Practice Test 11 - 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. Dice Game: Two fair six-sided dice have 36 equally likely outcomes. The compound event $C$ is "roll a sum of 7 and roll doubles" on the same roll. What is the probability $P(C)$?
2. A weather report says $P(R)=40\%$ for rain and $P(H)=30\%$ for high temperatures. The report treats $R$ and $H$ as independent events. What is the likelihood of both rain and high temperatures?
3. Which expression represents the complete factorization of $2x^3 - 18x$?
4. What is the complete factorization of $8x^3 - 27$?
5. Simplify: $\frac{(-12) + (-18)}{(-6) - (-3)}$
6. The slope of line segment AB is $-\frac{2}{5}$. If A has coordinates (-3, 8) and B has coordinates (12, y), what is the value of y?
7. The figure shows the graph of a function $f(x)$. What is the average rate of change of $f(x)$ from $x = 1$ to $x = 4$?
8. In the coordinate plane, the vertices of rectangle $WXYZ$ are $W(-2, 1)$, $X(4, 1)$, $Y(4, 5)$, and $Z(-2, 5)$. What is the perimeter of the rectangle?
9. What is the value of $(-3)^4 - (-2)^5 + (-1)^{10}$?
10. What is the reciprocal of $\frac{2}{3} \div \frac{4}{9}$?
11. A seamstress has $8\frac{1}{3}$ yards of fabric. She uses $2\frac{3}{4}$ yards for a dress and $1\frac{5}{6}$ yards for a skirt. How much fabric remains?
12. A sphere is inscribed in a cube with side length 10 centimeters. What is the volume of the sphere?
13. Which of the following expressions is equivalent to $6x^3 + 9x^2 - 6x - 9$?
14. A triangular prism has a triangular base with an area of 24 square inches and a height of 10 inches. What is the volume of the prism?
15. Which expression represents the factored form of $x^3 - 8$?
16. The double bar graph compares the number of students in two different schools over six months. Looking at the data, in March School B had exactly twice as many students reading books as School A. What was the total number of students reading books in March across both schools?
17. A rectangular aquarium measures 30 cm by 20 cm by 25 cm; what is its volume in cubic centimeters?
18. Which expression is the complete factorization of $16x^4 - 1$?
19. Kevin runs $4\frac{3}{5}$ miles each day for $2\frac{1}{4}$ days. What is the total distance he runs?
20. In a science experiment, evaluate the materials cost: $40 + (18 \div 3) \times 2^2 - 9$.

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