Practice Test 10 - 7th Grade Math

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

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1. A science club uses $\tfrac{1}{2}$ liter of solution to fill $\tfrac{1}{4}$ of a container. How many liters of solution are needed to fill 1 whole container at the same rate?
2. Which slice would produce a triangle as the cross-section? Choose the best option.
3. A right rectangular pyramid has a square base. Two different planes each cut the pyramid parallel to the base: one at 1/3 the height from the base, another at 2/3 the height from the base. If the lower cross-section has an area of 36 square units, what is the area of the upper cross-section?
4. A student is explaining how to solve the equation $3x + 7 = 22$. Which representation BEST demonstrates the concept of 'doing the same thing to both sides' when isolating the variable?
5. A water tank contains $\frac{3}{4}$ of its capacity. After using $15.5$ gallons, the tank is $\frac{1}{2}$ full. What is the total capacity of the tank?
6. A map has a scale where 2 inches represents 15 miles. If two cities are 4.8 inches apart on the map, what is the actual distance between them?
7. A class uses a weighted spinner with 3 colors. In 100 practice spins, the results were: Red 45, Blue 30, Green 25. Which probability model best matches the data?
8. A robot moves $-80$ meters (negative means backward) in $4$ seconds at a constant rate. What is its rate of change in meters per second? (Compute $(-80)\div 4$.)
9. A jar contains letter tiles: 4 A's, 6 B's, and 2 C's. Two tiles are drawn without replacement. What is the probability that both tiles are the same letter? Express your answer as a fraction in lowest terms.
10. Ben calculates $\frac{5}{6} ÷ (-4)$ on his calculator and gets $-0.208\overline{3}$. To check if this is reasonable, he wants to estimate the answer first. Which estimation approach makes the most sense?
11. On a number line, start at $3$ and add $5$. You move a distance of $|5|$ units in the direction of the sign of $5$. Where do you end up (what is $3+5$)?
12. Which choice correctly verifies the sum $6+(-9)$ using a number line interpretation?
13. A science museum sells tickets for $9$ each. There is also a one-time processing fee of $4.50$ for the whole order. If the total cost was $58.50$, how many tickets were bought?
14. Two gardeners measured the heights (in cm) of seedlings after 2 weeks. Garden A: 12, 13, 13, 14, 14, 15, 15, 16 Garden B: 18, 19, 19, 20, 20, 21, 21, 22 The mean height for Garden A is 14 cm with MAD = 1 cm. The mean height for Garden B is 20 cm with MAD = 1 cm. Which statement is correct?
15. The cost $C$ (in dollars) of buying pencils is proportional to the number of pencils $n$ purchased. A student writes the equation $C = 0.75n$ to model this relationship. If the student later discovers that $30$ pencils actually cost $18, what should the correct equation be?
16. A recipe calls for 3 cups of flour for every 2 cups of sugar. Maria wants to make a larger batch and uses 18 cups of flour. She creates a table showing the relationship between flour and sugar amounts. What is the unit rate of sugar per cup of flour, and how many cups of sugar should Maria use?
17. A triangular prism has a triangular base with base $9\text{ m}$ and height $4\text{ m}$, and the prism length is $5\text{ m}$. What is the volume of the prism?
18. A coach buys 23 water bottles and 77 sports drinks, each costing $7. The total cost is $7\times 23 + 7\times 77$. Which rewrite uses factoring to make the calculation easiest?
19. Which statement correctly shows that subtracting q is the same as adding -q for the expression -6-9?
20. A science teacher says your project score must be more than 85 points to earn an A. You already have 73 points, and each extra-credit task adds 4 points. Write, solve, and graph an inequality for the number of extra-credit tasks t needed. (Tasks must be whole numbers.)

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