Practice Test 4 - 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. In a data set of 9 consecutive even integers, the median is 16. What is the range of this data set?
2. What is the value of $\frac{(-4)^3 \times (-2)^2}{(-8) \div 2}$?
3. A garden's area is $A(x)=x^2+7x+12$. Which represents the factored form of $A(x)$?
4. A basketball team's scores for their last 8 games were: 78, 82, 85, 88, 91, 94, 98, 103. If the coach removes the highest and lowest scores before calculating statistics, what is the range of the remaining 6 scores?
5. In a geometric sequence, each term is multiplied by 3: $2, 6, 18, 54, 162, \dots$; what is next?
6. A sphere has the same volume as a cube with edge length 12 inches. What is the radius of the sphere to the nearest tenth of an inch?
7. A recipe for punch calls for $3\frac{1}{3}$ cups of fruit juice and $1\frac{3}{4}$ cups of soda water. If Maria wants to make $\frac{1}{2}$ of the recipe, how many total cups of liquid will she need?
8. A data set has 11 values with these characteristics: the mode is 25, the median is 28, and the range is 40. If the smallest value is 10, what is the largest value?
9. If $ax^2 + bx + c$ factors as $(4x - 3)(2x + 1)$, what is the value of $abc$?
10. Two points on a line are P(a, 3) and Q(a+4, 7). If the line has slope $m$, what is the value of $m$?
11. A fair coin is flipped 4 times. Compare the probability of getting exactly 3 heads to the probability of getting at least 3 heads.
12. Point $A$ is at $(-3, 2)$ and point $B$ is at $(1, 6)$. If point $C$ is such that triangle $ABC$ is a right triangle with the right angle at $B$, and $C$ is located at $(x, 2)$, what is the value of $x$?
13. A business charges $14 per item with $98 fixed cost; solve $14x-98\ge0$ for break-even $x$.​​
14. A geometric sequence has first term $a_1 = 4$ and common ratio $r = -2$. What is the sum of the first $6$ terms?
15. If $2x^2 - 7x - 4 = (2x + 1)(x + k)$ for some constant $k$, what is the value of $k$?
16. Temperatures over 14 days were $62, 65, 60, 63, 66, 62, 64, 67, 61, 62, 65, 68, 62, 64$; which appears most?
17. A swimming pool is $\frac{3}{4}$ full. After draining $\frac{1}{5}$ of the water currently in the pool, what fraction of the pool's total capacity is occupied by water?
18. Line segment $EF$ has endpoints $E(3, 7)$ and $F(-1, 1)$. What are the coordinates of the point that is $\frac{3}{4}$ of the way from $E$ to $F$?
19. A parallelogram has vertices at A(1, 2), B(5, 4), C(7, 8), and D(3, 6). What is the slope of diagonal AC?
20. A party budget is $75; snacks cost $5 each plus $15 for plates. Solve $5x+15\le75$.

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