Arithmetic Review 1 Simplify: 1. -15 (-6) Solve 1. 5.6 (.1)=. - * -7 1..4 (.)=. 7 9 14. 9 1 = 4. 16 (-4) * 6 15. 7 = 9 5. ( 49 * 6 * 16 ) 10 6. 17 0 = Solve: 1 1 16. 5 + = 7. 1 + 50 Solve 1. + = 15 5 9. + = 9 7 10. + = 9 5 1 1 17. 9 + = 4 5 1 1. = 9 4 4 1 19. 1 = 7 0. (. 9) = 11 1-1 =
1. (. 67) = 1. = what decimal? 4 Solve 7. + = 15 10 1 1. 7 = 4. = what decimal? 5. 95.0 x 1. 1 1 4. 5 = 6 9 5. 6. + 5 + 5 ( 9) ( 9) = ( 7) ( 7) = Solve 4. 99.99 x 4.11 1 1 5. + = 9 1 1 1 6. + = 5 7. +. =.. +.4 = 7. 0. 5 1.? 9. =. 75?. 0.09. 564? 0. =. 15?
1. -9. 1. 4. -14 5. 6. 1 7. -7 11. 15 11 9. 7 7 10. 45 1 11. 6 1. 11. 1. 10.75 14. 7 15. 11.5 5 16. 6 75 17. 9.75 or 65 1. 6 6 19. 7 Answers to Arithmetic Review Check your answers. If they do not match, try re-working the problem. Bring your work to the Math Center with specific questions. 0..151 1..449. 0 41. 55 4. 1 1 5. -.5 or - 6. - 6 1 7....7 9. 4 0. 0 1..75..60. 1.56 4. 410.959 5. 1 1 6. 0 11 7..64. 6.666667
Arithmetic Review 1 1 1) * 16 ) 1 5 4 16 ) 4) 5) 6) 4 n = 1+ 5 10 1 1 + 6 1 1 + 4 1 + 4 5 1 7) If a =, b = -5, then what does a b a equal? ) ( y ) 9) What percent is 1 of 0? 10) 4600 10 11) 1) 1) 1 9 17 1 16 5 10 14) + 16
15) 4.57. 5 16) 01 0. 01 17).6 (.001) 1) What is % of 704.50? 19) 7 1 0) What percent is of 0? 1) 40 = 0% of x ) 5 16.07 ) =. 7 x 4) 547 0. 01 4 5) Write as a decimal 1 6) 4110 15 7) 0.0 0. 1 ) 0. 0. 45 9) 100 0. 5
Arithmetic Review Answers 1. 65. 1/16. n = 1 4. 1 5. 4 6. 7.. 1y 1. x = 00 1.. x =.01 4. 54700 5..1904 6. 74 7..006..09 9. 5 9. 40% 10. 460 11. 4 1. 4 107 1. 1 14. 15. 160.7445 16..01 17..006 1. 577.69 1 19. 4 0. 15%
Arithmetic Review 1. If the average of 6. and n is 4.4, what is the number n?. What number divided by. is 1.9?. What is 16% of 0% of 4? 4. A shirt costing $16 is on sale for 15% off. If you were to apply a coupon for 10% off of the sale, what would you pay for the shirt? 5. Solve for n : + n 9 = 1 4 9 6. Solve for t : 1 6 t = 4 10 7. You have a rectangular yard that is 4 square feet in area in which you want to put a square garden surrounded by concrete. If the concrete takes up 1 square feet, what is the length of a side of a square garden?
. If a cylinder has a volume of 96π centimeters cubed, and stands 6 centimeters tall, find its radius. ( V= πr h) 9. If you ran around a rectangular park whose length is three times its width, and ran 1600 m total, what is the length and width of the park? 10. What is 456 divided by 100? 11. If you had a pole that extends out 10 times its original length of 14. feet, how long would the pole be if you fully extended it? 1. Find the equivalent values: A. 6 1 a. 50 b. 49 a. 5 6 B. 5 b. 6 5 c. 4 6 d. 15 c. 6 5 d. 5 6 1. You have two pies, one cut into fourths and the other into eighths. If Jim eats slices of the pie that is cut into eights, how many of the fourths would you have to eat in order to eat an equivalent amount of pie?
14. If you depart in an airplane from Philadelphia to Los Angeles ( hour time difference) at 7:00 am (Phila. Time), and the trip takes 5 hours, what time is it in Los Angeles when you arrive? 15. Solve: 16. Solve: 17. Solve: 5 9 + 6 = 7 9 = 9 4 = 6 1. If your train leaves at 6:5 am, and you arrive at 9: am, how long was your trip? 19. Solve for p : 6 (p ) + p = p 0. If a club sells tickets to a show at $1 for adults and $6 for children, makes a total of $4 on 6 total tickets, how many of each type did they sell?
Answers 1. n =.6. 7.. 1.15 4. $1.4 5. n = / 6. t = 7 7. length = 6 feet. radius = 4 cm 9. width = 00 m, length 10. 4.56 11. 14 ft 1. 1: b. 49 1. 1 piece of pie. 14. 9:00 am 19 1 15. or 11 1 16. 9 1 17. -1/ 1. :1 minutes 19. p = 4.5 : c.6 5 0. adult tickets and 14 children s tickets.
Algebra Review 1 1. (19t³ 5t²) (7t² t)+(-15t³ t) m * m * m * n * n 9. Simplify: r * r * s * s * s * s. (5y + 4)(y ). y²(y 7)(4y + 1) 10. b c 11. a -4 * a - 4. Factor: 1d² 6d 1. (m 5 ) - 5. Factor: x² 9 4 a 1. a 6. Factor: x² 54x + 4 7. Factor: r² 1r + 7 14. 9x 1w 6. Factor: 4s² 4s 15 15. 5(x ) = x 6( x) Algebra Review 1 Page 1
Answers to Algebra Review 1 Check your answers. If they do not match, try re-working the problem. Tutorials are available for additional assistances. Bring your work to the Math Center with specific questions. 1. 4t 1t 5t http://patrickjmt.com/polynomialsadding-subtracting-multiplying-andsimplifying-ex-1/ http://patrickjmt.com/polynomialsadding-subtracting-multiplying-andsimplifying-ex-/ http://patrickjmt.com/polynomialsadding-subtracting-multiplying-andsimplifying-ex-/. 16y 4 5y 14y http://patrickjmt.com/polynomialsadding-subtracting-multiplying-andsimplifying-ex-1/ http://patrickjmt.com/polynomialsadding-subtracting-multiplying-andsimplifying-ex-/ http://patrickjmt.com/polynomialsadding-subtracting-multiplying-andsimplifying-ex-/ 5. (x )(x + ) http://www.youtube.com/user/yourteach ermathhelp#p/search/5/accn_isdpy http://www.youtube.com/watch?v=co CIk0irz14&feature=related 7. (r 6)(r 1) http://www.youtube.com/user/yourteach ermathhelp#p/search/1/nj9ggam-dtq. 15y y http://patrickjmt.com/polynomialsadding-subtracting-multiplying-andsimplifying-ex-1/ http://patrickjmt.com/polynomialsadding-subtracting-multiplying-andsimplifying-ex-/ http://patrickjmt.com/polynomialsadding-subtracting-multiplying-andsimplifying-ex-/ 4. 6d(d 1) http://www.youtube.com/user/yourteach ermathhelp#p/search/5/accn_isdpy http://www.youtube.com/watch?v=co CIk0irz14&feature=related 6. (x 9)(x 9) or (x 9) http://www.youtube.com/user/yourteach ermathhelp#p/search/1/nj9ggam-dtq. (s 5)(s + ) http://www.youtube.com/user/yourteach ermathhelp#p/search/1/nj9ggam-dtq 9. m n r s 4 http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-1/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ 10. c b 6 9 http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-1/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ Algebra Review 1 Page
11. a -7 1 or 7 a http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-1/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ 1. a 1 http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-1/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ 1. m -10 1 or 10 m http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-1/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ x 14. w http://patrickjmt.com/radicalssimplifying-radical-expressionsinvolving-variables-ex-1/ 15. x = - http://www.youtube.com/watch?v=9tek XGoWIQM&feature=relmfu http://www.youtube.com/watch?v=xfa WLVLfeJM&feature=relmfu Algebra Review 1 Page
Algebra Review Foil: 1. (6z-)(z+4) Factor: 1. y + 14 y + 49. (b-)(b+5) Simplify: z + 10z + 5. z 5 Solve: 1. -y + = 1 Factor: 14. 16y 14y 15 4. 5. 6. 7.. b + 4b + 144 b 144 7 1 + z z 11 + b 5b 9z 6 5b 5 Simplify: 15. 14b 9z 4b + 10z 16. 5x + 1y x + y Solve 17. 5z + = 9 Factor 1. 1 y 9 y + 15 Simplify b x 19. x b 0. ( y + 7) Solve: 9. 7 (z - 5) + = z 49b 1. 5b 10. (b 4) + 10 = 7b 11. 16 y 4y + 6 Algebra Review Page 1
Simplify: 60z. 144z. ( 4y 6) x + y 9. ( ) 0. 5(x-1) = 1 1. 4(7b + ) = 9 b z 4. ( ) 9x y 5 5. ( ) Solve: b. a + b if b = 6 a = 1 5b z 6. 16z 5b. x x + y if x = - y = 60x 1y 7. y 1x Simplify: 4b b b 4. + 6 b + z. ( ) 5. 5x 4x 5x + 9 1 6 Algebra Review Page
Answers to Algebra Review Check your answers. If they do not match, try re-working the problem. Tutorials are available for additional assistances. Bring your work to the Math Center with specific questions. 1. 1z + 1z http://patrickjmt.com/solving-quadraticequations-by-factoring-basic-examples/ http://www.yourteacher.com/freevideo-jwp.php?vid=7070 http://www.youtube.com/watch?v=65b AsV0SKk&feature=relmfu. b + 7b 15 http://patrickjmt.com/solving-quadraticequations-by-factoring-basic-examples/ http://www.yourteacher.com/freevideo-jwp.php?vid=7070 http://www.youtube.com/watch?v=65b AsV0SKk&feature=relmfu. z z + 5 5 http://www.youtube.com/watch?v=jyjf GZUmUsg 4. b b + 1 1 http://www.youtube.com/watch?v=jyjf GZUmUsg 5. z http://www.youtube.com/watch?v=jyjf GZUmUsg 6. 57 5b http://www.youtube.com/watch?v=jyjf GZUmUsg 7. 9z 4 http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-1/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/. 5b http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-1/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ 9. 4 http://www.youtube.com/watch?v=9tek XGoWIQM&feature=relmfu http://www.youtube.com/watch?v=xfa WLVLfeJM&feature=relmfu 11. 4(y-)(y-) http://www.youtube.com/user/yourteach ermathhelp#p/search/1/nj9ggam-dtq 1. y = 7 http://www.youtube.com/watch?v=zj- 9Zc9yKYU 10. b= -.5 http://www.youtube.com/watch?v=9tek XGoWIQM&feature=relmfu http://www.youtube.com/watch?v=xfa WLVLfeJM&feature=relmfu 1. (y+7)(y+7) http://www.youtube.com/user/yourteach ermathhelp#p/search/1/nj9ggam-dtq 14. (y + 5)(y ) http://www.youtube.com/user/yourteach ermathhelp#p/search/1/nj9ggam-dtq Algebra Review Page
15. -10b + z http://patrickjmt.com/polynomialsadding-subtracting-multiplying-andsimplifying-ex-1/ http://patrickjmt.com/polynomialsadding-subtracting-multiplying-andsimplifying-ex-/ http://patrickjmt.com/polynomialsadding-subtracting-multiplying-andsimplifying-ex-/ 17. z = 6/5 http://www.youtube.com/watch?v=zj- 9Zc9yKYU 19. b 9x http://www.youtube.com/watch?v=xdo 4uQdbPWU&feature=related 1. -7/5 http://www.youtube.com/watch?v=ctdo pjomli. 16 y - 4y + 6 http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-1/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ 6 5. 1x y 10 http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-1/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ 7. 15/xy http://www.youtube.com/watch?v=4gh LP6YMcc 16. 4x + 16 y http://patrickjmt.com/polynomialsadding-subtracting-multiplying-andsimplifying-ex-1/ http://patrickjmt.com/polynomialsadding-subtracting-multiplying-andsimplifying-ex-/ http://patrickjmt.com/polynomialsadding-subtracting-multiplying-andsimplifying-ex-/ 1. (y-5)(4y-) http://www.youtube.com/user/yourteach ermathhelp#p/search/1/nj9ggam-dtq 0.. 1 5 y + 14y + 49 http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-1/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ http://www.youtube.com/watch?v=ctdo pjomli 9 4. b z http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-1/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ 6. 5b/ http://www.youtube.com/watch?v=4gh LP6YMcc 4. b + b z + z 6 http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-1/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ Algebra Review Page 4
9. 4 x + xy + y http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-1/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ http://patrickjmt.com/exponents-applyingthe-rules-of-exponents-basic-ex-/ 1. b = 1/ http://www.youtube.com/watch?v=9tek XGoWIQM&feature=relmfu http://www.youtube.com/watch?v=xfa WLVLfeJM&feature=relmfu. 4 http://www.youtube.com/watch?v=hmal VzYEbUU 5. 7x/6 http://www.youtube.com/watch?v=aoaj albujo 0. x = 17/15 http://www.youtube.com/watch?v=9tek XGoWIQM&feature=relmfu http://www.youtube.com/watch?v=xfa WLVLfeJM&feature=relmfu. 6/7 http://www.youtube.com/watch?v=hmal VzYEbUU 4. b/ http://www.youtube.com/watch?v=aoaj albujo Algebra Review Page 5
APPLICATION REVIEW 1. Find the cost of the carpet needed to cover the floor of a room that is 14 yards long and 10 yards wide if the carpet costs $1.00 per square yard.. A can of soup is in the shape of a right circular cylinder whose diameter is inches and whose height is 5 inches. (a) What is the volume of the can? (b) How much steel was used in constructing the can? Use pi.14. ( ). If a board is (x + 6) feet long and a piece (x 5) feet long is cut off, what is the length of the remaining piece? 4. Find the area of the rectangle with length 5a 7 and width a +. 5. Hans is renting a sofa for $1.75 per month. If a new sofa costs $06, how many months will it take for the rental fees to equal the cost of a new sofa? 6. A high school boasts that three-fifths of its teachers have a master s degree. If 45 teachers have a master s degree, how many teachers does the school have?
7. The charges for repairing a transmission were $55 including parts. If the mechanic worked for 4 hours and the parts cost $75, how much down the mechanic charge per hour?. An office purchased 50 reams of paper for which it paid $60. There are two types of paper. The lighter-weight paper cost $4.00 per ream and the heavier paper cost $7.00 per ream. How many reams of each type of paper were purchased? { { 0 reams of the lighter-weight paper 0 reams of the heavier paper 9. To rent a small truck from U-haul in Orlando for local use, the cost is $19.99 per day plus 59 cents per mile. If x represents the number of miles driven and y is the cost of one day, then y = 19.99 +.59x. a. Find the cost for one day if the truck was driven 5 miles. b. If it cost $67.19 for one day s rental, how many miles was the truck driven? c. Find three ordered pairs and draw the graph. (0,7.69), (0,67.19), (65,5.4)
d. From the graph, estimate the number of miles driven if the cost is $7.69. Verify your answer from the equation. 0 miles 10. A company purchases a piece of machinery for $0,000. The value, V(x), of the machinery as a function of the number of years after it was purchased, x, is given by V(x) = -100x + 0,000. a. Find the value of the machinery after 4 years. V(x) = -100x + 0,000 V(4) = -100(4) + 0,000 V(4) = -700 + 0,000 V(4) =,00 b. Find the value of the machinery after 10 years. V(x) = -100x + 0,000 V(10) = -100(10) + 0,000 V(10) = -1000 + 0,000 V(10) = 1,000 c. What does V() = 15,600 mean? After years, the value of the machinery is $15,600.
11. The length of a rectangle is 5 less than twice the width. If the area of the rectangle is 5 square centimeters, find the dimensions of the rectangle. 1. Find two consecutive odd integers whose product is 6. { {
1. Find the area of a triangle whose base is 5 inches and whose height is 4 inches. in 14. Find the quotient. Express answer reduced to lowest terms. If a car used 1 gallons of gas on a trip of 416 miles, what was the average miles per gallon 10 for the trip?
15. Two numbers differ by 4. If 4 of the smaller number is increased by 1 of the larger number, the sum is. Find the numbers. { { 16. A lawn mower uses quarts of gasoline to mow 1 acre of grass. How many acres can be mowed with 9 quarts of gasoline? 17. A machine can fill 600 cans in 5 minutes. How many cans can be filled in 70 minutes?
1. Find the original price of a dining room suite that was discounted by $1 if the discount rate was 0%. 19. Mark paid $664 for a suit that was discounted 0%. What was the original price of the suit? 0. The sum of the squares of two consecutive integers is 61. Find the integers. { {