Practice Test 10 - 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. A geometric sequence has ratio 5: $3, 15, 75, 375, 1,875, \dots$; what is next?
2. A rectangular prism is 10 cm by 2 cm by 3 cm; using $V=lwh$, what is its volume?
3. Calculate the total change in temperature: it rises $+7 \times 3$ degrees, then falls $-25$ degrees.
4. A construction worker pours concrete in three sections: $3\frac{2}{5}$ cubic yards in the morning, $2\frac{3}{10}$ cubic yards at lunch, and $1\frac{7}{10}$ cubic yards in the afternoon. What is the total amount of concrete poured?
5. A sequence follows the pattern: $2, 6, 18, 54, 162, ...$ If $S_n$ represents the sum of the first $n$ terms, what is $S_6$?
6. A store has a loss of $-12$ dollars per day for $4$ days, then a gain of $+30$; what is total profit/loss?
7. Point P(4, 9) lies on a line with slope $\frac{3}{2}$. If point Q also lies on this line and has coordinates (10, k), what is the value of k?
8. A composite solid consists of a cylinder topped with a hemisphere. The cylinder has a radius of 5 meters and height of 12 meters. What is the total volume?
9. A cylinder has radius 5 m and height 2 m; using $V=\pi r^2h$, what volume is it?
10. A rectangular garden has length $\frac{5}{6}$ meters and width $\frac{3}{4}$ meters. If the garden is divided into plots each with area $\frac{1}{8}$ square meters, how many plots can be created?
11. A cereal box is a rectangular prism 18 cm by 6 cm by 30 cm; what is its volume?
12. What is the value of $(-7) - (-12) + (-5) - 8$?
13. A line passes through points (4, -2) and (8, 6). Another line passes through (1, 3) and (5, k). If these two lines are parallel, what is the value of k?
14. For temperatures $58, 61, 63, 60, 65, 62, 59, 66, 64, 61, 60, 67, 62, 60$, what is the range?
15. A sequence follows the pattern where each term after the first two is the sum of the two preceding terms multiplied by 2, minus 1. If $a_1 = 1$ and $a_2 = 3$, what is $a_5$?
16. The graph shows a piecewise linear function $h(x)$. What is the rule for $h(x)$ when $2 \leq x \leq 5$?
17. Line segment PQ has slope $\frac{3}{4}$. If P has coordinates (7, 2) and Q has coordinates (a, 11), what is the value of a?
18. Simplify: $\frac{6^2 - 4 \times 3}{2^3 \div 4 + 1}$
19. A machinist needs to drill holes that are $\frac{3}{16}$ inch in diameter. If the drill bit creates holes that are $\frac{1}{32}$ inch larger than specified, what is the actual diameter of each hole?
20. In a certain game, Event A occurs with probability $\frac{3}{7}$ and Event B occurs with probability $\frac{4}{9}$. If the events are independent, which statement correctly compares the probability of both events occurring to the probability of at least one event occurring?

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