Practice Test 3 - ISEE Upper Level Mathematics Achievement

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

Start practice test

1. What is the complete factorization of $x^4 - 81$?
2. A pyramid has a square base with side length 8 meters and a height of 15 meters. What is its volume?
3. Points $M(-1, 3)$, $N(2, 7)$, and $O(5, k)$ are collinear. What is the value of $k$?
4. If $2x^2 - 8x + k$ can be factored as $2(x - a)^2$ for some constants $a$ and $k$, what is the value of $k$?
5. A water tank is $\frac{7}{8}$ full. After using $\frac{1}{3}$ of the water currently in the tank, what fraction of the tank's total capacity remains?
6. Two cards are drawn from a standard 52-card deck without replacement. Which probability is greater: drawing two hearts or drawing one heart and one spade?
7. A function $f(x)$ is defined such that $f(1) = 3$, $f(2) = 7$, $f(3) = 15$, and $f(4) = 31$. If this pattern continues, what is the value of $f(6)$?
8. A sequence is given by $u_n = 2^n - n$. What is the first term where $u_n > 100$?
9. The line plot shows the number of goals scored by a soccer team in their last 12 games. What is the difference between the range and the median?
10. A cube has a surface area of 150 square feet. What is the volume of the cube?
11. A cube has a volume of 343 cubic inches. What is the length of each edge?
12. Weather Forecast: In 100 days, rain happens on 30 days, and both rain and high temperatures happen on 12 days. If it is raining, what is the probability that temperatures are high? Give your answer in simplest form.
13. A car travels $\frac{2}{3}$ of a 240-mile journey in the first day. On the second day, it travels $\frac{3}{4}$ of the remaining distance. How many miles are left to travel?
14. A standard deck of 52 cards is shuffled. The top 3 cards are revealed. Compare the probability that all 3 cards are face cards (Jack, Queen, King) to the probability that all 3 cards are from the same suit.
15. A hexagonal prism has a base with an area of 36 square meters and a height of 8 meters. What is the volume of the prism?
16. Card Draw: A 52-card deck has 13 hearts and 39 non-hearts. A student draws one card, then a second card without replacement. If the first card is a heart, what is the probability the second card is also a heart?
17. A construction project is $\frac{2}{3}$ complete. If $\frac{3}{8}$ of the remaining work can be finished this week, what fraction of the entire project will be completed by the end of the week?
18. A chemist needs $12$ L of $25\%$ solution from $20\%$ and $40\%$. Solve $0.20x+0.40(12-x)=0.25\cdot12$.
19. A cone has a base radius of 5 inches and a volume of 100π cubic inches. What is the height of the cone?
20. A cone and cylinder have the same base radius and height. If the cylinder has a volume of 180π cubic units, what is the volume of the cone?

Practice tests