BROWNSVILLE CITY MATH MEETHOMER HANNA HIGH SCHOOL

APRIL 14,2004

GEOMETRY (HIGH SCHOOL)

~E _ SCHOOL, _

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UTBITSC MathematicsDepartment (858) 57+ee3eF8X(9se)57~37

Spring 2004

BlSD MATHEMATICS MEET GEOMETRY

1. Points A(3, -2), E(l, -2), and C(l, 2) are the vertices of a right triangle. Using the

formula A = ~bh, where b is the base and h is the height of the triangle, find the area of

!lABC.

[A] 8 (8] 2 [C] 64 [D] 4 [E] 16

2. Find the measure of one of the interior angles of a regular polygon with nine sides.

[A) 400 [B] 200 [C] 1400 [D] 1600

3. Compare the quantity in Column A with the quantity in Column B.Column A Colwnn Bthe measure of each exterior the measure of each exteriorangle of a regular pentagon angle of a regular hexagon

[A] The quantity in Colwnn A is greater. [B] The quantity in Column B is greater.

[C] The quantities are equal.

[0] The relationship cannot be determined on the basis of the information given.

4. Select the geometric figure that possesses all of the following characteristics:(1) four equal sides(2) both pairs of opposite sides are parallel(3) it does not contain a right angle

[A] square [B] parallelogram [C] isosceles triangle [0] rhombus

5. The two short sides of a kite are 2%+5 and 22 - y . The two long sides are 4x + 3 andy - 2. Find the values of the variables and the lengths of the sides.

[A] x=6,y= 19;27, 17

[el x=2! y-11" 9 102 ' "

[B] x = l,y= 12; 7,10

[D] X" 2, y - 13; 9, 11

6. Find the coordinates of the center and the radius of the circle with diameter CD.er-r, -3), D(9. 7)

[A] (4, 2), 5.fi [B] (4,2), 2m [e) (-5, -5), 3.fi [D] (-5, -5), 2.15

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BISD MATHEMA TICS MEET GEOMETRY

7. In the figure shown, BC " DE , AB = 5 yards, BC = 7 yards, AE = 16 yards, andDE = 28 yards. Find CE .

A

D E

[A] 15 yd [B] 20 yd [C] 12 yd (0] 4yd

8. What is the reflection of (-2,3) in the line y = -x? -~..[A] (3, -2) [B] (3,2) [C] (-3,2) [0] (-3, -2)

9. Compare the quantity in Column A with the quantity in Column B.

17

Column A Column Ba b

[A] The quantity in Column A is greater. [B] The quantity in Column B is greater.

[Cl The two quantities are equal.

[0] The relationship cannot be determined on the basis of the information supplied.

10. Which of the lines is not perpendicular to 2%+Y = 8 ?

[B] x-2y = 3 [C] 2x-y=4 (0] 2y-x = 4

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BlSD MATHEMATICS MEET GEOMETRY

1 1. Describe the locus of points in a plane a distance 5 from point X in that plane.

[A] a plane a distance 5 from the point X [B] a circle with center X and radius 5

(C] a line with X as the midpoint [0] a sphere with center X and radius 5

12. Find the area of the rectangle with the given base and height.5 yd 16 in., 24 yd

[A] 80 yd1 120 in.'

[el 120 ydl 80 in.l

[B] 130 yd? 864 ln.'

[D] 58 yd2 32 in.'

13. A solar energy collector needs several 3 in. by 3 in. square panels to cover an area 17 ftby 4 ft. How many of the square panels are needed?

[A] 1088 [B] 612 [e] 91 [D] 3264

14. The area ofa rectangle is decreased by 25%. Whieh of the following could havehappened?

[A] One side is decreased by 50%.

[e] Both sides are decreased by 25%.

[E] none of the above

[B] One side is decreased by 25%.

[D] Both sides are decreased by 50%.

15. The measures of two sides of a triangle are 10 and 11. Use an inequality to express therange of the measure of the third side, m.[A] 1 <m<21 [B] 10<m<21 [e] 1 <m< 13 [0] O<m<9 .

16. The area of a square is 200 ern", How long is the diagonal?

[A] 20 em [B] 28.2 em [Cl 14.1 em [D] 141.4 em [El none of the above

17. Find the area of a regular heptagon with an apothem 6.2 miles long and a side 6 mileslong.

[A) 11 1.6 mi2 (B] 260.4 mi2 [Cl 130.2 mi2 [D] 65.1 mi2

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srso MATHEMATICS MEET GEOMETRY

18. For a circle of radius 6 feet, find the arc length of a central angle of 24 0 •

8 12[B] -1t feet [C] -1t feet5 5[A] 1441tfeet 4[OJ -1t feet

5

19. Find the area of the shaded segment. Round your answer to the nearest hundredth.

[A] 19.63 ml [B) 12.5 ml [C] 7.13 ml . [0] 26.77 ml

20. What is the value of x?

8

[A] 20 [B] 2 [C] 3.25 [0] 5 [E] cannot bedetermined

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BISO MATHEMATICS MEET GEOMETRY

21. Calculate the volwne of the pyramid.

13 m

(B] 676 ml [e] 668 ml [0] 12~ ml3

22. Liola drives 13 Ian up a hill that is at a grade of 14°. What horizontal distance, to thenearest tenth of kilometer, has she covered?

[A] 13.6 Ian [B] 3.1 km [C] 12.6 km [0] 3.2 Ian

23. The shorter leg ofa 30°-60°-90° triangle is 6.4 inches long. Find the perimeter.

[A] 44.34 in. (B] 36.2 in. [Cl 28.25 in. [0] 30.29 in.

24. Which of the following cannot be the lengths of a 30 ° -60 ° -90 ° triangle?

[A] 7.. ~ 7 J33 J 3' 3

--

[B] 5, 10, 5../3 [e] 12, 6, 6../3 (0] 4, 2, 4/3

25. Find the volume of the cone that bas a diameter of 10 feet and a height of 17 feet. (Use3.14 for x.)

[A] 533.8 ftl [B] 1779.33 ftl [el 1334.5 ftl [0] 444.833 ft '

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SPRING 2004

arso MATHEMATICS MEET GEOMETRY

26. Compare the quantity in Column A with the quantity in Column B.B

A

D

Column A..-AB

Column B..-BC

[A] The quantity in Column A is greater. [B) The quantity in Column B is greater.

[C] The quantities are equal.

[0] The relationship cannot be determined on the basis of the information given.

- -27. In the figure shown HC IIGD and·m LABC = 104. Which of the following statements isfalse?

[A] LHBF and LAED are alternate interior angles. [B] m LDEF = 104

[Cl m LGEF = 104 [0] LABH and LAEG are corresponding angles.

28. Find the center of a circle if one chord has endpoints (-1, - 2) and (3, 4) and anotherhas endpoints (II, -10) and (11, 4).

[A] (7, - 3) [B) (6, -1) [C) (0, 0) [D) (11. - 3)

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BISO MATHEMA TICS MEET GEOMETRY

29. The measures of the angles of a quadrilateral are x + 15, 2x, x - 45, and 2x - 60. Whattype(s) of quadrilateral could this be?I. parallelogram II. rectangle III. trapezoid

[A] I only [B] I and III [C] III only [0] II only [E] I and II

30. Which statement is true for the triangles shown below?

D__-------'-L----------~~B

E

(A] AC = 9.6 (B] mLx=40 [C] CE = CBCA CD

[0] mLz * m Zw

31. To find the height of a pole, a surveyor moves 180 feet away from the base of the poleand then, with a transit 6 feet tall, measures the angle of elevation to the top of the pole tobe 400 . What is the height of the pole? Round answer to the nearest foot

[A] 151 ft [B) 157 ft [Cl 215 ft [0] 221 ft

32. Find the value of x to the nearest tenth. [A] 13.8 [B] 6.2 [el 15.1 [0] 11.6

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SPRlNG 2004

BlSD MATHEMATICS MEET GEOMETRY

33. Suppose a constellation of stars is plotted on a coordinate plane. The coordinates of thefirst star are (-2, -2). The second star is translated right 4 units. What are the newcoordinates?

(A] (2, -2) [B] (-6, -2) (C] (-2,-<5) [0] (-2,2)

34. Find the geometric mean of 108 and 3. [A] 36 [B) 55.5 [C] 9 [0] 18

35. Find the value ofx if AB = 23, BC = 9, and CD = 8. (not drawn to scale)

[A] 24.9 [B] 30.3 [C] 28.0 [0] 29.6

36. Compare the quantity in Column A with the quantity in Column B.Column A Column Bperimeter of a square perimeter of a rectangle that is not

with area 64 em! a square with area 64 cm1

[A] The quantity in Column A is greater. [B] The quantity in Column B is greater.

[C] The two quantities are equal.

[OJ The relationship cannot be determined on the basis of the information supplied.

37. In aABC, Jis on AB, Kis on BC, and JK" AC. Solve for x if JB = 8, AJ = 19,BK = x+9, and KC = 6x.

[A] 11453

29[B] m (C] E-

114[0] .!2!

29

38. A glass sphere weighs 0.55Ib. How much does another such sphere weigh if its diameteris three times as large?

[A] 7.55 Ib (B] 14.851b [C] 1.651b [0] 4.951b

UTBffSC MATHEMA TICSDEPARTMENT

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SPRING 2004

BISD MATHEMATICS MEET GEOMETRY

39. A photographer shines a camera light at a particular painting forming an angle of 40 0

with the camera platform. If the light is 54 feet from the wall with the painting, how highabove the platform is the painting?

x

54 ft

[A] 1.19 ft [B] 45.31 ft [e] 0.84 ft [D] 64.35 ft

40. Find the value of x.

~

_.

[A]3& [B] 255 [C] 3J3 [0] 6J1541. Compare the quantity in Column A with the quantity in Column B.

ColumnAAP

ColumnBAX

[A] The quantity in Column A is greater. [B] The quantity in Column B is greater.

[C] The two quantities are equal.

[D] The relationship cannot be determined on the basis of the information supplied.

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SPRING 2004

BISD MA THEMA TICS MEET

[AJ 46.3 em' [B] 70.9 ern'

42. Find the area of a regular nonagon With radius 4 em.

[C] 64.9 ern'

GEOMETRY

[D] 92.6 ern'

43. A gardener needs to cultivate a triangular plot of land. One angle of the garden is 26°,and the sides that surround it are 34.5 ft and 88.5 ft. What is the area of the plot ofland?

[A] 1372.lft2 [B] 645.6 ft2 [C] 669.2 ft2 [D] 1338.5 ft2

44. A small messenger company can only deliver in a small part of the city. Write anequation for the boundary where the company delivers, and find its radius.

... .. .. .. .. .. .. ..................... .

(A] (x _1)2 +(y_2)2 = 64; r = 64 blocks

[B] (.%+2)2 +(y+ 1)2= 128; r = 8 blocks

[C] (x-l)2 +(y_2)2 = 64; r=8 blocks

[0] (r + 2)2 + (y + 1)2 = 128; r = 64 blocks

45. Find mLA .

.--+-~~

[A] 90 [B] 28 [C] 62 [0] 47

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[E] none of the above

SPRING 2004

BISO MATHEMATICS MEET GEOMETRY

46. The area of a regular octagon is 50 ern". What is the area of a regular octagon with sidesfour times as large?

(AJ 865 crn ' (8] 800 cm ' (C] 200 ern' [0] 10000 em!

47. Find the value ofx to the nearest tenth. [A] 9.8 (BJ 15.7 [C] 8.5 (0] 16.3 •

-~'

48. A park maintenance person stands 17 m from a circular monwnent. If you asswne herlines of sight form tangents to the monument and make an angle of 310, what is themeasure of the arc of the monument that her lines of sight intersect?

[A] 149 [B) S9 [C] 121 [0] 118

49. A footbridge is in the shape of an arc of a circle. The bridge is 8 ft tall and 26 ft wide.What is the radius of the circle that contains the bridge? ROWld your answer to thenearest tenth. .

[A] 6.6 ft [C) 29.1 ft [0] 21.1 ft

50. A point P has coordinates (-8, -7). What are its new coordinates after reflecting point Pin the x-axis?

[A] (8, -7) [B] (-8, -7) [Cl (-8, 7) [0] (8, 7)

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SPRING 2004