Practice Test 6 - 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. For points $7, 11, 9, 16, 11, 13, 10, 8, 14, 11$, what is the range?
2. If $\frac{3x}{4} = \frac{9}{16}$, what is the value of $x \times \frac{2}{3}$?
3. The inequality $|2x - 6| \leq 8$ is equivalent to which of the following?
4. The sequence $5, 8, 13, 20, 29, ...$ follows a specific pattern. What is the next term after $29$?
5. A comparative box plot shows the response times (in seconds) for customer service calls at two different companies. Company X has a median response time of 45 seconds with quartiles at 30 and 60 seconds. Company Y has a median of 50 seconds with quartiles at 40 and 55 seconds. Which company provides more predictable customer service response times?
6. A submarine starts at sea level and descends $45$ feet. It then ascends $18$ feet, descends $27$ feet, and finally ascends $12$ feet. What is the submarine's final depth below sea level?
7. If $x = -4$ and $y = -6$, what is the value of $|x - y| - |x + y|$?
8. The dot plot displays the number of books read by students over summer break. What is the range of the data?
9. The sequence $2, 6, 12, 20, 30, ...$ can be expressed as $a_n = n(n+1)$. What is the $12$th term?
10. The range of a set of positive integers is 24. If the smallest value is increased by 5 and the largest value is decreased by 3, what is the new range?
11. A geometric sequence has common ratio 2: $7, 14, 28, 56, 112, \dots$; what is next?
12. Lottery Draw: A player chooses 3 numbers from 1 through 10, and 3 numbers are drawn without replacement. Which is more likely: matching the first drawn number, or winning by matching all 3 numbers?
13. An arithmetic sequence increases by 9 each term: $3, 12, 21, 30, 39, \dots$; what is next?
14. Evaluate: $\frac{24 - 3 \times 2^3}{4 + 2 \times 3}$
15. The frequency table shows the results of rolling a number cube 30 times. Which number is the mode?
16. A warehouse ships $-8$ boxes each hour for $5$ hours, then receives $+12$ boxes; what is the net change?
17. Given exam scores $64, 71, 85, 90, 77, 82, 68, 75, 88, 92, 71, 79, 83, 71, 86$, what is the median?
18. A box-and-whisker plot shows the distribution of daily temperatures for two cities over the same month. City A has a median of 72°F and an interquartile range of 8°F. City B has a median of 75°F and an interquartile range of 12°F. If both cities have the same range of temperatures (difference between maximum and minimum), which city likely has more extreme temperature outliers?
19. In a game with three rounds, the probability of winning each round is 0.7. What is the probability of winning at least two rounds?
20. For what value of $k$ does the equation $2(x + 3) = k(x - 1) + 14$ have no solution?

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