Practice Test 1 - 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 fitness trainer tracks the relationship between weekly exercise hours and weight loss for clients. The equation $y = 1.8x + 0.5$ models this relationship, where $x$ represents hours of exercise per week and $y$ represents pounds lost per week. What does the y-intercept of 0.5 most likely represent in this context?
2. A teacher collected data on hours studied and test scores for 10 students. A scatter plot is made with hours studied on the $x$-axis and score on the $y$-axis. Which point is most likely an outlier? Data pairs (hours, score): $(1,52),(2,60),(3,66),(4,72),(5,78),(6,83),(7,88),(8,92),(9,95),(10,40)$
3. Simplify the expression and write your answer as a single power: $\dfrac{(7^2)^3}{7^5}$
4. What is $\sqrt{18x^2} + \sqrt{8x^2}$ when simplified, assuming $x ≥ 0$?
5. Estimate $\pi^2$ by using $\pi \approx 3.14$ and then squaring. Which estimate is closest?
6. A conical tent has a base diameter of 14 feet and a slant height of 25 feet. The tent manufacturer needs to know the volume to determine ventilation requirements. What is the volume of the tent?
7. A school store sells notebooks and pens. A notebook costs $x$ dollars and a pen costs $y$ dollars. - 2 notebooks and 3 pens cost $11$. - 1 notebook and 2 pens cost $7$. This gives the system: $2x+3y=11$ $x+2y=7$ What is the solution $(x,y)$?
8. A movie theater charges a $6 ticket fee plus $2 per snack. The total cost is modeled by $y=2x+6$, where $x$ is the number of snacks and $y$ is the total cost in dollars. What do $m$ and $b$ represent in $y=mx+b$ for this situation?
9. A proportional relationship is graphed on a coordinate plane. The line passes through the points $(0,0)$ and $(3,12)$. What is the constant of proportionality $k$ in $y=kx$?
10. Lines $p$ and $q$ are parallel and cut by transversal $t$. $\angle 3$ and $\angle 6$ are alternate interior angles. If $m\angle 3 = 68^\circ$, which statement gives a correct argument to find $m\angle 6$?
11. The graph shows three lines labeled P, Q, and R. If line P represents $y = 3x + 1$ and line Q represents $y = -2x + 6$, what does the point where lines P and Q intersect tell us about the system formed by these equations?
12. Two friends start biking toward each other from towns that are 54 miles apart. One bikes at 12 mph and the other bikes at 6 mph. Let $t$ be the time in hours until they meet, and let $d$ be the distance (in miles) the 12 mph biker travels. Which system correctly models the situation, and what is $t$?
13. In a class discussion, a student says: "An isosceles triangle has two equal sides, so if a triangle has two sides of length 5 cm, it must be isosceles." What is the most important precision issue with this reasoning?
14. The table represents a linear function. If you were to graph this function on a coordinate plane, which statement about the graph would be true?
15. A student claims the distance between $( -3,2)$ and $(1,-4)$ is $|1-(-3)|+|-4-2|=4+6=10$. What is the correct distance between the points?
16. In a game, players draw cards from two separate, identical decks simultaneously. Compare this to drawing two cards consecutively from a single deck without replacement. Which statement best describes the probability relationship in each scenario?
17. Square $WXYZ$ has vertices $W(0, 0)$, $X(4, 0)$, $Y(4, 4)$, and $Z(0, 4)$. The square is dilated by scale factor $\frac{3}{2}$ centered at $W$, then rotated $180°$ about the origin. What is the $x$-coordinate of the final image of vertex $Y$?
18. A system of equations is represented by two lines that intersect at $(4, -3)$. Sarah incorrectly concludes that $(4, -3)$ is a solution to only one of the equations. What is the error in Sarah's reasoning about intersection points?
19. A scatter plot shows the relationship between number of pages read ($x$) and minutes spent reading ($y$). A student drew the line $y=2x+5$ as a model. How good is the fit of the line $y=2x+5$?
20. The cross-section view below shows a cylindrical pipe with inner radius 3 cm and outer radius 5 cm. If the pipe is 20 cm long, what is the volume of the material used to make the pipe (the volume between the inner and outer cylinders)?

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