Practice Test 9 - 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. Triangle ABC has vertices at A(2, 3), B(6, 3), and C(4, 7). What is the area of triangle ABC?
2. In a data set of 20 values, the smallest value is 15 and the largest value is 47. If 5 new values are added to the data set (12, 18, 35, 42, 50), what is the range of the new data set?
3. What is the factored form of $x^3 + 27$?
4. A cylinder has radius 3 cm and height 7 cm; using $V=\pi r^2h$, what volume results?
5. A rectangular prism measures 4 cm by 3 cm by 5 cm; using $V=lwh$, what is its volume?
6. An art cutout consists of a rectangle ($L=9\text{ cm}, W=4\text{ cm}$), a right triangle (legs $4\text{ cm}$ and $7\text{ cm}$) sharing its $4\text{ cm}$ leg with the rectangle's width, and a full circle (radius $1\text{ cm}$) glued externally with no overlap. The triangle extends from one $4\text{ cm}$ side, and the circle is separate but included in total material area. Use $\pi\approx3.14$ and compute in square centimeters. Ignore any seam allowances. Calculate the total area of the composite shape described.
7. A graduated cylinder experiment records 50 mL; since $1\text{ mL}=1\text{ cm}^3$, what volume is that?
8. The sequence $2, 5, 10, 17, 26, ...$ follows the pattern $a_n = n^2 + 1$. What is the $n$th partial sum $S_n = a_1 + a_2 + ... + a_n$?
9. A tile strip is $3\,3/4$ ft long; each tile is $5/8$ ft. Divide to find tiles needed.
10. Two cylinders have the same height. The first cylinder has a radius of 3 units, and the second has a radius of 6 units. What is the ratio of their volumes?
11. A budget allocates $3/5$ of $2\,1/2$ hours to homework. How many hours is that?
12. Line segment $AB$ has endpoints $A(-4, 1)$ and $B(8, 7)$. If point $C$ is on segment $AB$ such that $AC:CB = 2:1$, what are the coordinates of point $C$?
13. Emma drinks $1\frac{3}{8}$ liters of water in the morning and $2\frac{5}{6}$ liters in the afternoon. Her daily goal is $5$ liters. How much more water does she need to drink to reach her goal?
14. A circle is inscribed in a square with side length 12 cm. What is the area of the region inside the square but outside the circle?
15. A stage backdrop uses $x^2-11x+30$. What are the factors of $x^2-11x+30$?
16. A school reports average project scores (points out of 100) by class in the bar graph. A box-and-whisker plot summarizes the distribution of scores for Class 3: $\min=50$, $Q_1=62$, median $=70$, $Q_3=78$, $\max=92$. What does the median value in the box plot indicate about the data set?
17. A number is divided by $-4$, and then $7$ is subtracted from the result. If the final answer is $-12$, what was the original number?
18. A jar contains red and blue marbles in the ratio $3:5$. If there are 15 red marbles, how many blue marbles are there?
19. A student totals shopping costs; evaluate: $(25 - 9) \times 3 + 2^4 \div 4$.
20. A hiker climbs $+120$ ft, descends $-75$ ft, then climbs $+40$ ft; what is the net change?

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