Practice Test 11 - 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. What is the additive inverse (opposite) of $-12$?
2. Which property allows you to write $2 \cdot 3x \cdot 5y$ as $(2 \cdot 3) \cdot x \cdot 5y$?
3. A cafeteria tracked which fruit students chose over 80 lunches: Apple 36, Banana 28, Orange 16. If the cafeteria uses a probability model based on this data, about how many banana choices should it expect in the next 50 lunches?
4. A librarian wants to estimate the average number of pages in all the mystery books in the school library (the population). She randomly selects 25 mystery books and finds the sample mean is 218 pages. Which is the best inference about the population mean number of pages?​​
5. A hiker climbs $200$ meters up a trail and then walks $200$ meters back down. What is the hiker's net change in elevation?
6. A principal wants to know how students feel about a new cellphone policy. The school has 500 students. A survey is posted online, and students can choose whether or not to fill it out. After a week, 90 students responded. Which statement best describes the sample and whether the results can be generalized to all 500 students?
7. In triangle $\triangle ABC$, the interior angles are labeled $m\angle A = x$, $m\angle B = 2x$, and $m\angle C = 3x$. What is the value of $x$?
8. A circular pond has an area of $78.5$ square meters. What is the circumference of the pond?
9. A rectangular prism is sliced by a vertical plane that is perpendicular to the base and cuts from the front face straight to the back face (like making a straight up-and-down cut). What 2D shape is the cross-section?
10. The figure shows a prism with a pentagonal base. If each of the 5 triangular sections of the base has an area of 12 square meters, what is the volume of the prism?
11. The relationship between distance $y$ (in miles) and time $x$ (in hours) for a bike ride is given by the equation $y=4.5x$. What is the constant of proportionality $k$?
12. When $\frac{7}{11}$ is converted to a decimal, the decimal representation will be:
13. A student is told to construct $\triangle PQR$ where $PQ=4\text{ cm}$, $PR=5\text{ cm}$, and the included angle $\angle QPR=70^\circ$. How many different triangles are possible with these conditions (up to flipping/rotation)?
14. A coach says the total practice time can be written as $3(2x-5)$. Expand the expression using the distributive property.
15. A coach splits a $-60$ point penalty evenly among $12$ players. What is each player's share of the penalty? (Compute $(-60)\div 12$.)
16. Carmen's problem-solving strategy for 'Find the circumference of a circle with diameter $14$ cm' was: Step 1: Use $C = \pi d$. Step 2: $C = \pi \times 14 = 14\pi$ cm. Step 3: $14\pi \approx 44$ cm. Which part of the problem-solving model is she still missing?
17. For the inequality $2s + 9 ≤ 21$, a student creates this word problem: "Amy can spend at most 21 dollars on s items costing 2 dollars each plus a 9 dollar membership fee." What makes this word problem effective?
18. A student records a change in a bank of points in a classroom game. Evaluate: $-1.5 - \frac{3}{4}$ (convert to decimals or fractions).
19. A craft store sells beads in packs. Each pack costs $3.25, and there is a $5.50 shipping fee for the entire order. If the total was $31.50, how many packs did Lee buy? Write an equation and solve.
20. A recipe uses fractional cups of ingredients. Calculate: $\frac{1}{2}+\left(-\frac{3}{4}\right)$.

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