Kansas City Area Teachers of Mathematics 2011 KCATM Math Competition GEOMETRY GRADES 7-8

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1 Kansas City Area Teachers f Mathematics 2011 KCATM Math Cmpetitin GEOMETRY GRADES 7-8 INSTRUCTIONS D nt pen this bklet until instructed t d s. Time limit: 20 minutes Yu may use calculatrs. Mark yur answer n the Scantrn sheet by FILLING in the val. Yu may nt use rulers, prtractrs, r ther measurement devices n this test. Letter E is Nne f the abve. It is a crrect answer fr sme f the prblems. Use the key n yur calculatr.

2 1. What is the area f a square with a perimeter f 28 inches? A. 14 in B. 49 sq. in C. 7 sq. in. D. 14 sq. in. 2. T the nearest tenth f an inch, find the base f a parallelgram when the area is 24 sq. m and the height f the parallelgram is 3.7 m. A m B. 6.5 m C. 8.3 m D. 4.6 m 3. T the nearest whle percent, find the gemetric prbability f landing n a shaded square if yu tss a marker n the crsswrd puzzle in Figure 1. A. 36% B. 37% C. 20% D. 21% Figure 1 4. Find the area f the blck letter E in Figure 2. A. 52 cm 2 B. 50 cm 2 C. 72 cm 2 D. 48 cm 2 Figure 2 5. Determine the value f x in the issceles triangle given in Figure 3. Figure 3 A. 75 B. 40 C. 50 D. 60

3 6. The number line in Figure 4 includes bth psitive and negative integers. What is the lcatin f pint A if A is the midpint f BC, and C is the midpint f DE. D B E Figure 4 A. -5 B. -4 C. -3 D Find the cmplement f a 42 angle. A. 42 B. 58 C. 138 D. 48 Use Figure 5 fr Prblems #8-10. Given: line m is parallel t line n. m n Figure 5 8. Name a pair f alternate interir angles in Figure 5. A. 1 and 4 B. 2 and 7 C. 3 and 5 D. 4 and 8 9. If m find m 6. A. 132 B. 58 C. 48 D If m 3 3x 5 and m 5 x 9 determine the value f x. A. 21 B. 44 C. 7 D What is the central angle f a standard dart bard? See Figure 6. A. 15 B. 18 C. 20 D. 24 Figure 6

4 12. Which tw shapes n the gebard have the same area? See Figure 7. A. Rectangle and right triangle B. Right triangle and issceles triangle C. Issceles triangle and ctagn D. Octagn and rectangle Figure A Pythagrean Triple is defined as a set f three whle numbers such that wrk in the Pythagrean Therem. Which set f 3 whle numbers is NOT a Pythagrean Therem? A. 6, 8, 10 B. 5, 12, 13 C. 11, 60, 61 D. 9, 40, If a 36 bard is cut int 3 pieces with a rati f 2: 3: 7, determine the length f the largest piece. A. 21 in. B. 14 in. D. 28 in. D. 9 in. Use the rhmbus ABCD in Figure 8 fr prblems # Given: AE = 3 cm, and CE = 4 cm A B 4 3 E 15. If m 74 ACD, what is BAD C m? D Figure 8 A. 74 B. 37 C. 16 D If AE = 3 cm, and CE = 4 cm, find the perimeter f the rhmbus. A. 24 cm B. 20 cm C. 28 cm D. 26 cm 17. If AE = 3 cm, and CE = 4 cm, find the area f the rhmbus. The frmula is A = ½ (d 1 )( d 2 ). A. 24 sq. cm B. 48 sq. cm C. 28 sq. cm D. 25 sq. cm

5 18. Determine the length f the chrd CE in circle O in Figure 9 with the given infrmatin: A. 8 C B B O 6 E D Figure 9 C. 16 D Determine the crdinates f C when ABC is reflected ver the vertical axis in Figure 10. A. (4, 1) B. (-4, 1) C. (-4, -1) D. (4, -1) Figure If the translatin rule is (x - 3, y 4), determine the crdinates f A in Figure 11 if A(2, 2). Y A Figure 11 X A. (0, 6) B. (4, 4) C. (-1, -2) D. (-7, 3) 21. Find ne interir angle measure f a regular hexagn. A. 90 B. 120 C. 135 D What is the area f a circle with circumference f 16 inches? A. 16 in 2 B. 64 in 2 C. 4 in 2 D. 256 in 2

6 23. If yu cut the 4 large circles ut f a piece f cnstructin paper, t the nearest sq. inch, hw much waste is there? The size f the square is 12. See Figure A. 31 sq. inches B. 116 sq. inches C. 29 sq. inches D. 12 sq. inches Figure If yu are 16 years ld, then yu can get a driver s license. Which f the fllwing statements is the cnverse? Determine if the cnverse is true r false. A. If yu aren t 16 years ld, then yu cannt get a driver s license. False B. If yu dn t get a driver s license, then yu are nt 16 years ld. True C. If yu get a driver s license, then yu are 16 years ld. False D. If yu are at least 16 years ld, then yu can get a driver s license. True 25. Determine the expressin fr the area f the rectangle with dimensins (x + 2) and (x + 4) as demnstrated in Figure 13 with Algebra Tiles: A. x 2 2x + 8 B. x 2 + 4x + 8 C. x 2 + 6x 8 D. x 2 + 6x + 8 Figure What is the expressin fr the perimeter f the parallelgram in Figure 14? A. 4x - 6 B. 8x - 12 (x +2) (x-3) C. 5x - 9 D. 3x 2 17x - 24 (3x 8) Figure Which shape best describes a quadrilateral with all right angles and fur cngruent sides? A. Rectangle B. Parallelgram C. Rhmbus D. Square

7 28. Which shape describes the set f all pints equidistant frm ne pint in space? A. Square B. Cube C. Sphere D. Circle 29. In the rectangle given in Figure 15, 1 (3x 8) Figure 15 x m Determine the value f x. A. 62 B. 124 C. 56 D Shaun White is a prfessinal skatebarder and snwbarder. If he des rtates tw cmplete turns, what degree did he rtate? See Shaun White in Figure 16. A. 180 B. 360 C. 540 D. 720 Figure Determine the value f x given an exterir angle f a triangle as shwn in Figure 17. Figure 17 A. 65 B. 10 C. 25 D Which methd can be used t prve the 2 triangles cngruent in the Figure 18? Given: AD CB and AB CD B D A C Figure 18 A. SSS B. SAS C. AAS D. HL

8 33. Slve fr distance, d, acrss the lake given tw similar triangles in Figure 19. C d A. 25 m B. 30 m C. 35 m D. 75 m Figure What is the hyptenuse value f a triangle with side length 9? A B. 9 2 C D What effect des dubling all sides f a cube have n the vlume f the cube? A. Stays the same B. Dubles the vlume C. Fur times the vlume D. Eight times the vlume 36. T the nearest ft, determine hw tall the flagple is if its shadw is 23 ft. Yu are 5 3 tall and yur shadw is 11 ft. lng. See Figure 20. A. 11 ft. tall B. 48 ft. tall C. 12 ft. tall D. 23 ft. tall Figure Which statement shws hw t slve fr the height f the ledge in Figure 21? A. B. C. Figure 21 D.

9 38. Determine x when given the central angle measure f 74 in the circle in Figure A. 74 B. 33 C. 27 D. 37 Figure Determine the equatin f a line perpendicular t the given line in Figure 23: A. y = 2/7 x - 5 B. y = -2/7x + 1 C. y = -7/2 x + 2 D. y = 7/2 x + 4 Figure Tw angles frm a linear pair. The btuse angle is six less than twice the measure f the acute angle. Determine the measure f the btuse angle. A. 122 B. 118 C. 116 D. 120