SECTION II TIME - 30 minutes 25 QUESTIONS :RA In this section solve each problem, using any available space on paper for scratchwork. Then decide which is the best of the choices given and select the answer. :RA The following information is for your reference in solving some of the problems. 2 Circle of radius r: Area = #r ; Circumference = 2#r The number of degrees of arc in a circle is 360^. The measure in degrees of a straight angle is 180^. Definitions of symbols: = is equal to ^ is parallel to > is greater than [ is perpendicular to :RA :SB :SP257079203024179079257079 :SP203079203024203024203024 :SH1126A D B :SH0330C :SF Triangle: The sum of the measures in degrees of the angles of a triangle is 180. If <CDA is a right angle, then (1) area of {ABC AB x CD = ------- 2 2 2 2 (2) AC = AD + DC :RA :SD Note: Figures which accompany problems in this test are intended to provide information useful in solving problems. They are drawn as accurately as possible EXCEPT when it is stated in a specific problem that its figure is not drawn to scale. All figures lie in a plane unless otherwise indicated. All numbers used are real numbers. :RA :Q1 1. The number of cubic yards in a bin 8' x 6' x 3' is: (a) 5 1/3 (b) 16 (c) 48 (d) 6 (e) 144 :RCA :Q1 2. If the quotient of two numbers is 1, their difference is: (a) 1 (b) -1 (c) 0 (d) 2 (e) half of each number :RCC :Q1 3. If 3/5 of the voters voted for candidate A, and 3/4 of the remaining votes were cast for B, what fraction of the votes was cast for candidates other than A and B? (a) 1/5 (b) 3/10 (c) 1/10 (d) 4/9 (e) 1/4 :RCC :Q1 _______ / 2 2 4. If c = \/ a + b , find c when a = 3 and b = 4. (a) 5 (b) 25 (c) 7 (d) 625 (e) 75 :RCA :Q1 2 5. If mx = m + m, x = ? 2 (a) m (b) 2m (c) m (d) m + 1 (e) It cannot be determined from the information given. :RCD :Q1 MN 6. If -- = 1 and M = N, then in terms L of M, L = 2 1 M 1 (a) -- (b) -- (c) -- (d) 2M 2 2 2M M (e) None of the above. :RCE :Q1 7. In making a round trip between two river ports 48 miles apart, a ship averages 9.6 miles an hour. If the ship takes 6 hours one way, how many hours does the return trip take? (a) 6 (b) 4 (c) 44 (d) 1 (e) 12 :RCB :Q1 8. The thickness of a ring is equal to the radius of the inner circle. If the area of the outer circle is 100# sq. in., the area of the ring is: (a) 25# sq. in. (b) 50# sq. in. (c) 66 2/3# sq. in. (d) 75# sq. in. (e) It cannot be determined from the information given. :RCD :Q1 9. In terms of its perimeter p and its height h, the area of a rectangle is: (a) p - 2h (b) h(p - 2h) p h (c) - - h (d) - (p - 2h) 2 2 (e) It cannot be determined from the information given. :RCD :Q1 :SB :SC200035200055225055225055 :SP225038225055200038225038 :SH0829O :SH0834E :SH0629D :SH0430A :SH0634C :SF 10. ODCE is a rectangle, and radius OA = 8'. Find DE. _ (a) 4\/2' (b) 8' _ _ (c) 4\/3' (d) 8\/2' (e) It cannot be determined from the information given. :RCB :Q1 :SD :SB :SC165040235040200055165040 :SH0525A :SH0535B :SH0830O :SF 11. Right {AOB has an area of 32 square units. AO[BO Find the number of square units in the area of the; circle whose center is O. (a) 128 (b) 32# (c) 16# (d) 128# (e) 64# :RCE :SD :Q1 :SB :SP175023266023245023263040 :SP175071266071231071263040 :SH0326A E B :SH1026C F D :SH04332x^ :SH0635x^ :SH09312x^ :SF 12. AB^CD. Find x. (a) 36 (b) 45 (c) 60 (d) 72 (e) 30 :RCD :SD :Q1 :SB :SP252032182071252071252032 :SP210056210071210071210071 :SH1026A E C :SH0437B :SH0730D :SF 13. DE = 4, AE = 5, and EC = 10. The length of BC is: (a) 8 (b) 12 (c) 12.5 (d) 18.75 (e) 7.5 :RCB :SD :Q1 14. If the vertex angle of an isosceles triangle contains m^, each base angle contains: m m^ (a) (90- -)^ (b) -- (c) (180 - m)^ 2 2 (d) (180 - 2m)^ (e) (90 - m)^ :RCA :Q1 15. At the time when a vertical yardstick casts a shadow on the ground 2 feet in length, what is the length of the shadow of a man 6 feet tall? (a) 3 ft. (b) 4 ft. (c) 9 ft. (d) 12 ft. (e) 6 ft. :RCB :Q1 16. Six equal squares are placed side by side in a line to form a rectangle whose area is 150 sq. in. How many inches are there in the perimeter of the rectangle? (a) 70 (b) 35 (c) 25 (d) 20 (e) 60 :RCA :Q1 1 1 1 17. If - = - + -, then y = ? y 2 3 (a) 5 (b) 5/2 (c) 6 (d) 5/6 (e) 6/5 :RCE :Q1 7 3 18. -- - - equals: 12 8 (a) 1 (b) 1/3 (c) 5/24 (d) 1/6 (e) 20 :RCC :Q1 19. If the circumference of a circle is to be equal to the perimeter of a square of side s, the radius of the circle = 2 2s s (a) -- (b) -- (c) 4s - 2# # 2# _ (d) 2\/2/# (e) s/# :RCA :Q1 20. Henry can repair a car in 6 hours. When Ted helps him, they do it together in 4 hours. How many hours would it take Ted alone to repair the car? (a) 2 (b) 5 (c) 10 (d) 12 (e) 15 :RCD :Q1 21. A liter is equal to a cubic decimeter. A centimeter is 1/10 of a decimeter. To the nearest tenth, how many liters will a glass tank hold whose dimensions are 14 cm. x 23 cm. x 5 cm.? (a) 161 (b) 16.1 (c) 1.61 (d) 1.6 (e) .2 :RCD :SB :SG157068156262067147 :SP156068164076172084186100 :SP186100200108214128227104 :SP227104241096255068255068 :SH0525Distance Feet :SH07271 1 2 3 3 4 :SH08220 6 2 8 4 0 6 2 :SH11224 :SH1315Depth 8 :SH1515Feet 12 :SH172116 :SF Questions 22 through 24 refer to the accompanying graph. It shows the contour of a river bed obtained by taking soundings at various distances from the left bank along the channel width. :RA :SD :Q1 :SB :SG157068156262067147 :SP156068164076172084186100 :SP186100200108214128227104 :SP227104241096255068255068 :SH0525Distance Feet :SH07271 1 2 3 3 4 :SH08220 6 2 8 4 0 6 2 :SH11224 :SH1315Depth 8 :SH1515Feet 12 :SH172116 :SF 22. Find in feet the maximum depth of the river. (a) 14 (b) 15 (c) 16 (d) 42 (e) 24 :RCB :SD :Q1 :SB :SG157068156262067147 :SP156068164076172084186100 :SP186100200108214128227104 :SP227104241096255068255068 :SH0525Distance Feet :SH07271 1 2 3 3 4 :SH08220 6 2 8 4 0 6 2 :SH11224 :SH1315Depth 8 :SH1515Feet 12 :SH172116 :SF 23. A boat normally sails in 9 feet of water. Allowing a foot on each side for clearance, find in feet the maximum width it may have to pass through the channel safely. (a) 15 (b) 11 (c) 16 (d) 20 (e) 13 :RC :SD :Q1 :SB :SG157068156262067147 :SP156068164076172084186100 :SP186100200108214128227104 :SP227104241096255068255068 :SH0525Distance Feet :SH07271 1 2 3 3 4 :SH08220 6 2 8 4 0 6 2 :SH11224 :SH1315Depth 8 :SH1515Feet 12 :SH172116 :SF 24. A barge draws 3 feet of water. Allowing 2 feet on each side for clearance, find the maximum width in feet of a barge that will pass through the channel safely. (a) 31 (b) 33 (c) 29 (d) 26 (e) 32 :RCC :SD :Q1 :SB :SC200034330034330074200074 :SP200074200034200034200034 :SH0429A :SH0438E B :SH1129D :SH1138F C :SH0729O :SF 25. ABCD is a rectangle. AB = 12, and AD = DF = FC. Find the number of square units in the area of circle O. (a) 18# (b) 72# _ (c) 36# (d) 36#\/2 (e) 8# :RCA :ET :ET
