Practice Test 5 - 8th 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. A data set has 6 values: $a, b, c, d, e, f$ where $a < b < c < d < e < f$. The mean is 30 and the median is 28. If values $a$ and $f$ are removed, what can be concluded about the new mean and median?
2. Two relationships are given: Relationship A follows $y = 5x$ and Relationship B follows $y = 5x + 0.001$. A student claims both are "essentially proportional" because the constant term in B is "negligibly small." Evaluate this mathematical reasoning.
3. A simulation models the probability of scoring a goal in soccer by drawing cards from a standard deck. Face cards (J, Q, K) represent goals. After 52 draws with replacement, 15 goals are scored. The simulation is then repeated with 104 more draws, resulting in 28 additional goals. What is the relative frequency of scoring goals in the combined simulation?
4. A sports magazine wants to estimate what percentage of middle school students play organized sports. They survey students at a basketball tournament where several schools are competing. What makes this sampling method problematic for their research goal?
5. A student simulates the probability of getting exactly 2 heads when flipping 3 coins. She represents each coin flip with a random number: 1-5 means heads, 6-10 means tails. After generating 300 sets of three random numbers, she counts 117 sets with exactly 2 numbers in the range 1-5. What is her experimental probability?
6. Two different brands of batteries were tested for how long they last in hours. The boxplots shown represent the results. A consumer wants to choose the brand that offers both good longevity and reliable performance. Based on these boxplots, which recommendation is most appropriate?
7. In a card game, you draw two cards from a standard deck without replacement. What is the probability that the first card is a heart AND the second card is also a heart?
8. Two schools collected data on students' daily screen time. School A surveyed 50 students and found a mean of 4.2 hours with a range of 6 hours. School B surveyed 45 students and found a mean of 3.8 hours with a range of 2.5 hours. Based on this information, which inference is most reasonable?
9. A calculator displays $\pi$ as 3.141592654. A student argues that since this decimal terminates on the calculator screen, $\pi$ must be rational. What is the flaw in this reasoning?
10. A bike ride is modeled by $y = 12x + 3$, where $y$ is the total distance in miles and $x$ is the time in hours. What does the $y$-intercept 3 mean in this context?
11. A game involves drawing cards from a standard 52-card deck. Two cards are drawn without replacement. What is the probability that the second card is an ace, given that the first card drawn was a king?
12. Ray $BX$ bisects $\angle ABC$. If $m\angle ABC = 80^\circ$, then $m\angle ABX = 40^\circ$ and $m\angle XBC = 40^\circ$. The entire figure is reflected to form $\angle A'B'C'$ with bisector ray $B'X'$. What is $m\angle A'B'X'$?
13. A school wants to survey students about cafeteria food quality. Method A surveys 50 randomly selected students. Method B surveys 200 students who eat lunch in the cafeteria on a particular day. Which comparison is most accurate?
14. Which conclusion about Maria does NOT logically follow from the rule and the fact given?
15. A line passes through points $P(-2, 1)$ and $Q(3, -4)$. To find where this line intersects the y-axis, Miguel uses the fact that slope is constant between any two points. What is the y-intercept of this line?
16. A rectangular swimming pool has an area of $156\frac{1}{4}$ square meters. If the length is $2\frac{1}{3}$ times the width, what is the width of the pool?
17. A student is placing $\sqrt{5}$ on a number line. Since $\sqrt{4}=2$ and $\sqrt{9}=3$, which statement best describes where $\sqrt{5}$ should go?
18. The stem-and-leaf plots below show test scores for two different math classes. Which statement comparing the distributions is most accurate?
19. A student wants the distance between $T(-1,4)$ and $U(5,-4)$. Which expression correctly represents the distance?
20. A bike ride's distance is modeled by $y = 12x + 3$, where $y$ is the distance in miles and $x$ is the time in hours. What does the $y$-intercept 3 mean in this context?

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