```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. problemsor close facsimiles. I would welcome any interesting or challengingproblems from geometry teachers,students  or anyone else interested. I introduce each class session with a "pre-class" problem. The instantthe student gets to the classroom she or he knows they must be tried.After a time the students actually look forward to these problems.  Theyare all closely related to S.A.T. problems and they are appropriate tothe material covered in the previous classroom sessions. These problems are very useful. The class always gets started quickly andtime on task is maximized. Students are excited by the problems. The factthat they are from S.A.T. tests challenge and motivate the students. Theconcepts of geometry are reinforced. Since the problems involve severalconcepts, review is built into the process. Geometry problems constitute 30% of the S.A.T. My feeling is that usingthis format helps the students to higher scores in the S.A.T. as well asa 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 ofeach angle.6. If the ratio of 2 complementary angles is 2:3 find the measure of thelarger angle.7. If the ratio of 2 supplementary angles is 1:3 find the measure of theangles.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 thetriangle 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 ofthe 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 45degrees and its diameter is 24.15. The legs of a right triangle are in the ratio of 5:12. If thehypotenuse 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 theirperimeters and the ratio of their areas.19. A triangle has sides of 6,6,x. What are all numbers x for which thetriangle is obtuse?20. How many cubes with an edge of 2 will fit into a cube with an edge of4?21. A sector of a circle has a central angle of  120 degrees. if the areaof 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 minimumand its maximum.23. Find the area of a circle if  its circumference is 16.
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