 2:3 Correct answer.
  3. 3:2
  4. 2:5

Explanation

Write the ratio 12:18 and divide both parts by their GCF, 6: 12 divided by 6 = 2 and 18 divided by 6 = 3, giving 2:3.

Question 7Ratios, expressions and equations

A car travels 180 miles in 3 hours at a constant speed. What is the unit rate in miles per hour?

  1. 60 miles per hour Correct answer.
  2. 540 miles per hour
  3. 3 miles per hour
  4. 90 miles per hour

Explanation

A unit rate is the amount per one unit. Divide miles by hours: 180 divided by 3 = 60 miles per hour.

Question 8Ratios, expressions and equations

If 3 pounds of grapes cost $4.50, what is the price per pound?

  1. $1.50 Correct answer.
  2. $13.50
  3. $0.67
  4. $1.35

Explanation

A unit price is cost per one pound. Divide total cost by pounds: 4.50 divided by 3 = $1.50 per pound.

Question 9Ratios, expressions and equations

In a recipe, the ratio of flour to sugar is 3:5. If 12 cups of flour are used, how many cups of sugar are needed?

  1. 10
  2. 18
  3. 36
  4. 20 Correct answer.

Explanation

Set up equivalent ratios: 3/5 = 12/x. Since 12 is 3 times 4, multiply 5 by 4 to get 20 cups of sugar.

Question 10Ratios, expressions and equations

What is 20% of 80?

  1. 160
  2. 4
  3. 100
  4. 16 Correct answer.

Explanation

Convert the percent to a decimal: 20% = 0.20. Then multiply: 0.20 x 80 = 16. You can also find 1/5 of 80, which is 16.

Question 11Geometric measurement and coordinate reasoning

What is the area of a triangle with a base of 10 units and a height of 6 units?

  1. 30 square units Correct answer.
  2. 60 square units
  3. 16 square units
  4. 32 square units

Explanation

The area of a triangle is one-half the base times the height: A = (1/2)(10)(6) = 30 square units.

Question 12Geometric measurement and coordinate reasoning

What is the area of a parallelogram with a base of 8 cm and a height of 5 cm?

  1. 40 square cm Correct answer.
  2. 13 square cm
  3. 20 square cm
  4. 26 square cm

Explanation

The area of a parallelogram is base times height: A = 8 x 5 = 40 square cm. The height must be perpendicular to the base.

Question 13Geometric measurement and coordinate reasoning

On the coordinate plane, what is the distance between the points (2, 5) and (2, -3)?

  1. 2 units
  2. 3 units
  3. 13 units
  4. 8 units Correct answer.

Explanation

The points share the same x-coordinate, so the distance is the difference in y-values: |5 - (-3)| = |8| = 8 units.

Question 14Geometric measurement and coordinate reasoning

In which quadrant is the point (-4, 3) located?

  1. Quadrant I
  2. Quadrant II Correct answer.
  3. Quadrant III
  4. Quadrant IV

Explanation

A negative x-coordinate and positive y-coordinate place a point in the upper-left region, which is Quadrant II.

Question 15Geometric measurement and coordinate reasoning

What is the area of a trapezoid with parallel side lengths of 6 cm and 10 cm and a height of 4 cm?

  1. 32 square cm Correct answer.
  2. 60 square cm
  3. 20 square cm
  4. 40 square cm

Explanation

The trapezoid area formula is one-half the sum of the parallel sides times the height: A = (1/2)(6 + 10)(4) = (1/2)(16)(4) = 32 square cm.

Question 16Data, sampling and probability

Which of the following is a statistical question?

  1. How many minutes did I spend on homework last night?
  2. How many minutes do students in my class spend on homework each night? Correct answer.
  3. What is the capital of Florida?
  4. How many days are in a week?

Explanation

A statistical question anticipates variability in the data collected to answer it. Asking about all students' homework times produces a range of answers, making it statistical.

Question 17Data, sampling and probability

What is the mean of the data set 4, 7, 9, 12, and 8?

  1. 9
  2. 8 Correct answer.
  3. 7
  4. 40

Explanation

The mean is the sum divided by the count: (4 + 7 + 9 + 12 + 8) = 40, and 40 divided by 5 = 8.

Question 18Data, sampling and probability

What is the median of the data set 3, 5, 8, 9, 11, and 14?

  1. 8
  2. 8.5 Correct answer.
  3. 9
  4. 11

Explanation

With an even number of values, the median is the mean of the two middle numbers. The middle values are 8 and 9, so the median is (8 + 9)/2 = 8.5.

Question 19Data, sampling and probability

What is the mode of the data set 5, 3, 8, 3, 9, 3, and 6?

  1. 8
  2. 3 Correct answer.
  3. 5
  4. 6

Explanation

The mode is the value that appears most often. The number 3 appears three times, more than any other value, so the mode is 3.

Question 20Data, sampling and probability

What is the range of the data set 14, 6, 9, 3, and 11?

  1. 8
  2. 9
  3. 17
  4. 11 Correct answer.

Explanation

The range is the difference between the greatest and least values: 14 - 3 = 11. It measures how spread out the data is.

Question 21Rational numbers and operations

What is 8.4 divided by 0.4?

  1. 2.1
  2. 210
  3. 21 Correct answer.
  4. 0.21

Explanation

Multiply both numbers by 10 to make the divisor a whole number: 84 divided by 4 = 21. Dividing by a number less than 1 gives a quotient larger than the dividend, which makes sense here.

Question 22Rational numbers and operations

What is the product of 2/3 and 3/5?

  1. 5/8
  2. 2/5 Correct answer.
  3. 6/15
  4. 1/5

Explanation

Multiply numerators and denominators: (2 x 3)/(3 x 5) = 6/15. Simplify by dividing top and bottom by 3 to get 2/5.

Question 23Rational numbers and operations

What is 3/4 divided by 2/3?

  1. 1/2
  2. 6/12
  3. 9/8 Correct answer.
  4. 8/9

Explanation

To divide by a fraction, multiply by its reciprocal: 3/4 x 3/2 = 9/8. The reciprocal of 2/3 is 3/2.

Question 24Rational numbers and operations

A recipe needs 2/3 cup of flour per batch. How many batches can be made with 4 cups of flour?

  1. 8/3
  2. 2 2/3
  3. 12
  4. 6 Correct answer.

Explanation

Divide total flour by flour per batch: 4 divided by 2/3 = 4 x 3/2 = 12/2 = 6 batches. Dividing by a fraction less than 1 increases the count.

Question 25Rational numbers and operations

Maria buys 3.5 pounds of apples at $1.20 per pound and 2 pounds of grapes at $2.50 per pound. What is the total cost?

  1. $8.70
  2. $7.70
  3. $9.20 Correct answer.
  4. $4.20

Explanation

Apples cost 3.5 x 1.20 = $4.20 and grapes cost 2 x 2.50 = $5.00. Adding gives 4.20 + 5.00 = $9.20 total.

Question 26Rational numbers and operations

What is the greatest common factor (GCF) of 24 and 36?

  1. 6
  2. 12 Correct answer.
  3. 72
  4. 4

Explanation

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 and of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The greatest factor they share is 12.

Question 27Rational numbers and operations

What is the least common multiple (LCM) of 6 and 8?

  1. 48
  2. 2
  3. 24 Correct answer.
  4. 14

Explanation

Multiples of 6 are 6, 12, 18, 24 and multiples of 8 are 8, 16, 24. The smallest multiple they share is 24.

Question 28Rational numbers and operations

What is the value of 2 cubed times 3 squared, written as 2^3 x 3^2?

  1. 36
  2. 30
  3. 48
  4. 72 Correct answer.

Explanation

Evaluate each power first: 2^3 = 8 and 3^2 = 9. Then multiply: 8 x 9 = 72.

Question 29Rational numbers and operations

Which expression shows 60 written as a product of prime factors using exponents?

  1. 2^2 x 3 x 5 Correct answer.
  2. 2 x 3 x 10
  3. 4 x 15
  4. 2^2 x 15

Explanation

Factor 60 into primes: 60 = 4 x 15 = (2 x 2) x (3 x 5) = 2^2 x 3 x 5. All factors must be prime numbers.

Question 30Rational numbers and operations

The mixed number 1 5/8 is equivalent to which decimal?

  1. 1.625 Correct answer.
  2. 1.58
  3. 1.85
  4. 1.5625

Explanation

Convert the fraction: 5/8 = 0.625 because 5 divided by 8 = 0.625. Adding the whole number gives 1 + 0.625 = 1.625.

Question 31Rational numbers and operations

What is 3/5 written as a percent?

  1. 35%
  2. 60% Correct answer.
  3. 53%
  4. 6%

Explanation

Divide to convert: 3 divided by 5 = 0.6, and 0.6 = 60%. A percent means parts per hundred, so 0.6 = 60/100 = 60%.

Question 32Rational numbers and operations

What is the sum of the integers -5 and 8?

  1. 3 Correct answer.
  2. -3
  3. 13
  4. -13

Explanation

Adding integers with different signs, subtract the smaller absolute value from the larger: 8 - 5 = 3, and keep the sign of the larger absolute value (positive). So -5 + 8 = 3.

Question 33Rational numbers and operations

What is the product of the integers -4 and 6?

  1. -24 Correct answer.
  2. 24
  3. -10
  4. 2

Explanation

When multiplying two integers with different signs, the product is negative. Multiply the absolute values: 4 x 6 = 24, then apply the negative sign to get -24.

Question 34Rational numbers and operations

The temperature was -3 degrees at 6 a.m. and rose 10 degrees by noon. What was the temperature at noon?

  1. 7 degrees Correct answer.
  2. -13 degrees
  3. 13 degrees
  4. -7 degrees

Explanation

A rise in temperature means addition: -3 + 10 = 7 degrees. Since 10 is larger than 3 and positive, the result is positive 7.

Question 35Rational numbers and operations

What is the value of 2 1/4 multiplied by 1 1/3?

  1. 2 1/12
  2. 3 Correct answer.
  3. 3 1/3
  4. 2 1/4

Explanation

Convert to improper fractions: 2 1/4 = 9/4 and 1 1/3 = 4/3. Multiply: (9 x 4)/(4 x 3) = 36/12 = 3.

Question 36Rational numbers and operations

What is 4 1/2 divided by 3/4?

  1. 3 3/8
  2. 1 1/2
  3. 6 Correct answer.
  4. 3 1/3

Explanation

Convert 4 1/2 to 9/2, then multiply by the reciprocal of 3/4: 9/2 x 4/3 = 36/6 = 6.

Question 37Rational numbers and operations

Which decimal is equivalent to the fraction 7/20?

  1. 0.72
  2. 0.35 Correct answer.
  3. 0.27
  4. 3.5

Explanation

Convert to an equivalent fraction with denominator 100: 7/20 = 35/100 = 0.35. Alternatively, 7 divided by 20 = 0.35.

Question 38Rational numbers and operations

What is the value of 5.6 plus 3.45?

  1. 9.05 Correct answer.
  2. 8.01
  3. 9.5
  4. 8.15

Explanation

Line up the decimal points and add: 5.60 + 3.45 = 9.05. Writing 5.6 as 5.60 helps align the place values.

Question 39Rational numbers and operations

On a number line, which number is located exactly halfway between -6 and 2?

  1. -2 Correct answer.
  2. -4
  3. -1
  4. 0

Explanation

The midpoint is the average of the two values: (-6 + 2)/2 = -4/2 = -2. The number -2 sits exactly halfway between -6 and 2.

Question 40Rational numbers and operations

Rewrite the sum 18 + 24 as the greatest common factor multiplied by the sum of two whole numbers.

  1. 6(3 + 4) Correct answer.
  2. 2(9 + 12)
  3. 3(6 + 8)
  4. 6(2 + 4)

Explanation

The GCF of 18 and 24 is 6. Factor it out: 18 = 6 x 3 and 24 = 6 x 4, so 18 + 24 = 6(3 + 4). Using the greatest common factor gives the simplest form.

Question 41Rational numbers and operations

What is the difference -2 minus 5?

  1. 3
  2. -7 Correct answer.
  3. 7
  4. -3

Explanation

Subtracting 5 is the same as adding -5: -2 + (-5) = -7. Both numbers are negative, so you add their absolute values and keep the negative sign.

Question 42Rational numbers and operations

What is -18 divided by 3?

  1. 6
  2. -15
  3. -21
  4. -6 Correct answer.

Explanation

A negative divided by a positive gives a negative quotient. Divide the absolute values: 18 divided by 3 = 6, then apply the negative sign to get -6.

Question 43Rational numbers and operations

What is the value of |-8| + |3|?

  1. -11
  2. 5
  3. 11 Correct answer.
  4. -5

Explanation

Find each absolute value first: |-8| = 8 and |3| = 3. Then add: 8 + 3 = 11. Absolute values are always non-negative.

Question 44Rational numbers and operations

What is the value of 4 cubed, written as 4^3?

  1. 12
  2. 16
  3. 43
  4. 64 Correct answer.

Explanation

An exponent of 3 means multiply the base by itself three times: 4 x 4 x 4 = 64. The exponent tells how many factors of 4 to use.

Question 45Rational numbers and operations

What is the greatest common factor of 16 and 40?

  1. 4
  2. 8 Correct answer.
  3. 80
  4. 16

Explanation

The factors of 16 are 1, 2, 4, 8, 16 and of 40 are 1, 2, 4, 5, 8, 10, 20, 40. The greatest factor they share is 8.

Question 46Rational numbers and operations

What is the least common multiple of 9 and 12?

  1. 36 Correct answer.
  2. 108
  3. 3
  4. 21

Explanation

Multiples of 9 are 9, 18, 27, 36 and multiples of 12 are 12, 24, 36. The smallest multiple shared by both is 36.

Question 47Rational numbers and operations

Which decimal is equivalent to 1/8?

  1. 0.18
  2. 0.8
  3. 1.8
  4. 0.125 Correct answer.

Explanation

Divide 1 by 8: 1 divided by 8 = 0.125. This is a terminating decimal because 8 is a product of only 2s.

Question 48Rational numbers and operations

A scientist records water levels of -2.5 cm, 1.8 cm, and -0.6 cm. What is the sum of these measurements?

  1. -4.9 cm
  2. 4.9 cm
  3. 1.3 cm
  4. -1.3 cm Correct answer.

Explanation

Add step by step: -2.5 + 1.8 = -0.7, then -0.7 + (-0.6) = -1.3 cm. Combining the negatives and positive gives a negative total.

Question 49Rational numbers and operations

What is the product of 0.25 and 0.4?

  1. 1.0
  2. 0.01
  3. 10
  4. 0.1 Correct answer.

Explanation

Multiply 25 x 4 = 100, then count three decimal places (two in 0.25, one in 0.4): 0.100, which equals 0.1.

Question 50Rational numbers and operations

What is 6.3 divided by 0.7?

  1. 0.9
  2. 90
  3. 9 Correct answer.
  4. 0.09

Explanation

Multiply both numbers by 10: 63 divided by 7 = 9. Making the divisor a whole number keeps the quotient the same.