ISEE Upper Level Word Problems Practice Test 24

1. Mr. Lear recorded the number of inches of rain on each day during the month of February in the table below.

What is the mode of the data?

• A. 2
• B. 3
• C. 5
• D. 12

2. From a club of 7 members, 3 will be chosen for President, Vice President, and Treasurer. How many different arrangements of members are possible for the 3 positions?

• A. 18
• B. 35
• C. 210
• D. 343

3. Use the diagram to answer the question.

If the radius of Circle O is 6, what is the area of the shaded region?

• A. 9π – 18
• B. 9π – 36
• C. 12π – 18
• D. 36π – 36

4. If the number of students in a classroom is increased from 20 to 25, what is the percent increase in the number of students?

• A. 20%
• B. 25%
• C. 55%
• D. 80%

5. If x is the square root of a number that is not a perfect square, y is the square root of a different number that is not a perfect square, and neither x nor y is a factor of the other, which one of the following could be a rational number?

• A.
• B.
• C.
• D.

6. Triangle ABC is similar to triangle PQR. The length of is 7 cm, and the length of is 4 cm. If the length of is 16 cm, what is the length of ?

• A. 28
• B. 21
• C. 14
• D. 4

7. What is the value of (x + 4)(x – 5)?

• A. x² – 1
• B. x² – 20
• C. x² – x – 20
• D. x² + x – 20

8. The measures of three of the angles of a quadrilateral are shown in the diagram.

What is the measure of the fourth angle?

• A. 105
• B. 115
• C. 205
• D. 215

9. The equation x = is true for what value(s) of x?

• A. –2
• B. 0
• C. all real numbers
• D. There are no values for x that would make the equation true.

10. What expression is equivalent to 3a³b⁵ + 2a²b⁴ – (7a²b⁴ – 4a³b⁵)?

• A. –4a³b⁵ + 6a²b⁴
• B. 5a³b⁵ – 3a²b⁴
• C. –5a³b⁵ + a²b⁴
• D. 7a³b⁵ – 5a²b⁴

11. If x is an odd number, which one of the following expressions is an even number?

• A. x(x + 8)
• B. (x + 2)(x – 4)
• C. x² – 2
• D. x² – x

12. The height of a tree is 30 feet, and it casts a shadow of 18 feet, as shown in the diagram.

If Carmella is 5 feet tall, what is the length of her shadow at the same time of day?

• A. 2 feet
• B. 3 feet
• C. 4 feet
• D. 6 feet

13. What is the value of ?

• A. 8x⁶
• B. 8x¹⁸
• C. 32x⁶
• D. 32x¹⁸

14. The table below shows the results of a survey of 90 people at a movie theater. Each person was asked to name his or her favorite type of movie, by category.

If this data is used to make a circle graph, what is the central angle of the portion of the graph representing Comedy?

• A. 15°
• B. 60°
• C. 150°
• D. 240°

15. There are 2 purple beads, 5 black beads, and 9 yellow beads in a bag. If 2 beads are selected at random without replacing the first bead, what is the probability of picking a yellow bead and then a purple bead?

• A.
• B.
• C.
• D.