Practice Test 1 - 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 coin is flipped three times. What is the probability of getting exactly two heads, given that at least one head occurred?
2. If the garden's circular pond radius doubles, how does the pond's area change within the composite plan?
3. A rectangle has vertices at $A(1, 2)$, $B(5, 2)$, $C(5, 6)$, and $D(1, 6)$. If the rectangle is translated by vector $\langle -3, 4 \rangle$, what are the coordinates of the image of vertex $B$?
4. Tom's morning jog consists of three segments: $2\frac{1}{6}$ miles uphill, $1\frac{3}{4}$ miles on flat ground, and $1\frac{5}{12}$ miles downhill. What is the total distance of his jog?
5. A business earns $9 per item after costs and must cover $135 rent; solve $9x-135\ge0$.​​
6. A carpenter cuts a $10\frac{1}{2}$-foot board into pieces that are each $1\frac{3}{4}$ feet long. How many complete pieces can be cut?
7. A cylinder has diameter 8 cm and height 10 cm; using $V=\pi r^2h$, what is its volume?
8. The histogram shows the distribution of commute times for employees at a company. The company wants to implement a flexible work policy for employees whose commute times fall in the longest 15% of all commutes. Based on the histogram, approximately what should be the minimum commute time to qualify for this policy?
9. Which of the following is equivalent to $2x - 3(x + 4) \geq 5$?
10. A box-and-whisker plot displays the test scores for two different classes. Class A has a median of 78, first quartile of 72, and third quartile of 84. Class B has the same median but an interquartile range that is 50% larger than Class A's interquartile range. If Class B's first quartile is 70, what is Class B's third quartile?
11. A sequence alternates signs and has the pattern $\frac{1}{2}, -\frac{2}{3}, \frac{3}{4}, -\frac{4}{5}, \frac{5}{6}, ...$ What is the $10$th term?
12. The center of circle $K$ is at $(h, k) = (-1, 2)$ and the circle has radius $r = 3$. Which equation represents circle $K$?
13. A box contains 10 balls: 4 red, 3 blue, and 3 green. If 3 balls are drawn without replacement, what is the probability that exactly 2 are red?
14. A fair octahedral die (8 faces numbered 1-8) is rolled twice. Compare the probability that the product of the two rolls is even to the probability that the sum of the two rolls is even.
15. Triangle $ABC$ has vertices at $A(-2, 3)$, $B(4, 1)$, and $C(0, -5)$. What is the area of triangle $ABC$?
16. The histogram shows the distribution of daily temperatures in degrees Fahrenheit for a city during the month of March. Based on this data, approximately what percentage of days had temperatures between 45°F and 65°F, inclusive?
17. A rectangular prism has dimensions 6 cm by 4 cm by 9 cm. If each dimension is doubled, by what factor does the volume increase?
18. In an arithmetic sequence, each term increases by 11: $9, 20, 31, 42, 53, \dots$; what is next?
19. Jason runs $3\frac{2}{5}$ miles on Monday and $2\frac{3}{4}$ miles on Tuesday. If he wants to run a total of $10$ miles over three days, how many miles must he run on Wednesday?
20. If $\sqrt{2x - 5} + 3 = 8$, what is the value of $x$?

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