FINL EXM REVIEW Math 00 Spring 007 The final eam will be on Monda, Ma 14 from 7:00-9:00 in room. The eam will cover all material covered in class this semester, all of chapters 1,, 3, and 7. ll of the Geometr Sections. Plus the following sections: 4.1 4.4 6.1 6.5, 6.7 8.1 8.3, 8.6 9.1, 9. 10.1 No homework is due at the eam. You ma use our calculator on this eam. You ma NOT use our notes, homework, book, or neighbors on this eam. You do get an 8 1 / X 11 cheat-sheet for this eam. elow is a review for this eam. nthing on the review could possibl be on the eam. The eam will be shorter than the review.
Math 000 Final Eam Review 1. Simplif: 4 8i 3+ 8 ( 7). Simplif: 11 ( 9) + 6(10 4) + 3 4 3. Simplif ( 5+ 7) 3( ) 8 6 4. Simplif: 5. Simplif: 6. Evaluate (4 ) 3 9 i 4 7 3 3 4 + 5 when = and = 3 For eercises 7-9, solve for. 7. ( 3) + 5= 8( 1) 8. 9. 1 3 1 + = 1+ 3 5 5 3 + = 3 6 For problems 10-15, define a variable in words, write an equation, solve algebraicall, and write our answer in a complete sentence. 10. Seven subtracted from five times a number is 08. Find the number 11. n 87-inch board is cut into three pieces. The longest piece is 10 inches longer than twice the shortest piece and the middle-sized piece is 17 inches longer than the shortest piece. How long are the pieces? 1. landscape architect charged a customer $971, listing $350 for plants and the remainder for labor. If the architect charged $3 per hour, how man hours did the architect work? 13. universit with 176 people on the facult wants to maintain a student-to-facult ratio of 3:. How man students should the enroll to maintain that ratio? 14. To earn a in a course, a student must have a final average of at least 80%. On the first three eaminations, a student has scores of 76%, 74%, and 78%. What must the student earn on the fourth eamination to earn a in the course? 15. motorccle traveling at 50 mph overtakes a car traveling at 30 mph that had a three-hour head start. How far from the starting point are the two vehicles.
Write each of the values below in decimal or standard notation. 5 16. 3.113 10 17. 1.01 10 9 Write each of the values below in scientific notation. 18. 87,000,000 19. 0.000017 Perform the indicated operations. Leave our answer in simplified form. 0. ( + 9 + + 1) + ( 4 + 3 11) 1.. (7 8+ 11) (7+ 9+ 1) 3 3 3 ab(7ab + ab 4 a) 3. (+ 4)( 3+ 1) 4. 3 3 ( 3+ 11) 5. ( 9)( + 9) Completel factor each of the following epressions. If the epression cannot be factored write PRIME. 6. m + 1m+ 36 7. 8. 9. 30. r + 4 v v 3 p t 100 + t 15 3 31. + 8 + 6 Perform the indicated operations and simplif the answer. p 7 p + 1 3. + p p 33. 3c 7 c 9 c+ c+ 34. Solve P= l+ w for w 35. Solve S = P+ Prt for t
36. Sketch the line 5+ 4= 0 using - and -intercepts and a checkpoint on the ais provided. Label the and intercepts. 37. Sketch the line = 3 6 using - and -intercepts and a checkpoint on the ais provided and label the and intercepts. 38. Use the slope and -intercept to sketch intercept. 1 = + 3 on the aes provided. State the slope and the -
39. Sketch the line with slope other points on the graph. 3 m = that contains the point ( 1, 3). Label the given point and at least 40. Find an equation for the line with -intercept of (0,4) and parallel to the line = 3. Leave the final answer in slope-intercept form. 41. Find the slope of the line that passes through the points (3, -4) and (5, 0). 4. Find an equation for the line with undefined slope which passes through the point (-7, ). 43. Find an equation for the line with slope of 1 which passes through the point (0, -1) Simplif each epression. Leave our answer in the form of a simplified radical, if necessar. 44. 49 54 6 45. 5 16 46. 5 16 47. 48. 16 7 6 18a b Use the product rule for square roots to simplif. DO NOT use a calculator to approimate an answer. 49. 7 50. 40 51. 34
5. 700 53. The length of a rectangular garden is 4 feet longer than the width. If the area of the garden is 140 sq. feet, find the dimensions of the garden. Solve the quadratics using the method of our choice. 54. 16t 4 = 0 55. 56. 3 + = 10 8 + = 1 57. sailboat has a triangular sail with an area of 16 square feet and a base that measures 1 feet. Find the height of the sail. 58. Find the area and perimeter of the figure. 15 in. 7 in. 5 in. 0 in 59. If m = 135, find the measure of the remaining angles. 1 4 3 60. If m = 6and m = + 5 and the angles are supplementar, find the measure of the angles.
61. In the given figure MP NQ and C M 3 4 5 P N 1 65 C Q a) Classif triangle C in the figure above. a. b) Find the measures of angles 1-5 in the figure above. m 1= m = m 3= m 4 = m 5= In the given figures, find the measures of the remaining angles. 6. C 63. C 0 (3 ) ( 30) 64. nswer the following true or false: a. n obtuse triangle can have 3 obtuse angles. b. ll isosceles triangles have congruent sides and two congruent angles. c. n equilateral triangle is also equiangular.
For eercises 65-66, use the figure below where ΔC ΔMOP. O C M P 65. Name the congruent angles and the proportional sides. 66. Find C if = 8, MO = 104 and OP = 78. 67. Find the height of a tree that casts an 80 foot shadow at the same time that a telephone pole 18 feet tall casts a 1 foot shadow. 68. Complete the following table: Polgon heagon triangle octagon quadrilateral pentagon Number of sides of polgon 69. Draw an octagon and state the number of diagonal in the octagon. 70. Find the measures of the angles in the given parallelogram. D C 70 71. For the given parallelogram, find 1 + 5 7 + 15
7. Use the Pthagorean Theorem to find the lengths of the missing sides of the right triangle in the table below. Leave our answers in simplified radical form. ssume all units are in centimeters. C C a) 10 8 b) 1 10 c) 15 8 C 73. Solve the following problem b ) defining a variable, ) writing an equation, C) solving the equation and D) answering the question in a complete sentence. 13 foot ladder is set 5 feet from the base of the wall. How far up the wall will the ladder reach? 74. Solve the inequalit, show the answer in set notation and graph our solution on the number line. 30 < 5 75. Solve the inequalit, show our answer in interval notation and graph our solution on the number line. 33+ 33 3(4+ 3) 76. If l m, find and justif the answer. l m 1 145 3 4 5 Use the figure below for eercises 77-78. The figure CD is a parallelogram with diagonal C. ssume that m C = 5 and m CD= 110 C D 77. Find m CD and justif the answer. 78. Find m CD and justif our answer. 79. If the diameter of a circle is 10 cm, find the circumference and area of the circle. Leave the answer in terms of π.
80. Divide and simplif our answer. 4+ 8 5+ 10 5 10 81. Solve the equation and state an restrictions. 7 = + 5
Math 000 Final Eam Review Solutions 1) 5 ) 4 3) -19 3 4) 16 9 5) 6) 9 7) = 8) = 7 9) = -4 10) The number is 43. 11) The lengths of the pieces are 15 inches, 3 inches and 40 inches. 1) The architect worked 7 hours. 13) The should enroll 04 students. 14) The student needs 9% or better on test 4 to earn a in the course. 15) It is 5 miles from the starting point. 16) 0.00003113 17) 1,01,000,000 7 18) 8.7 10 19) 1.7 10 5 0) + 5 + 4 + 10 1) 17+ 3 6 3 4 3 4 ) 1ab + 3ab 1ab 3) 6 10+ 4 5 4 3 4) 6 9 + 33 5) 81 6) ( + 6) 7) Prime 8) (v 3)( v+ 1) 9) ( p 10)( p+ 10) 30) ( t+ 5)( t 3) 31) ( + 3)( + 1) 3) 3 33) 1 P l 34) w = S P 35) t = Pr 36) 37)
38) 39) 40) = 3+ 4 41) m = 4) = 7 1 43) = 1 44) 1 45) 3 46) 1 47) 3 3 48) 3ab a 49) 6 50) 10 51) 34 5) 10 7 53) The dimensions of the garden are 10 feet b 14 feet. 1 54) t =± 5 55) =, = 3 1 1 56) =, = 4 57) The height of the sail is 1 feet. 58) rea = 70 in ; Perimeter = 40 in 59) m 1= 45, m 3= 45, m 4= 135 60) m = 150 and m = 30 61) isosceles triangle,
m 1= 65 m = 115 m 3= 65 m 4= 50 m 5= 65 6) m = 80, m = 80 63) m = 40, m = 35, m C = 105 64) a. false, b. true, c. true 65) M, O, C P are congruent angles and C C = = are proportional sides MO OP MP 66) 6 67) The tree is 10 feet tall. 68) Polgon Number of sides of polgon heagon 6 triangle 3 octagon 8 quadrilateral 4 pentagon 5 69) 0 diagonals 70) m = 110, m = 70, m CD= 110, m D= 70 71) = 7) C = 6; C = 11; = 17 73) The ladder will reach 1 feet up the wall. 74) { > 150} 8 75) 7 76) The m 1= 35 since it is supplementar to 145. m 1+ m + m 3 = 180 where 3because it s to be an isosceles triangle. Let a = m = m 3 then 35 + a+ a = 180 a = 145 a = 7.5 Since and are alternate interior angles, therefore congruent, then = 7.5 77) Since CD is a parallelogram, consecutive angles, ( D and CD ) are supplementar, thus m C + m CD + m CD = 180. Let = m CDthen 5 + + 110 = 180, so m CD= 45. 78) Since CD is a parallelogram, CD. C would be a transversal intersecting the parallel lines. CD and C are alternate interior angles and are congruent. Since m C = 5 then m CD = 5 79) C = 10 π cm and = 5 π cm 80) 4 81) = RESTRICTIONS: 5,0