Practice Test 6 - 8th Grade Math

16 of the 20 questions below are in this test; the other 4 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 science class models the height of a plant with the linear equation $y = 1.5x + 20$, where $y$ is the plant's height in centimeters and $x$ is the number of hours of sunlight per day. What does the slope $1.5$ mean in this situation?
2. Based on the data in the table, which statement correctly compares the relationships for Person A and Person B?
3. A figure is rotated $90^\circ$ counterclockwise about the origin. How do the coordinates of any point change?
4. Solve the system by inspection (use simple reasoning). $\begin{cases} x + y = 10 \\ x = 6 \end{cases}$
5. A student claims that the expression $\frac{2x + 6}{4}$ is equivalent to $\frac{x + 3}{2}$. Which approach demonstrates the most precise mathematical reasoning to verify this claim?
6. At a school fundraiser, hamburgers cost $5 each and hot dogs cost $3 each. The goal was to sell 200 items and raise $800. Due to supply issues, they were short 20 hamburgers but had extra hot dogs. If they still sold exactly 200 items, how much less money did they raise compared to their goal?
7. Sarah creates a mapping where she assigns to each student in her class their birth month. She then realizes that three students were born in March and two students were born in July. If Sarah wants to create a function, which modification should she make?
8. Which graph represents the equation $y = -\frac{2}{3}x + 4$?
9. A student claims they proved the Pythagorean Theorem by writing: "Assume $a^2+b^2=c^2$. Therefore, $a^2+b^2=c^2$." What is the best evaluation of this argument?
10. When simplifying $4x + 2(3x + 1) + 5$, Elena wrote: $4x + 2(3x + 1) + 5 = 4x + 6x + 2 + 5 = 10x + 7$ Which properties did Elena use, in the correct order?
11. The triangle shown has sides of length 15, 20, and 25. To verify this is a right triangle and find which angle is the right angle, what should you check?
12. A surveyor needs to determine if two property lines are parallel. Property line 1 passes through points $P(2, 7)$ and $Q(8, 1)$. Property line 2 passes through points $R(-1, 4)$ and $S(5, -2)$. A third boundary line must be perpendicular to both property lines. What is the slope of this boundary line?
13. Refer to the scatter plot below. Which equation best represents a line of fit for the data shown?
14. If $t$ represents the number of text messages over 500, which inequality represents Sarah's constraint, and what is the maximum number of additional texts she can send?
15. A taxi charges a base fee plus a per-mile rate. The graph shows the relationship between miles traveled and total cost. For which distances will the total cost be less than $25?
16. A teacher recorded quiz scores: 6, 8, 9, 10, 12. She realizes she made an error and needs to add a score of 7 that was missing. After adding this score, what is the relationship between the change in mean and the change in median?
17. When asked to explain why $\frac{1}{2} + \frac{1}{3} = \frac{5}{6}$, a student responds: "You add the tops and bottoms differently." Which revision would make this explanation mathematically precise?
18. The graph shows the relationship between distance traveled and time for a moving object. Which table shows the same linear relationship?
19. Refer to the coordinate plane showing the graph of $f(x) = x^2 - 4x + 3$. At which x-values does the function equal zero?
20. When solving $\frac{x + 3}{4} = \frac{x - 1}{2}$, what is the first step that will eliminate the fractions?

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