1. A farmer wants to partition a rectangular 24 feet by 30 feet garden into smaller square plots. What is the length, in feet, of the sides of the largest square plots into which the farmer can partition the garden so that no land is left over?

2. For which of the following expressions is x – y a factor?
I.y³ – x³
II.(x² – y²)⁵
III.x³ – 3x²y + 3xy² – y³

3. The measures of the angles of a triangle are in the ratio 2:3:5. What is the measure of the smallest angle?

4. A science book has scale drawings of insects. The scale shows that 1 centimeter in the drawing represents 2.5 centimeters of actual length. What is the length (in centimeters) of the scale drawing of a grasshopper if the grasshopper is actually 9.0 centimeters long?

5. If the perimeter of triangle ABC is 60 centimeters, what is the perimeter in centimeters of the triangle formed by connecting the midpoints of the sides of triangle ABC?

6. The measures of the angles of a triangle are in the ratio 2:3:5. What is the measure of the smallest angle?

7. A science book has scale drawings of insects. The scale shows that 1 centimeter in the drawing represents 2.5 centimeters of actual length. What is the length (in centimeters) of the scale drawing of a grasshopper if the grasshopper is actually 9.0 centimeters long?

8. A farmer wants to partition a rectangular 24 feet by 30 feet garden into smaller square plots. What is the length, in feet, of the sides of the largest square plots into which the farmer can partition the garden so that no land is left over?

9. To estimate the number of turtles in a lake, a team of biologists captures and tags 20 turtles and then releases the turtles unharmed back into the lake. Two weeks later, the team returns to the lake and captures 30 turtles, 6 of which have tags indicating that they are recaptured turtles. Based on this capture-recapture method, what is the best estimate of the number of turtles in the lake?

10. A college student recently worked four weeks in a new summer job. In the fourth week, the student worked 20% more hours than in the third week. In the third week, the student worked 25% more hours than in the second week. In the second week, the student worked 40% more hours than in the first week. The student worked 42 hours in the fourth week on the job. How many hours did the student work in the first week on the job?

11. To estimate the number of turtles in a lake, a team of biologists captures and tags 20 turtles and then releases the turtles unharmed back into the lake. Two weeks later, the team returns to the lake and captures 30 turtles, 6 of which have tags indicating that they are recaptured turtles. Based on this capture-recapture method, what is the best estimate of the number of turtles in the lake?

12. If f(x) = x² + x + 1 and , then what is the value of

13. In the preceding figure with angle measures as shown, which segment is longest?

14. Three daughters and two sons inherit land from their parents. The older son inherits of the land, and the oldest daughter inherits . The three remaining children equally share the remaining land. What fraction of the land does the younger son inherit?

15. Which of the following sets of numbers could NOT be the lengths of the sides of a triangle?
I.8, 14, 18
II.6, 16, 24
III.2, 3, 5

16. The number of elements in the union of sets A and B is 160, and the number of elements in the intersection of sets A and B is 20. If the number of elements in set A is 50, what is the number of elements in set B?

17. When m + n = –6, what is the value of the above expression?

18. Which of the following sets of numbers could NOT be the lengths of the sides of a triangle?
I.8, 14, 18
II.6, 16, 24
III.2, 3, 5

19. A water tank can be filled in 6 hours when the input valve is open and the outlet valve is closed. When the input valve is closed and the outlet valve is open, the same tank can be emptied in 10 hours. If a tank is filled with both valves open, how long, in hours, will it take to fill the tank?

20. The number of elements in the union of sets A and B is 160, and the number of elements in the intersection of sets A and B is 20. If the number of elements in set A is 50, what is the number of elements in set B?