MTH052: Introduction To Algebra And Geometry

Transcription

1 MTH05: Introduction To Algebra And Geometr FINAL EXAM REVIEW Do this assignment on another sheet of paper and show our work. This is to help ou prepare for the final eam. Answers are included at the end of the review. Do not turn this assignment in. For problems -, write a meaning in English for each... S. N For problems -9, simplif each epression b performing an operations possible ( )( ) ( 8)() ( a ) 7. ( t)( t ).. ft. ft 5. (.5D 9 cm) 6. a( a) 6a 7. n n 8. (t 0) 9. n (5.7 mi ) For problems 0-, evaluate each of the epressions for the indicated values of the variables. Include an units of measurement. 0. S 5 if S.5. w 5 for. and w.. ( ) for 7 and. dh v when d 5 inches and h = 8. inches. B A 0.5 ps if A = 0 square millimeters, p =.7 millimeters, and s = 5. millimeters For problems 5-, solve each of the equations. Include units of measurement n a 7a 9. 6( n) n (p) 5( p ). 9 6 ( 0) 5. A h( L w) for L if A = 8 square meters, h = 7 meters, and w = meters dh. v for h when v = 00 cubic ards and d = 5 ards 5. A rectangular bin has a length (L) of feet and a width (w) of feet. If the area (A) of the sides of the bin is square feet, how high (h) is the bin? A h( L w) 6. An anti-freeze solution calls for liters of anti-freeze to 6 liters of water. Write the ratio of anti-freeze to water. TM/05/F'06//0/009

2 7. An anti-freeze solution calls for liters of anti-freeze to 6 liters of water. Write the ratio of anti-freeze to total solution. For problems 8-0, first a) set up a proportion and then b) solve the proportion to answer the question. 8. An anti-freeze solution calls for liters of anti-freeze to 6 liters of water. How much anti-freeze should be used in a cooling sstem having a capacit of 5 liters? 9. A milling machine turning at 00 revolutions per minute (rpm) cuts inches of a certain metal in one minute. How long would it take the milling machine to make a 7 inch cut at 00 rpm? 0. A length of 5 chains is 0 feet. How man chains is a distance of 580 feet? For problems -5, perform the conversions using the cancellation of units method.. 8 m to km. 7 ft to ards. 50 gal/min to ft sec. 86 cm kg to mm kg 5. A milling machine is turning at 00 revolutions per minute. What is the milling machine turning in revolutions per second? 6. For the figure shown to the right, determine the measure of ABC if BAC 5 and AB = AC. 7. A corner brace is to be placed against the wall of a garage at an angle of 9 as indicated in the diagram at the left. What angle does the brace make with the floor? 9 brace A C B floor 8. A root barrier is to enclose a flower bed with sides of 6. meters,.8 meters, 5.5 meters, and 7. meters. The plastic barrier is sold in 0-meter lengths. How much is left over if two lengths are purchased? Use the diagram illustrated to the right for problems Identif and name three geometric forms involved in the figure. Use the most specific names ou can appl. 50. Determine the perimeter. 5. Calculate the unshaded area. m 7 m 8 m m m 8.06 m Use the diagram of the floor, illustrated to the right for problems 5 & Determine the length of baseboard needed to go around the floor diagrammed to the right if there is a -foot door opening to the room. 7ft 9ft ft 9ft TM/05/F'06//0/009

3 5. Calculate the cost to cover the floor with a tile that costs 55 per square foot. 6cm 5 Calculate the area of the shaded region in the figure at the right. cm cm 55. A spherical storage reservoir is 5 feet in diameter. How man gallons of paint is needed to give the reservoir a coat of rust preventative paint? Each gallon of paint covers 00 square feet. 56. Determine the surface area of a rectangular bin that is feet high, feet wide, and feet long. 57. Calculate the lateral area of a clindrical tank having a diameter of meters and a height of meters. 58. Determine the total surface area of the geometric form illustrated to the right. 7ft 59. Give the -coordinate of each of the points. a) (-, 7) b) (9, -5) c) (,8) d) (5,-) 0ft 60. On a rectangular coordinate sstem, what are the coordinates of the origin? 5ft 9in. 5ft 6. Use the equation 5 to complete the table at the right: 6. Draw the graph of the equation on a piece of graph paper Use the graph to fill in the table. 6. From the graph below, what is height when time is seconds? What is the -intercept of the graph in problem #6? Include units Time (seconds) 66. What is the slope of the line in problem #6? Include units. TM/05/F'06//0/009

4 67. A 5-foot concrete walkwa starts at a point inch below a doorwa and slopes down /8 inch per foot. a) Draw a graph that represents the walkwa where is the horizontal distance from the doorwa and is the vertical height below the doorwa. b) At what horizontal distance from the doorwa is the concrete walk inches lower than the doorwa? 68. A beam has a distributed load that increases linearl from 0 lbs/ft to 90 lbs/ft as indicated in the diagram. a) Draw a graph that represents the distributed load on the beam b) Estimate the slope on the graph. c) What does the slope describe? d) Estimate the load on the beam 5 ft from the left end. 0 lbs/ft Beam ft 90 lbs/ft Answers:. the square root of. times S cubed. the cube root of N a t..5 ft 5. D + 6cm a t mi V 99.6in. B 9.88mm 5. = 7 6. = - 7. n = a = n =.5 0. = 0. p =.5. = 0. L = m. h 0.9 d 5. h =.75ft 6. / 7. /5 8. a) liters liters b) 6 liters liters 0 liters 9. a) min 7 in. b) min in. minutes 0. a) chains 580 ft b) 80 chains 5 chains 0 ft. 0.8 km. ards. ft 0.56 sec mm kg TM/05/F'06//0/009

5 5. rev 5 sec m 9. square, quarter circle, trapezoid (rectangle & triangles also possible) m m ft 5. $ cm 55.. gal ft m ft 59. a) 7 b) 5 c) 8 d) 60. (0, 0) ft ft ft per second 67. a) b) 6 feet 68. a) b) 5 lbs/ft c) 8 lbs/ft ft TM/05/F'06//0/009