Practice Test 2 - 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 student deposits $35 into a school store account and later withdraws $35. What is the net change in the account balance?
2. A rectangular pyramid is sliced by a vertical plane that passes through the apex (top point) and the center of the base. What 2D shape is the cross-section?
3. A circular track has radius $9 \text{ m}$. A student claims the circumference is $C=\pi r$. Which statement best corrects the student using the meaning of $\pi$ (the ratio $\dfrac{C}{d}$)?
4. Two fair six-sided dice are rolled. There are $36$ equally likely ordered outcomes $(1,1)$ through $(6,6)$. What is the probability that the sum is 7? Give your answer in simplest form.
5. A student flips a coin, then flips the coin again. Which set correctly represents the complete sample space?
6. The equation $4(2x - 3) = 6x + 14$ represents a real-world situation where costs must be equal. After solving algebraically to get $x = 13$, which arithmetic verification correctly confirms this solution?
7. A bicycle wheel has a circumference of $94.2$ inches. If $\pi \approx 3.14$, which expression best represents the diameter of the wheel?
8. Estimate and then compute exactly to check reasonableness: A water tank is -1.8 liters (it needs 1.8 L to be full). First, 3 1/2 liters are added. Then 0.6 liter leaks out. Finally, 1/4 of the current amount of water is drained for cleaning. What is the final amount of water in the tank (in liters)?
9. Which equation correctly shows that subtracting a negative is the same as adding a positive?
10. A small park is shaped like a rectangle with two identical right triangles attached on the left and right sides. The rectangle is $6\text{ m}$ long and $4\text{ m}$ wide. Each triangle has base $4\text{ m}$ (the same as the rectangle's width) and height $3\text{ m}$. What is the total area of the park?
11. A car uses gasoline at a constant rate: it travels 65 miles per gallon. If $y$ is miles traveled and $x$ is gallons of gas used, what is the constant of proportionality $k$ in $y=kx$?
12. If $|m - 2| = 7$, what are all possible values of $m$, and what do they represent on a number line?
13. The temperature dropped $2\frac{1}{4}$ degrees over $\frac{3}{4}$ hour. At this rate, how much would the temperature change in $1$ hour?
14. Choose the set of expressions that are all equivalent to $-4$. (You may use the fact that $-(p/q)=(-p)/q=p/(-q)$ for integers $p,q$ with $q\ne 0$.)
15. A researcher collected data on study hours per week and wants to create a histogram with 4 equal intervals. The data ranges from 2 hours to 18 hours. What should be the width of each interval?
16. Alex plays a game where he rolls two number cubes and records the sum. The sample space for possible sums is shown in the organized list below. If Alex wants to find outcomes where the sum is either less than 5 OR greater than 10, how many total outcomes from the sample space satisfy this condition?
17. On a number line, you start at $-2.5$ and add $1.75$. You move a distance of $|1.75|$ units in the direction of the sign of $1.75$. What is $-2.5+1.75$?
18. A bakery sells cupcakes in boxes. Small boxes hold 6 cupcakes and cost $9. Large boxes hold 10 cupcakes and cost $13. Mrs. Johnson needs exactly 84 cupcakes and wants to spend the least amount possible. What should she buy?
19. A game booth works like this: You roll a fair die twice. You win a prize if both rolls are even (2, 4, or 6). Which simulation would correctly estimate the probability of winning?
20. Triangle PQR has sides of length $9$, $12$, and $15$. Triangle STU has sides of length $6$, $8$, and $10$. A student claims these triangles are similar and calculates a scale factor of $\frac{2}{3}$. What should the student check to verify this claim?

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