Practice Test 5 - ISEE Upper Level Mathematics Achievement

20 questions. Answer them in any order, then submit to see your score and every explanation.

Start practice test

1. Lottery Draw: A school raffle uses numbers 1 through 10. A player wins by matching all 3 drawn numbers, and the order does not matter. What is the likelihood of winning with one ticket?
2. If $\frac{x}{y} = \frac{4}{5}$ and $x + y = 27$, what is the value of $x - y$?
3. In the figure, triangle PQR is a right triangle with the right angle at Q. If PQ = 9 cm and QR = 12 cm, and square QSTU is constructed on the hypotenuse PR, what is the area of square QSTU?
4. A cube has side length 9 cm; using $V=s^3$, what volume does it occupy?
5. A garden patio is a rectangle ($L=8\text{ m}, W=8\text{ m}$) with a semicircular seating area (radius $4\text{ m}$) attached along one full side and a right triangular planter (legs $8\text{ m}$ and $6\text{ m}$) attached along the opposite $8\text{ m}$ side. Both additions extend outward from the rectangle. The shared attachment edges are not part of the exterior boundary. Use $\pi\approx3.14$ and compute total paving area in square meters. Calculate the total area of the composite shape described.
6. A carpenter needs to cut a board that is $8\frac{1}{3}$ feet long into pieces that are each $1\frac{2}{9}$ feet long. How many complete pieces can be cut from the board?
7. A box plot shows exam scores with the following five-number summary: minimum = 62, Q1 = 74, median = 81, Q3 = 88, maximum = 96. Using the 1.5×IQR rule for outliers, if a new student scored 45 on the exam, how would this affect the box plot display?
8. If $\frac{3x + 2}{x - 1} = 5$ and $x \neq 1$, what is the value of $x$?
9. A teacher recorded the number of absences for each student in her class over a semester. The data shows: 0 absences (8 students), 1 absence (6 students), 2 absences (4 students), 3 absences (3 students), 4 absences (2 students), 5 absences (1 student). What is the median number of absences?
10. An elevator starts at floor $-2$ (2 floors below ground level). It goes up $7$ floors, then down $12$ floors, then up $8$ floors. On which floor does the elevator end up?
11. An isosceles triangle has a base of 16 cm and equal sides of length 10 cm each. What is the area of the triangle?
12. Two cards are dealt from a shuffled deck. What is the probability that the second card is an Ace, given that the first card was a King?
13. A student reads $\frac{2}{5}$ of a book on Monday and $\frac{1}{4}$ of the remaining pages on Tuesday. What fraction of the entire book has the student read after Tuesday?
14. A circle has an area of $144\pi$ square cm. What is the circumference of the circle?
15. Evaluate: $\frac{1}{2} + \frac{1}{3} \times \frac{1}{4} - \frac{1}{6}$
16. A geometric sequence multiplies by 8: $1, 8, 64, 512, 4,096, \dots$; what is next?
17. A lab uses $3\,1/5$ mL solution; $4/5$ mL is transferred. What is the remaining volume?
18. Which of the following expressions cannot be factored using integer coefficients?
19. A sphere has a diameter of 12 centimeters. What is its volume in cubic centimeters?
20. The stem-and-leaf plot shows test scores for a math class. What is the median score?

Practice tests