Practice Test 8 - 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 lab order is calculated; evaluate: $(14 + 10) \times (2^2) \div 4 - 3$.
2. A function $p(x)$ is defined recursively by $p(0) = 3$, $p(1) = 7$, and $p(n) = 2p(n-1) - p(n-2) + 4$ for $n \geq 2$. What is the explicit formula for $p(n)$?
3. Which expression represents the complete factorization of $x^4 - 16$?
4. A geometric sequence has common ratio 10: $1, 10, 100, 1,000, 10,000, \dots$; what is next?
5. Which expression is equivalent to $9x^2 - 30x + 25$?
6. If $p = 4$ and $q = 3$, evaluate $p^2 \div 2 + q(p - 1) - 2q + 5$
7. A bag contains 8 red marbles, 6 blue marbles, and 4 green marbles. Two marbles are drawn without replacement. What is the probability that both marbles are the same color compared to the probability that the two marbles are different colors?
8. In a dice game, you roll two fair six-sided dice, so there are 36 equally likely outcomes. The event $D$ is "you roll doubles," which includes $(1,1)$ through $(6,6)$. What is the probability $P(D)$?
9. If $3(x - 2) + 5 = 2(x + 1) - 4$, then $x =$
10. A survey of 25 students asked how many hours they spent on homework last week. The results were: 5 hours (3 students), 6 hours (5 students), 7 hours (8 students), 8 hours (6 students), 9 hours (3 students). If the two students who spent the least time are removed from the data, what is the new mode?
11. The temperature dropped from $7°C$ to $-14°C$ over a 6-hour period. If the temperature dropped at a constant rate, what was the temperature after the first 2 hours?
12. The solution to $-2(3x - 4) \geq 5x + 1$ is:
13. A triangle has vertices at A(2, 6), B(8, 3), and C(5, 9). What is the slope of the altitude from vertex C to side AB?
14. A cylindrical can has a volume of 200π cubic inches and a height of 8 inches. If the height is increased to 12 inches while keeping the same radius, what is the new volume?
15. A sequence is defined by $a_n = n^2 + 2n - 1$. What is the difference between the $10$th and $8$th terms?
16. A circular sector has a central angle of 120° and a radius of 9 cm. What is the perimeter of the sector?
17. If a bank account changes by $-24 \div 6$ and then by $+15$, what is the net change?
18. If $3x - 7 = 2x + 11$, then what is the value of $5x - 3$?
19. A square and an equilateral triangle have the same perimeter. If the area of the square is 144 square units, what is the area of the triangle?
20. A business must cover $200 fixed cost and earns $16 per item; solve $16x-200\ge0$.​​

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