# Free STAAR Grade 6 Mathematics Practice Test Questions

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1. Which expression best shows the prime factorization of 750?
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a. 2 x 3 x 5^{3}

b. 2 x 3 x 5^{2}

c. 2 x 3 x 5 x 25

d. 2 x 3 x 5^{2}x 25

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2. Enrique used a formula to find the total cost, in dollars, for repairs he and his helper, Jenny, made to a furnace. The expression below shows the formula he used, with 4 being the number of hours he worked on the furnace and 2 being the number of hours Jenny worked on the furnace.
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20+35(4+2)+47

**What is the total cost for repairing the furnace?
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a. $189

b. $269

c. $277

d. $377

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3. At the middle school Vanessa attends, there are 240 Grade 6 students, 210 Grade 7 students, and 200 Grade 8 students. Which ratio best compares the number of students in Grade 8 to the number of students in Grade 6 at Vanessa's school?
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a. 5 : 6

b. 5 : 11

c. 6 : 5

d. 7 : 8

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4. A trash company charges a fee of $80 to haul off a load of trash. There is also a charge of $0.05 per mile the load must be hauled. Which equation can be used to find c, the cost for hauling a load of trash m miles?
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a. 80(*m*+0.05)

b. 0.05(*m*+80)

c. 80*m*+ 0.05

d. 0.05*m*+80

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5. Omar drew a circle on paper by carefully tracing completely around the outside of a CD from a computer game. He measured across the center of the CD and found the distance to be 12 centimeters. Which expression can be used to find the distance, in centimeters, around the circle Omar made?
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a. 12(π)

b. 2(12)(π)

c. (12x2)(π)

d. 2(π x12)

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6. Stephen researched the topic of solar-powered lights for his science project. He exposed 10 new solar lights to five hours of sunlight. He recorded the number of minutes each light continued to shine after dark in the list below.**

63, 67, 73, 75, 80, 91, 63, 72, 79, 87

**Which of these numbers is the mean of the number of minutes in Stephen's list?
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a. 28

b. 63

c. 74

d. 75

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7. Petra installed 10 light fixtures at a new warehouse that was being built. Each of the fixtures required 3 light bulbs. The bulbs come in packages of 5 and cost $8 per package. What was the total cost for the bulbs required for all of the fixtures Petra installed at the warehouse?
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a. $16

b. $48

c. $120

d. $240

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8. Nadia is working summer jobs. She earns $5 for every dog she walks, $2 for bringing back a trashcan, $1 for checking the mail, and $5 for watering the flowers. Nadia walks 3 dogs, brings back 5 trashcans, checks the mail for 10 neighbors, and waters the flowers at 6 houses. Which expression can be used to find out how much money Nadia earned?
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a. $2(5) +$6(10) + $1

b. $10(6) + $1 + $5

c. $5(3+6) + $2(5) + $1(10)

d. $15 + $10 + $16

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9. A club is making necklaces in school colors. They plan to use an equal number of blue beads and silver beads on each necklace. The blue beads come in bags of 60 and the silver beads come in bags of 80. What is the smallest number of bags of each color the club can purchase to have an equal number of each color bead with no beads left when the necklaces are finished?
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a. 3 bags of blue and 4 bags of silver

b. 4 bags of blue and 3 bags of silver

c. 40 bags of blue and 30 bags of silver

d. 80 bags of blue and 60 bags of silver

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10. Alma collected coins. In the bag where she kept only dimes, she had dimes from four different years. She had 20 dimes minted in 1942, 30 minted in 1943, 40 minted in 1944, and 10 minted in 1945. If Alma reached into the bag without looking and took a dime, what is the probability that she took a dime minted in 1945?
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a. ^{2} / _{5}

b. ^{3} / _{10}

c. ^{1} / _{5}

d. ^{1} / _{} 10

## Grade 6 Mathematics Answer Key

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1. Answer: A
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There is more than one way to solve this problem. One method is to use the fact that the number ends in 0. This means 10 is a factor. So, 10 x 75 = 750. The factor 10 has prime factors of 2 and 5. The factor 75 has factors of 3 and 25 and the 25 has two factors of 5. Putting the prime factors in order, least to greatest, and showing the three factors of 5 with an exponent of 3 gives us answer A: 2 x 3 x 5

^{3}.

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2. Answer: C
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To solve this formula, follow the order of operations. First, add what is in the parenthesis, 4 + 2, to get 6. Then, multiply the 6 by 35 to get 210. Last, we should add 20 + 210 + 47 to get 277.

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3. Answer: A
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One way to answer this question is to name the ratio: 200 to 240, then write the ratio in simplest terms by dividing both terms by the greatest common factor, 40, to get 5 to 6. It should be noted that the number of Grade 7 students is not important for this problem. Also, the order of the ratio matters. Since it asks for the ratio using the number of Grade 8 students first, the ratio is 200 to 240 and not the other way around.

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4. Answer: D
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The amount charged for miles hauled will require us to multiply the number of miles by $0.05. The charge for each load of $80 is not changed by the number of miles hauled. That will be added to the amount charged for miles hauled. So, the equation needs to show 0.05 times miles plus 80, or

*c*=0.05

*m*+80.

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5. Answer: A
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The distance across the center of the circle, 12 centimeters, is the diameter of the circle. The distance around the circle, drawn by Omar, is the circumference of that circle. The formula for finding the circumference of a circle is: C= πd. The expression that can be used substitutes the 12 for d and we get 12π.

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6.Answer: D
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The mean is just the average. To calculate this, find the total of all 10 numbers by adding. Then, divide that total by 10 because that is the number of data points. The total is 750, so the mean of this group of numbers is 75.

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7. Answer: B
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To answer this question, find the total number of bulbs required by multiplying 10 by 3. The number of packages of bulbs required can be found by dividing this total number of bulbs, 30, by 5, to find that 6 packages are needed. Then, multiplying 6 by the cost per package, 8, we find that the total cost for all the bulbs needed was $48.

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8. Answer: C
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Since she earns $5 for walking dogs and watering flowers, this term can be combined to simplify the equation. The other terms for bringing back trashcans and checking the mail are straight multiplication.

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9. Answer: B
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There is more than one way to solve this problem. One method is to find the least common multiple of 60 and 80. To do this, first find the prime factors of each number.

60 = 2 x 2 x 3 x 5

80 = 2 x 2 x 2 x 2 x 5

The factors common to 60 and 80 are 2, 2, and 5. The factors that are not common to both numbers are two factors of 2 from 80 and a factor of 3 from 60. To find the least common multiple, multiply all the factors without repetition. That is, multiply the common factors (2, 2, and 5) and the other factors (2, 2, and 3) together:

2 x 2 x 2 x 2 x 3 x 5 = 240

240 is the least common multiple. This is the total number of beads needed of each color. To find how many bags the club will need to purchase, divide this total by the number of beads that come in each bag for each color bead. 240 x 60 = 4 (4 bags of blue). 240 x 80 = 3 (3 bags of silver).

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10. Answer: D
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By adding all of the dimes, we find that there are a total of 100 dimes in the bag. 10 of them were minted in 1945. The probability, then, of choosing a dime minted in 1945 is 10 out of 100, which is equivalent to the fraction

^{1}/

_{10}.

by Enoch Morrison

Last Updated: 07/05/2018