:Q 1. Find the angle y between the minute and hour hands of a clock at 3:20. (a) 15^ (b) 20^ (c) 25^ (d) 30^ (e) 5^ :RCB 1. (b) 20^ Ans. The face of the clock represents 360^, the arc from 3 to 4 (one of the 12 equal divisions) = 1/12 (360^) = 30^. Therefore in the hour from 3 to 4, the minute hand will turn through 360^, the hour hand will turn through 30^. Since 3:20 represents only 1/3 of an hour after 3, the hour hand will turn ( from the division marked 3) through 1/3 of 30^ = 10^. Then <y = 30^ - 10^ <y = 20^ Ans. :RA :Q 2. A flag pole casts an 8-foot shadow at the same time that a 6-foot man casts a 2-foot shadow. Find the height (x) of the pole. (a) 2 ft. (b) 2 2/3 ft. (c) 24 ft. (d) 32 ft. (e) 30 ft. :RCC 2. (c) 24 ft. Ans. Since the shadows are cast at the same time, the angles of elevation of the sun (<A and <A') are equal. :RA Therefore {ABC is similar to {A'B'C', and their corresponding sides are in proportion. HEIGHTS SHADOWS height pole shadow pole ----------- = ----------- height man shadow man y 8 - = - 6 2 2y = 48 y = 24 feet Ans. :RA :SD :Q :SB :SP196040259040259064196064 :SP196040196064196064196064 :SP217016217088238088238016 :SP238016217016217016217016 :SF 3. When an open box is unfolded, its 5 square faces form the pattern shown in the diagram. If the total outside surface area of the box is 45 sq. in., find the length of a side of each square. (a) 2 1/4 in. (b) 2 3/16 in. (c) 3 in. (d) 4 1/2 in. (e) 2 1/2 in. :RCC 3. (c) 3 in. Ans. Let y = the number of inches in a side of each square face. 2 Then y = the number of square inches in the area of each square face. 2 And 5y = the number of square inches in the total area of the open box. :RA 2 Equation: 5y = 45 2 Solve for y: y = 9 Take positive root: y = 3 in. Ans. :RA :SD :Q 4. Two-fifths of a bushel of corn occupies 1 cubic foot of space. To what level should a bin 12 ft. long and 10 ft. wide be filled to hold 240 bushels of corn? (a) 1/5 ft. (b) 10 ft. (c) 6 ft. (d) 5 ft. (e) 8 ft. :RCD 4. (d) 5 ft. Ans. Let y = number of ft. in the depth. Then 12 x 10 x y = 120y = number of cubic ft. in volume of bin. Since each cubic foot holds 2/5 of a bushel of corn, 2/5 x 120y = number of bushels in bin. 2 Therefore: - x 120y = 240 5 Solve for y: 48y = 240 y = 5 ft. Ans. :RA :SD :Q :SB :SP224072196134252134224072 :SH0933L :SH1829Driveway :SF 5. A light (L in diagram) illuminates 44 feet of a driveway. If an automobile is moving at 15 miles an hour on the driveway, how long will the car be in the lighted portion of the drive? (a) 1/2 sec. (b) 2 sec. (c) 30 sec. (d) 30 min. (e) 2 hr. 56 min. :RCB 5. (b) 2 sec. Ans. :RA 15 mi. per hr. = 15 x 5280 ft. per hr. 15 x 5280 = --------- ft. per min. 60 15 x 5280 = --------- ft. per sec. 60 x 60 = 22 ft. per sec. distance 44 time = -------- = -- rate 22 = 2 sec. Ans. :RA :SD :Q :SB :SP196103217032259103196103 :SP196103259103248128196103 :SP217032217103248103248128 :SH1328A :SH0432B :SH1438C :SH1737D :SH1432E F :SF 6. Find the ratio of the area of {ABC to {ADC. If: AC = 6, BE = 6, DF = 2, AE = 2 and FC = 1 (a) 3:1 (b) 1:3 (c) 9:1 (d) 1:9 (e) 3:8 :RCA 6. (a) 3:1 Ans. AC is the common base for both triangles, {ABC and {ADC. Since triangles having the same base are to each other as their altitudes, {ABC altitude BE 6 3 ---- = ----------- = - = - {ADC altitude DF 2 1 6 3 - = - = 3:1 Ans. 2 1 :ET :ET
