Practice Test 11 - 8th Grade Math

20 questions. Answer them in any order, then submit to see your score and every explanation.

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1. A school's enrollment E after t years follows the equation $E = 850 + \frac{4t - 15}{3}$. In what year will the enrollment first exceed $900$ students?
2. Which transformation is represented by the rule $(x,y)\to(-x,\,y)$?
3. A student uses the rule $f(x)=2x+1$ to calculate a score based on the number of practice problems $x$. What is $f(3)$?​​
4. Triangle ABC is dilated with center P to create triangle A'B'C'. If PA = 8, PA' = 12, and the area of triangle ABC is 20 square units, what is the area of triangle A'B'C'?
5. Simplify: $\frac{(3^{-2})^4 \cdot 3^{-1}}{3^{-5} \cdot 3^{-4}}$
6. Which student demonstrates the best understanding of scatter plot interpretation?
7. In a right triangle, the hypotenuse is 13 m and one leg is 5 m. What is the length of the other leg?
8. A science website lists the EarthMoon distance as about $4\times10^5$ km and the EarthSun distance as about $1.5\times10^8$ km. About how many times farther is the Sun than the Moon (from Earth)?
9. A number line from 2 to 3 is shown with tenths marked. Where should $\sqrt{5}$ be placed on the number line?
10. A classroom has a cylindrical container for storing rice. The container has radius $3\text{ cm}$ and height $10\text{ cm}$. What is the volume of the container? (Give the answer in terms of $\pi$.)
11. If $a = 4$ and $b = 9$, what is the value of $\frac{\sqrt{a}}{\sqrt{b}} + \frac{\sqrt{b}}{\sqrt{a}}$?
12. A savings account balance grows according to the formula $B = 500 + \frac{3t + 12}{4}$, where B is the balance in dollars and t is the time in months. After how many months will the account balance reach $533?
13. The sum of two siblings' ages is 45 years, and the older sibling is 5 years older than the younger sibling. Let $o$ be the older sibling's age and $y$ be the younger sibling's age. What are their ages?
14. Classify the system (one solution, no solution, or infinitely many solutions). $\begin{cases} 2x + y = 5 \\ 2x + y = 8 \end{cases}$
15. A marine biologist collected data on water temperature and the number of fish observed at a coral reef. The linear model $y = -2.3x + 78$ represents the relationship, where $x$ is the water temperature in degrees Celsius and $y$ is the number of fish observed. If the water temperature increases from 22°C to 26°C, what is the predicted change in the number of fish observed?
16. Pentagon $ABCDE$ has vertices $A(1,1)$, $B(3,1)$, $C(4,2)$, $D(2,4)$, and $E(0,2)$. Pentagon $A'B'C'D'E'$ has vertices $A'(1,-1)$, $B'(3,-1)$, $C'(4,-2)$, $D'(2,-4)$, and $E'(0,-2)$. Which transformation maps $ABCDE$ onto $A'B'C'D'E'$?
17. The equation $5x - 3 = 2x + 12$ has the same solution as which of these equations?
18. A health researcher wants to study exercise habits of adults in a city. She randomly selects 10 gyms, then surveys all members at those gyms. What is the main limitation of generalizing these results to all adults in the city?
19. Two similar pentagons have a scale factor of 2:3. If the first pentagon undergoes a sequence of transformations to map onto the second pentagon, and the sequence includes a dilation, a rotation of 45°, and a translation, in which order must these transformations be applied?
20. A teacher collected data from 80 students about grade level (6th or 8th) and whether they are in an after-school activity (Yes/No): - 6th grade: 25 in activities, 15 not in activities - 8th grade: 30 in activities, 10 not in activities How many students in the survey are not in an after-school activity?

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