Math 0302 Course Review

Transcription

1 89 Solve the following: Math 0302 Course Review ) 4y + 23 = 47 2) 6(2y + 3) 4 = 2y 22 3) 5y+ 6 2y 4 3 = 2 4) = 3 5) = 7 y + pg (solve for y) 6) = 0 7) ac bc = ab + vh (solve for a) 8) 2 = 8 9) ( 4)( + 7) = + 5 0) 2 (6 5) = 6 ) 0 2 ( 2) 9( 2) 5( 2) = 0 2) = 27 3) a = f h, solve for f 4) S = a 5b 6b for b 5) 5 6 d = ) 6.9 = ) = 66 5 Simplify. Write your answer without negative eponents: 8) ) 8( 6b + ) 6(b 3) 20) 9(3 + 7) (89 4) ) 32 5 z z 22) The product of twice 3 6 and ) 52 ( 5) 2 24) 7 5 y (4 2 y 5 8y) 25) 6c 3 ( 5b 2 + 6c 9) 26) ( ) (0.4) 27) (8 5)( ) 28) ) ( 7) 3 30) y 7 y 3 3) 7 ( 5) 2 a 4 b 3

2 90 Simplify the following: 32) (7 2 y + 4y 2 ) (2 2 3y 5y 3 ) 33) ( y)2 34) 9 3 y 2 (5 2 6y + 3 4y 4 ) 35) (4 3y)(4 + 3y) 36) ( ) 37) ( 2)(3 + 5) 2 38) 8(a 2 4a + 3b) 7(b 2 8a + 5b) 39) ( 2 8 5)( ) 40) (ab 4 ) 5 ( 2a 3 b 2 ) 4 ( a 5 b) 5 4) ( 2 3 y) 3 0 z 3 w 8 y 3 ( 3y) 4 y 2 Set - up the equation and solve the following: 42) Oscar the Grouch had to take a 5% pay cut since the Federal Government is cutting back on its financial support of PBS. If his new salary is $2.75 per hour, what was his salary before the pay cut? 43) Use the formula F = 9 C to find what 48.2 F is equal to in 5 Celsius. 44) Juan paid $650 in taes. If this is 26% of his total salary, what was his total salary? Find the equation of the line satisfying the following conditions: 45) Passes through the points ( 2, 5) and (7, 5). 46) Passes through the points (9, 2) and (6, 4). 47) Passes through the points ( 4, 7) and (4, 3). 48) Passes through the points (, 6) and ( 4, 2). 49) The line passes through ( 5, 2) and is parallel to 5y 3 = 2. 50) The line passes through (2, 7) and is perpendicular to 7 + 3y =. 5) The line passes through ( 0.5, 2) and is parallel to = 3. 52) The line passes through (4, ) and is perpendicular to = 3.

3 Find the slope and y-intercept (if possible) and graph the following: 53) 3y = 6 54) 2 y = 4 55) 3 = ) y = Find the -intercept and the y-intercept (if possible) and graph the following: 57) 3 + 4y = 2 58) y = 5 59) 4 6y = 3 60) y = Convert the following: 6a) Write 67,500 into scientific notation. 6b) Write in scientific notation. 62a) Write in standard notation. 62b) Write in standard notation. Simplify the following, leaving your answers in scientific notation: ) 64) (9 0 )(8 0 ) 6 0 Consider the following epression: 8 2 z 4p a) What is the numerical coefficient of the second term? 65b) List the variable terms and the constant terms. Factor the following completely: 66) y 67) y 2 68) ) 4a 5 b 3 + 2a 4 b 4 70) ) 3 (y a) + 64(y a) 72) ) 2 9y 0y 2 74) 27 3 y 3 8y z 3 8z 3 75)

4 92 Factor the following completely: 76) y y2 77) ) ( 3y) 2 (2 + y) 2 78) 35 3 y y y 3 80) a 2 2 5a 2 + 4a 2 + b 2 2 5b 2 + 4b 2 8) ) z 20 35z 83) 9 3 y y 2 + 8y 2 84) 2 (y z) 8(y z) 9(y z) Simplify: 85) 87) 32 5 (y 4 ) 2 z y 7 z ) (8 2 y 36y y 2 ) (6y) ) 42a 8 b 6 56a 7 b 7 +28a 6 b 8 4a 7 b 7 89) ( ) (3 4) 90) ( ) ( + 3) 9) If m and n are positive integers where m > n, use critical thinking to determine which answers are always true, sometimes true, or never true: 92) a) ( m y) n = mn y n b) ( y) m = m y m for all and y. c) m n = for all 0. d) ( y ) m = m if y 0. m y e) (5 + n) m = 5 m + n m. Set up the equation and solve: 93) A diamond pendant was worth for $000. It's value increases by 20% of its original worth every decade. Write an equation for the value of the pendant and sketch the graph using the horizontal ais for decades and the vertical ais for the pendant's value.

5 Set up the equation and solve: 94) An airplane descends 22 ft over a horizontal distance of 3 miles. What is its rate of descent? (Hint, 5280 ft = mile). 95) A ball is thrown from the top of a cliff with an upward velocity of 64 feet per second. How many seconds after the ball is thrown will it hit the ground if the ground is 80 feet below the cliff. Use the formula h = vt 6t 2 where h is the height, v is the velocity, and t is the time. (hint: the height is negative when the ball hits the ground). 96) The area of a triangle is 70 square inches. If the base is si inches less than twice the height of the triangle, find the length of the base and height of the triangle. 97) One leg of a right triangle is si centimeters more than twice the other. The hypotenuse is si centimeters less than three times the length of the shorter leg. Find the lengths of the sides of the triangle. 98) If the dimensions of a square are tripled, the area of the square increases by 200 square inches. Find the original dimensions of the square ) Two pipes can fill a tank in 3.75 hours. If it takes the smaller pipe four more hours to fill the tank working alone than the larger pipe, how many hours does it take each pipe to fill the tank working alone? Find the domain of the following. Write your answer in interval notation: 00) ) ) )

6 94 Simplify: 04) ) ) ) ) ) ) ) 5 2 p 4 2 2p ) ) Given the graph, find the intercepts (if possible) and write the equation of the line: 4) 5)

7 95 Given the graph, find the intercepts (if possible) and write the equation of the line: 6) 7) Find the indicated lengths of the following: 8) 9) 20) 48 ft 5 ft 5 ft y h 9 2 m Solve: 24 ft 5 ft 2) = 2 22) 5 + = ) +4 3 = ) 5 2 p 4 = 2 2p 8 25) = ) 3 =

8 96 Set up the equation(s) and solve: 8) Find the diagonal of a square if each side is 5 inches long. 9) The red army is five miles south and si miles west of Warrington while the blue army is one mile north and eight miles east of Warrington. a) How far apart are the two armies? b) If the two armies marching toward each other at the same rate, where will they meet relative to Warrington? 20) A baseball diamond is a square with each side equal to 90 feet. How far does Mike Piazza have to throw a baseball from ten feet behind home base to second to catch a runner trying to advance on a wild pitch? second Solve the following: home 2) Given ABC ~ DEF, BC = 7 cm, EF = 28 cm, DF = 8 cm, m D = 75, & m E = 55, find m C and AC. 22) Given ABC DEF, AB = 6 m, DF = 20 m, m D = 4.4, and m B = 90, find AC, BC, DE, and the measure of C? 23) If a tree casts 3.5 foot shadow at the same time that a five-foot person casts.8 foot shadow, how tall is the tree? 24) On WXY, there is a point P on XY and a point Q on WY such that PQ XW. If XP = 9 in, PQ = 5 in, and XW = 25 in, find PY (hint, let v = PY, then v + 9 = XY). X 9 in P v 25 in 5 in Y Q (Drawing not to scale.) W

9 Set up the equation and solve: 25) One printer can print 9000 copies of a manuscript in 8 hours. A second printer do the same job in 4 hours, Working together, how long will it take the two printers to complete the job? 26) Leroy drove 324 miles in the same amount of time as Juanita drove 378 miles. If Juanita was driving 2 miles per hour faster than Leroy, how fast were they driving? 27) Maria took a canoeing trip, traveling 30 miles upstream against a 2 mph current and then returning to the same point downstream. If the total trip took 8 hours, how fast can she paddle in still water? 28) Larry and Cindy can rebuild a car engine in 2 hours working together. If Larry takes 0 hours longer to the rebuild the engine working alone than Cindy, how would it take each of them to rebuild the engine working alone? 97 29) In a recent small town election, Evelyn Merriweather received 624 votes out of 0,468 total votes to become the new mayor. If 4 7 of the women and how many women voted? 5 8 of the men voted for her, how many men and Find the equation (in slope intercept-form if possible) of the line passing through the given points: 30) ( 4, 6) and (, 6) 3) (5, 6) and (8, 2) 32) (3.2, 4) and (3.2, 9.)

10 33) The graph below shows median home value, y, every ten years beginning in 940. All values have been adjusted for inflation and are measured in 2000 dollars. In other words, the values are measured in what a dollar was worth in the year (Source: 40,000 20,000 Median Home Values 98 00,000 80,000 (5, 000) 60,000 40,000 (2, 58600) 20, a) Find the slope of the line. Year ( = 0 corresponds to 939) b) Find a linear equation for the line. c) Predict the median home value (in 2000 dollars) in the year 200 (to the nearest hundred).

11 99 Answers: ) y = 6 2) All Real Numbers 3) y = 3 4) {0.5, 7} 5) y = 7 7pg 6) {, 6} 7) a = vh+bc c b 0) { 8) {0, 8 } 9) { 3, } 2 3, 0, 3 2 } ) { 3 5, 2, 5 2 } 2) {, 0, 9} 3) f = ah a+ h 4) b = a 6S + 5 5) d = 6) = ) ) 22) ) 54b ) ) z 7 23) ) 28 7 y y 2 25) 30b 2 c 3 36c c 3 26) ) ) ) 30) 5y 3 3) 49b3 y 7 25a ) 5 2 8y + 4y 2 + 5y ) y y2 34) 45 5 y y y y 6 35) 6 2 9y 2 36) ) ) 8a a b 7b 2 39) ) 6a 42 b 33 4) 8w 8 5 z ) His salary was $5. 43) The temperature is 9 C. 44) His salary was $2, ) y = 5 46) y = ) y = ) y = ) y = ) y = ) = ) y =

12 200 53) The Slope is. 3 54) The Slope is 2. The y-intercept is (0, 2). The y-intercept is (0, 8). 55) The Slope is undefined. 56) The Slope is 3 5. There is no y-intercept. The y-intercept is (0,.5).

13 20 57) The -intercept is (4, 0). 58) There is no -intercept. The y-intercept is (0, 3). The y-intercept is (0, 5). 59) The -intercept is ( 3 4, 0). 60) The -intercept is ( 5 3, 0). The y-intercept is (0, 2 ). The y-intercept is (0, 3 2 ). 6a) b) a) b) 8,40,000 63) ) a) The coefficient is 4. 65b) The variable terms are 8 2 z, 4p, and 7. The constant term is 2. 66) 3 2 (4 y) 67) 5( 4y)( + 4y) 68) ( 6)( 3) 69) 7a 4 b 3 (2a + 3b) 70) or prime 7) (y a)( + 4)( )

14 202 72) 6( 2)( + 2) 73) ( 0y)( + y) 74) (3 2)( )(y + z)(y 2 yz + z 2 ) 75) ( 4)( + 4)( 2 + 9) 76) 7 ( 3y)2 77) 2( ) 78) ( + 4y)(3 2y) 79) 7 2 y 2 (5 + 2y ) 80) (a 2 + b 2 )( 4)( ) 8) 3( ) 82) (3 5)(4 + 7z) 83) 9y( + 3y) 2 84) (y z)( 9)( + ) 85) 4y 3z 6 86) 3 6y + 4y 87) a 88) b 4 + 2b a 3 89) ) ) a) always 92b) never 92c) sometimes 92d) always 92e) never 93) v = 200d + 000, where d is the number of decades and v is the value. 94) The rate of descent is ) It takes five seconds. 96) The base is 4 inches and the height is 0 inches. 97) The legs are 5 cm and 36 cm respectively and the hypotenuse is 39 cm. 98) The square was 5 inches by 5 inches. 99) The larger pipe takes si hours whereas the smaller pipe takes ten hours. 00) (, 3) U ( 3, 2) U ( 2, 2) U (2, ) 0) (, 3) U ( 3, 0) U (0, 5 6 ) U ( 5 6, ) 02) (, 9 2 ) U ( 9, ) U (, ) 03) (, ) 2

15 203 04) 08) 2) ) 09) 3) ( 4)(+ ) 4 (5+ 3)(+ 9) 3 ( 2) 06) 0) (3+)(2 3) ( 5) 2 07) ) (+4)(3 2) 4) The -intercept is ( 6, 0). 5) The -intercept is (5, 0). There is no y-intercept. The y-intercept is (0, 3). The equation is = 6. The equation is y = ) There is no -intercept. 7) The -intercept is (4, 0). The y-intercept is (0, 2). The y-intercept is (0, 2). The equation is y = 2. The equation is y = ) y ft 9) h 4.33 ft 20) = 9 m 2) { 38 5 } 22) { 4 } 23) { 3 } 24) { } 25) { } 26) { 2 3 } 27) The diagonal is 2.23 ft long. 28a) The armies are 5.23 miles apart. 28b) They will be 2 miles south and mile east or Warrington when they meet. 29) He has to throw the ball ft 30) m C = 50, AC = 34 7 cm or cm 22) AC = 20 m, BC = 2 m, DE = 6 m, m C = ) The tree is 37.5 feet tall 24) PY = 3.5 in 25) It will take the printers hours to complete the job. 26) Leroy was driving at 72 mph and Juanita was driving at 84 mph. 27) She can paddle 8 mph. 28) It takes Cindy 20 hr. & Larry 30 hr. 29) 4840 men and 5628 women voted in the election. 30) y = ) y = ) = a) m = b) y = c) The median home value will be $29,400. 3