Practice Test 6 - 5th Grade Math

20 questions. Answer them in any order, then submit to see your score and every explanation.

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1. A solid is made of unit cubes, and there are no hidden cubes. You can find the volume by counting cubes. The solid has 3 layers: - Bottom layer: 5 cubes in a row - Middle layer: 5 cubes in a row directly on top of the bottom layer - Top layer: 2 cubes in a row directly on top of the leftmost 2 cubes of the middle layer Which counting method is correct for finding the volume?
2. A factory produces 4,284 toys in 6 days. If they produce the same number of toys each day, and each day's production is packaged into boxes of 34 toys each, how many boxes are filled each day?
3. A right rectangular prism is a stackable drawer with length 4 ft, width 3 ft, and height 5 ft. The base is the 4 ft by 3 ft rectangle, and the height is 5 ft. The volume formula should match the number of 1-foot cubes that would fill it. How does the base area help find volume?
4. A class is counting markers. The total is represented by $[15 + 5] \times 4$. What is the value of $[15 + 5] \times 4$?
5. A full tank of gas is one whole tank. A scooter used $\tfrac{2}{3}$ of a tank during the week. If $\tfrac{5}{6}$ of a tank was in the scooter at the start of the week, what fraction of a tank was left at the end of the week?
6. The company plots this schedule on a coordinate plane where x represents the day number and y represents which pool is checked (A=1, B=2, C=3). On Day 12, multiple pools are checked. Which points represent Day 12's activities?
7. Examine the figure showing three different rectangular prisms, all with the same volume of 24 cubic units. Each prism is made of unit cubes. Based on their dimensions shown, which statement correctly explains how different dimensions can yield the same volume?
8. A science club has $\tfrac{1}{4}$ of a bottle of colored water. They split that amount equally among 3 small containers. Picture an area model: a whole bottle is divided into 4 equal parts, and then one of those parts is divided into 3 equal smaller parts. Dividing a fraction by a whole number creates smaller equal parts. What is the result of $\tfrac{1}{4} \div 3$?
9. If Maya follows her budget exactly, how many weeks will it take her to save enough money for the bike?
10. Alex has $\frac{1}{15}$ liter of liquid medicine that needs to be divided equally into 5 doses. After preparing the doses, what volume of medicine will each dose contain?
11. A ribbon is cut from the same whole roll of ribbon (the whole roll is the same length each time). Jada cut off $1\tfrac{1}{2}$ yards, then cut off $\tfrac{3}{4}$ yard more. She uses equivalent fractions to combine them: $\tfrac{1}{2}=\tfrac{2}{4}$. What is the total length of ribbon she cut?
12. A hiker walked $5.08$ km on Monday and $3.90$ km on Tuesday. To find how much farther Monday was, subtract by aligning decimals: $5.08 - 3.90$. What does the difference represent, and what is its value? (Decimal operations rely on place value understanding and correct alignment of place values.)
13. The line plot shows the weight of each kitten at an animal shelter. What is the combined weight, in pounds, of the two heaviest kittens?
14. One whole batch of trail mix is the same-sized whole. A recipe uses $\tfrac{3}{4}$ batch of cereal. Then it adds raisins equal to $\tfrac{2}{5}$ of the cereal amount. Since fraction multiplication represents taking part of a quantity, what is the correct answer to the problem: What fraction of a whole batch is the raisins amount?
15. Sofia claims that $y = 8$ makes the equation $5y - 7 = 3y + 9$ true. To verify her claim, which calculation proves whether she is correct?
16. A rectangle is tiled with unit squares of side length $\frac{1}{10}$ inch. There are 15 squares along the length and 8 squares along the width. Which expression correctly represents both the area calculation by counting squares and by multiplying side lengths?
17. Tom collected data on how many books his classmates read last month. The data shows: 3, 5, 2, 8, 4, 6, 3, 7, 5, 4. He calculated that the mean is 4.7 books. Now Tom wants to determine if this average is a reasonable representation of his classmates' reading habits. What should he do next?
18. In a science notebook, two patterns describe how two plants grow each week. Plant A pattern rule: start at 2 and add 5. Terms: 2, 7, 12, 17, 22. Plant B pattern rule: start at 2 and add 3. Terms: 2, 5, 8, 11, 14. The paired terms are graphed as ordered pairs $(A, B)$ in the first quadrant. Which statement best explains why one pattern grows faster than the other?
19. A right rectangular prism is built from unit cubes in layers. One layer has 9 cubes across and 2 cubes deep, and the prism is 3 cubes tall (3 layers). The cubes pack the prism with no gaps or overlaps, so counting cubes is the same as multiplying the three whole-number dimensions. What is the volume of the prism?
20. A measuring cup has $\tfrac{1}{3}$ cup of juice. The juice is poured equally into 3 small cups. Picture the $\tfrac{1}{3}$ cup amount being partitioned into 3 equal parts. What does the quotient $\tfrac{1}{3} \div 3$ represent?

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