Practice Test 12 - 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 runner runs at a constant speed of 6 miles per hour. Let $d$ be the distance (in miles) and let $h$ be the time (in hours). Which equation models this proportional relationship?
2. A student flips a coin twice. Using the sample space {HH, HT, TH, TT}, which outcomes match the event "at least one head"?
3. A weather station records precipitation on 84 days out of 120 days observed. If this pattern continues, which best describes what should happen over the next 300 days?
4. A swimmer's time improves by subtracting a negative amount. Evaluate: $5.2 - (-1.5)$.
5. A bike rental costs $12 per hour plus a one-time $6 helmet fee. If the total cost was $78, how many hours did the bike rental last?
6. A circle's circumference is $C=18\pi\text{ cm}$. What is the circle's area? (Hint: First find $r$ from $C=2\pi r$.)
7. A science club measured the lengths (in cm) of two types of leaves. Type 1: 9, 10, 10, 11, 11, 12, 12, 13 Type 2: 15, 16, 16, 17, 17, 18, 18, 19 The mean length of Type 1 is 11 cm with MAD = 1 cm. The mean length of Type 2 is 17 cm with MAD = 1 cm. How many times the MAD is the difference in means, and what does that suggest about overlap?
8. In a probability experiment, a student reports "The chance of getting heads is 50-50." What would make this statement more mathematically precise while maintaining the same meaning?
9. What is the value of $\frac{2\frac{1}{3} \div \frac{4}{9}}{1\frac{2}{7} + \frac{3}{14}}$?
10. A hiking trail is shown on a map with scale $1:50{,}000$. The trail measures $6\text{ cm}$ on the map. What is the actual length of the trail in kilometers?
11. A company's profit is proportional to the number of items sold. When 120 items are sold, the profit is $840. A competitor's profit follows the equation $P = 6.5n$, where $P$ is profit in dollars and $n$ is number of items sold. How many more items must the competitor sell to earn the same profit as the first company when it sells 200 items?
12. A hiker starts at an elevation of $450\text{ m}$ above sea level. The trail goes down $275\text{ m}$, then up $180\text{ m}$, then down another $\frac{1}{2}$ of $60\text{ m}$. What is the hiker's final elevation?
13. A store compared checkout times (in minutes) for two cashiers. A random sample of 8 customers was recorded for each cashier. Cashier A: 4, 5, 6, 5, 4, 6, 5, 5 Cashier B: 3, 7, 4, 8, 5, 6, 4, 7 Which statement is correct about the sample means and ranges?
14. Two fair coins are flipped. A student says the probability of getting two heads is $\frac{1}{2}$ because "heads has a $\frac{1}{2}$ chance." What is the correct probability of two heads using the compound sample space $\{HH,HT,TH,TT\}$?
15. A contractor needs to convert measurements from a blueprint. The blueprint shows a hallway that is $0.75$ inches wide and $4.5$ inches long, using a scale of $\frac{1}{4}$ inch $= 1.5$ feet. How many square yards of carpet are needed for this hallway?
16. Which statement about dividing rational numbers is always true?
17. On a number line, point $P$ is at $-3.2$ and point $Q$ is at $2.8$. If point $R$ satisfies $|R| = |P|$, how many possible positions are there for point $R$?
18. A recipe calls for $2\frac{1}{4}$ cups of flour, but the measuring cup is marked in milliliters. Using the conversion $1$ cup $= 236.6$ milliliters, how many milliliters of flour are needed? Round to the nearest $10$ milliliters.
19. Maria is trying to construct a triangle using three given angle measures: $65°$, $45°$, and $80°$. After checking her work, she realizes there's an issue with these measurements. What should Maria conclude about constructing a triangle with these angle measures?
20. A science class records how often a plant's leaves are found to be dry or wet at the start of class over 50 days: Dry 32 days, Wet 18 days. Using a probability model based on this data, which is the best estimate for $P(\text{wet})$?

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