Practice Test 7 - 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 certain school, 60% of students play sports, 40% play music, and 15% play both sports and music. If a student is selected at random, what is the probability that the student plays sports given that the student plays music?
2. For a travel meal plan, evaluate: $(9 + 15) \div 3 + 2^3 \times 4 - 10$.
3. A recipe calls for $\frac{3}{4}$ cup of flour and $\frac{2}{3}$ cup of sugar. If Maria wants to make $\frac{1}{2}$ of the recipe, how many cups of flour and sugar combined will she need?
4. A rhombus has a side length of 13 cm and one diagonal of length 24 cm. What is the area of the rhombus?
5. A chef prepares soup using $2\frac{1}{2}$ pounds of vegetables per batch. If she makes $1\frac{3}{5}$ batches, how many pounds of vegetables does she use?
6. Two box plots are displayed side by side, showing the number of hours spent studying per week for students in honors classes versus regular classes. The honors class box plot has a higher median but also shows several outlier points below the lower whisker. What does this pattern most likely indicate about the studying habits in the honors class?
7. Calculate the range of math scores $55, 62, 70, 68, 74, 81, 77, 90, 85, 62, 79, 88, 73, 66, 62$.
8. A jar contains 5 red balls and 3 blue balls. Three balls are drawn without replacement. Which is more likely: drawing exactly 2 red balls or drawing exactly 2 blue balls?
9. Evaluate: $\frac{2^4 + 3 \times 4}{8 - 2^2} + 7$
10. A parallelogram has adjacent sides of lengths 12 cm and 8 cm, with an included angle of 60°. What is the area of the parallelogram?
11. Points E(2, 5), F(6, 8), and G(10, 11) are collinear. If point H is on the same line and has x-coordinate 14, what is the y-coordinate of point H?
12. A recipe that serves 8 people calls for $\frac{5}{6}$ cup of flour. How much flour is needed to serve 12 people?
13. What is the complete factorization of $5x^2 - 45$?
14. A regular octagonal prism has a base area of 48 square centimeters and a volume of 384 cubic centimeters. What is the height of the prism?
15. A cube-shaped storage box has side length 6 cm; using $V=s^3$, what volume fits inside?
16. The histogram shows the distribution of test scores. What is the mode of the test scores?
17. A spherical balloon has a radius of 6 inches. If the radius is increased by 50%, by what percent does the volume increase?
18. A recipe uses $1\,1/2$ cups flour; you add $3/4$ cup more. What is the total flour?
19. A rectangular patio has area $x^2-9$. Which expression is equivalent when factored completely?
20. A bank account has a balance of $-\$127$. After three transactions of $+\$45$, $-\$38$, and $+\$92$, what is the new balance?

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