Date: Sep 30, 1992 11:05 AM Author: Bernie Ivens, ivens@forum.swarthmore.edu Subject: Some S.A.T. problems Dear Colleagues and Geometers,

Listed are about 23 geometry problems which are actual S.A.T. problems

or close facsimiles. I would welcome any interesting or challenging

problems from geometry teachers,students or anyone else interested.

I introduce each class session with a "pre-class" problem. The instant

the student gets to the classroom she or he knows they must be tried.

After a time the students actually look forward to these problems. They

are all closely related to S.A.T. problems and they are appropriate to

the material covered in the previous classroom sessions.

These problems are very useful. The class always gets started quickly and

time on task is maximized. Students are excited by the problems. The fact

that they are from S.A.T. tests challenge and motivate the students. The

concepts of geometry are reinforced. Since the problems involve several

concepts, review is built into the process.

Geometry problems constitute 30% of the S.A.T. My feeling is that using

this format helps the students to higher scores in the S.A.T. as well as

a deeper understanding of the concepts of geometry.

1. If the perimeter of a square is 40 find its area.

2. If the area of a square is 144 find its perimeter.

3. If the circumference of a circle is 14p find its area.

4. If the area of a circle is 81p find its circumference.

5. If the ratio of the angles of a triangle is 2:3:5 find the measure of

each angle.

6. If the ratio of 2 complementary angles is 2:3 find the measure of the

larger angle.

7. If the ratio of 2 supplementary angles is 1:3 find the measure of the

angles.

8. Find the area of an isosceles right triangle if its hypotenuse is 12.

9. Find the hypotenuse of an isosceles right triangle if the area of the

triangle is 50.

10. If the perimeter of a square is 32 find the length of its diagonal.

11. If the diagonal of a square is 12, find the perimeter and the area of

the square.

12. If the perimeter of an equilateral triangle is 36, find its area.

13. If the area of a square is 20 find the length of its diagonal.

14. Find the area of a sector of a circle if its central angle is 45

degrees and its diameter is 24.

15. The legs of a right triangle are in the ratio of 5:12. If the

hypotenuse is 26, find the area of the triangle.

16. Find the ratio of a side of a square to its perimeter.

17. Find the ratio of a side of a square to its diagonal.

18. The ratio of the sides of 2 squares is 2:3. Find the ratio of their

perimeters and the ratio of their areas.

19. A triangle has sides of 6,6,x. What are all numbers x for which the

triangle is obtuse?

20. How many cubes with an edge of 2 will fit into a cube with an edge of

4?

21. A sector of a circle has a central angle of 120 degrees. if the area

of the sector is 12p, find the radius of the circle.

22. A triangle has sides of 5,7,x. If x is an integer find its minimum

and its maximum.

23. Find the area of a circle if its circumference is 16.