Practice Test 8 - 7th Grade Math

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

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1. Maria is planning a school fundraiser selling bracelets for $3 each and keychains for $2 each. She wants to raise at least $240 and plans to sell twice as many bracelets as keychains. If she sells $k$ keychains, which step should come FIRST in solving this problem?
2. A game uses a bag with 5 equal-sized slips of paper labeled A, B, C, D, and E. A player draws one slip, records it, and puts it back each time. What is the best prediction for how many times the player will draw an A in 200 draws?
3. A math teacher wants students to write a word problem for the inequality $3y - 10 > 14$. Which student response demonstrates the clearest understanding?
4. In football, a team gains $15$ yards on one play and loses $15$ yards on the next play. What is the net change in yards?
5. Parallelogram ABCD is shown on the coordinate plane. After a reflection across the x-axis followed by a translation 6 units right, vertex C moves from its original position to point (8, 2). What were the original coordinates of vertex C?
6. A number $N$ has exactly 12 positive divisors. If $N = 2^x \cdot 3^y$ for some non-negative integers $x$ and $y$, how many different values of $N$ are possible?
7. A baker uses the expression $(-\frac{3}{4}) \times (-\frac{8}{9}) \times (\text{flour amount})$ to adjust a recipe. If this expression must equal $\frac{1}{2}$ cup of flour, what was the original flour amount?
8. Lisa writes the number $144$ as $12^2$. Her teacher says this is not the prime factorization. What should Lisa write instead?
9. A student is told to construct a triangle with angles $40^\circ$ and $60^\circ$, and the side between those two angles is $7\text{ cm}$. How many different triangles can be constructed with these conditions?
10. A movie theater charges $8 for adult tickets and $5 for child tickets. On Saturday, they sold 120 tickets total and collected $780. If $a$ represents the number of adult tickets sold, which system of equations represents this situation?
11. A student draws one colored tile from a bag, does not put it back, and then draws a second tile. The bag contains 2 red tiles (R) and 1 blue tile (B). If outcomes are written in order (first draw, second draw), which list is the complete sample space?
12. A classroom raffle has 100 tickets. Mia holds 50 tickets, and Noah holds 10 tickets. Which statement correctly compares their chances of winning (using probabilities between 0 and 1)?
13. Two points on a number line are at -4 and 3. What is the distance between them? (Use absolute value of a difference.)
14. Two groups tracked how many minutes they read each day for a week. Group A (minutes): 18, 20, 22, 24, 26, 28, 30 Group B (minutes): 22, 24, 26, 28, 30, 32, 34 Use the mean as the center and the range as the variability. Which statement is most accurate?
15. A landscaping company's profit $P$ (in dollars) is proportional to the number of lawns $n$ they service each week. When they service $24$ lawns, their profit is $960. If their goal is to earn $1400 profit next week, which equation should they use to find how many lawns to service?
16. A rectangular pyramid and a triangular pyramid both have heights of $15 \text{ cm}$. The rectangular pyramid has a base area of $24 \text{ cm}^2$, and the triangular pyramid has a base area of $36 \text{ cm}^2$. What is the ratio of the rectangular pyramid's volume to the triangular pyramid's volume?
17. A school has 800 students. A principal wants to estimate the percent of students who walk to school. Which method best uses random sampling?
18. Which expression gives the distance between 10 and 3 on a number line, and what is that distance?
19. A student draws a card from a standard deck, records whether it is a heart, and puts it back each time. After 400 draws, the student got 110 hearts. What is the best estimate for $P(\text{heart})$ from this data?
20. A farmer wants to create a trapezoidal field where one parallel side is twice as long as the other. If the shorter side is $50$ meters, the height is $30$ meters, and he needs to know the total area for seed calculations, what is the area in square meters?

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