Practice Test 6 - 7th Grade Math

19 of the 20 questions below are in this test; the other one can't be scored yet. Answer them in any order, then submit to see your score and every explanation.

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1. When explaining why $\frac{0}{5} = 0$ but $\frac{5}{0}$ is undefined, a student says "You can't divide by zero, but zero divided by anything is zero." What would improve the mathematical precision of this explanation?
2. Angles $\angle 1$ and $\angle 2$ form a linear pair on a straight line. Their measures are $m\angle 1 = 3x$ and $m\angle 2 = 2x$. What is the measure of $\angle 1$?
3. Two number cubes labeled 1-6 are rolled. The ordered pair $(a,b)$ means (first cube, second cube). How many outcomes are in the event "the sum is 8"?
4. Calculate the quotient: $15\div(-3)$.
5. Start at 0 on a number line and add -4. Which statement correctly describes the movement and the final position?
6. A class is collecting cans for a food drive. They already collected 18 cans. Each student who helps brings in 6 more cans. The class wants to collect at least 60 cans total. Write, solve, and graph an inequality for the number of helping students s needed. (Students must be whole numbers.)
7. A fair coin is flipped 10 times and lands on heads 7 times. Which statement best describes what this result means about $P(\text{heads})$?​​
8. Which expression shows the commutative property applied to $5x^2 \cdot 3y \cdot 2x$?
9. A student tracked how they got to school for 50 days: Bus 22 days, Car 18 days, Walk 10 days. A probability model is created from the data. Which set of probabilities is correct and sums to 1?​
10. The equation $3(w + 4) = 30$ can be rewritten as $3w + 12 = 30$. Which word problem better matches the original form $3(w + 4) = 30$?
11. A science class records water temperature changes. The water starts at $-2.5^\circ\text{C}$. The teacher warms it by $7\tfrac{1}{2}^\circ\text{C}$, then a student adds ice that lowers the temperature by $\tfrac{3}{4}^\circ\text{C}$. What is the final temperature?
12. The figure shows a composite shape made of a rectangle and a trapezoid. What is the total area of this composite shape?
13. A student simplifies $4x - 2(3x - 1) + 6$ and gets $4x - 6x + 2 + 6 = -2x + 8$. Which property was applied correctly in the first step?
14. A school wants to estimate the average number of minutes students spend on homework each night. Two different random samples are taken. - Sample 1 (40 students): mean = 52 minutes - Sample 2 (40 students): mean = 47 minutes Which statement best compares these samples and what they suggest about the population mean?​​
15. Sarah earns $12 per hour babysitting and $15 per hour tutoring. Last week she worked a total of 18 hours and earned $246. If $b$ represents hours babysitting and $t$ represents hours tutoring, which system of equations represents this situation?
16. A student factored the expression $12x + 18y - 6$ and wrote $6(2x + 3y - 1)$. To verify this is correct, which property should be applied?
17. A student council wants to estimate the proportion of all 7th graders who prefer having a longer lunch period. They take a random sample of 60 seventh graders and 39 say they prefer a longer lunch. Which is the best estimate for the population proportion who prefer a longer lunch?
18. A figure undergoes a translation of 4 units left and 1 unit up, followed by a reflection across the x-axis. If a point on the original figure was at (3, -2), and you want to return this point to its original position using a single transformation, which transformation should you apply to the final image?
19. A school display is shaped like a "house": a rectangle with a triangle on top. The rectangle is $8\text{ in}$ wide and $5\text{ in}$ tall. The triangle on top has the same base as the rectangle ($8\text{ in}$) and height $3\text{ in}$. What is the total area of the display?
20. To pass a class, your score must be more than 75 points. You have 68 points now. Each completed practice quiz adds 2 points. Let $q$ be the number of quizzes. Solve the inequality and state the smallest whole number of quizzes you must complete. Inequality: $68 + 2q > 75$

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