Practice Test 2 - ISEE Upper Level Mathematics Achievement

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

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1. The data in the table represents a quadratic function $q(x) = ax^2 + bx + c$. What is the value of $a + b + c$?
2. A store tracks weekly sales (in units sold) for four products in the bar graph. It also summarizes the distribution of weekly sales for Product B with a box-and-whisker plot: $\min=18$, $Q_1=24$, median $=30$, $Q_3=36$, $\max=50$ (units). What does the median value in the box plot indicate about the data set?
3. Point $S$ is located at $(3, -2)$ and point $T$ is located at $(-1, 4)$. If point $U$ is the reflection of point $S$ across point $T$, what are the coordinates of point $U$?
4. If $\sqrt{3x + 1} = 5$, then $x =$
5. The equation $\frac{2x + 1}{x - 3} = \frac{x + 5}{x - 3}$ has how many solutions?
6. A rectangular swimming pool is 20 feet long, 15 feet wide, and has an average depth of 6 feet. How many cubic feet of water are needed to fill the pool completely?
7. Events A and B are mutually exclusive with P(A) = 0.3 and P(A∪B) = 0.7. What is P(B|A∪B)?
8. If $x^2 + bx + 20$ factors as $(x + 4)(x + 5)$, what is the value of $b$?
9. A bag contains 5 red, 4 blue, and 6 yellow marbles. Two marbles are drawn without replacement. What is the probability that they are different colors?
10. Lottery Draw: Numbers 1 through 10 are used, and 3 numbers are drawn without replacement. A player chooses 3 numbers, and the order does not matter. What is the probability of matching exactly 2 of the 3 drawn numbers?
11. Points P(-4, 2) and Q(8, -1) lie on line ℓ. If line m is perpendicular to line ℓ and passes through the point R(3, 5), what is the slope of line m?
12. A line passes through points $A(2, 7)$ and $B(-4, -5)$. If this line is reflected across the $y$-axis, what are the coordinates of the image of point $A$?
13. If $|3x - 9| = 12$, what are all possible values of $x$?
14. In a class survey, the number of pets owned by students follows this pattern: 5 students own 0 pets, 8 students own 1 pet, 12 students own 2 pets, 8 students own 3 pets, and 2 students own 4 pets. What is the difference between the mode and the median number of pets?
15. What is the value of $\frac{5}{6} \div \frac{2}{9} - \frac{1}{4}$?
16. Which of the following expressions is completely factored?
17. Lisa is making a quilt that requires $6\frac{3}{8}$ yards of fabric. She has already purchased $2\frac{1}{4}$ yards of blue fabric and $1\frac{5}{6}$ yards of green fabric. How much more fabric does she need?
18. A spinner has three sections: red (probability 0.4), blue (probability 0.3), and green (probability 0.3). The spinner is spun twice. What is the probability that red appears exactly once?
19. A sequence is defined by $v_1 = 5$ and $v_{n+1} = \frac{v_n + 6}{2}$ for $n \geq 1$. What value does this sequence approach as $n$ approaches infinity?
20. A cylindrical water tank has a radius of 3 feet and a height of 8 feet. If the tank is filled to 75% of its capacity, how many cubic feet of water does it contain?

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