I. Operations with Integers

Transcription

1 Simplify each of the following. 8 th to 9 th Grade Summer Math Packet I. Operations with Integers (1010)

2 II. Fraction Practice Simplify each of the following. Put your final answer in the form of a mixed number when appropriate. Put all fractional answers in reduced form

3 III. Order of Operations Simplify ( ) 2 Substitute and simplify. 7. 8x 2 x 9 for x x 2y z for x, y 4, z xy x y for x, y y 2 x 1 for x 2 y y 2 x 1 for x 2, y m 2 n 2 5 m 2n for m 6, n 5m 2 2mn n 2

4 IV. Solving Equations Solve each of the equations for the given variable. 1. 4x 10 6x 2 2. y k k 6 2k 4. 1 d d f 25 5f m 5 7m 4m r 5 5r 1 5r w 12 6w 4w 2w 9. 5p 2p 5 2p n 2 7n 5 2n 2 n h 7 h 2h v 4 v 2v 6 9 4

5 V. Rates, Ratios and Proportions Calculate the unit rate gallons in 5 minutes 2. 6 people for tables. $5.60 for 16 apples miles in.5 hours Solve each proportion a c x y The ratio of apples to oranges in the basket was 5:7. If the basket had a total of 84 apples and oranges, how many apples were in the basket? 10. If Beth can walk two and a half miles in 28 minutes, how many minutes will it take her to walk 10 miles? 11. One day Bob kept track of how far he walked during the day. If he walked 6,000 feet in one day, how many miles would he walk in one week? (nearest hundredth of a mile) Convert each of the following ft. = yds pints = gallons 5

6 VI. Linear Equations 1. Find the slope of the line containing the points (, 7) and (-4, 10). 2. Given the equation y 9x 2, state the slope and y-intercept.. Graph y 1 x 2 4. Find the equation of the line with a slope of 2 5 and containing the point (10, 6). 5. Find the equation of the line containing the points (-, -10) and (12, 0). 6. Find the equation of the line that is perpendicular to the line y 8x 17 and contains the point (24, 8). 7. Are the two lines below parallel, perpendicular or neither? y 2 7 x 4 21y 6x 6 6

7 VII. Statistics 1. Twelve students were given a math quiz and the times they took to complete it (in minutes) are listed below. Find the range of these times. 10, 9, 12, 11, 8, 15, 9, 7, 8, 6, 12, A running race was completed by 7 students, and their race times are given below (in minutes). What is the median time? 1.2, 14.5, 17.9, 1.1, 15.6, 14.1, 12.. Given below are the daily high temperatures (in degrees Farenheit) for one winter week in Chicago. What is the mode of these temperatures? 9, 42, 4, 7, 9, 44, The average annual wind speed for the 5 windiest cities in the U.S. is given below in miles per hour. What is the mean of the annual wind speeds? 1.4, 14.0, 1.5, 1.2, The number of tornadoes that have occurred in the U.S. in the last 8 years is listed below. Find the median umber of tornadoes. 684, 764, 11, 656, 702, 10, 856, Students in a 4 th grade class were asked how many baseball caps they owned. The results are given in the line plot below. What is the mode, median and mean number of caps. x x x x x x x x x x x x x x Number of baseball caps owned 7. Heather s test scores are 81, 9, 74, and 95. What is the score she must earn on the next test in order to get a mean of 85 on the five tests? 8. The mean of a set of numbers is 108. The sum of the numbers is 2,052. How many numbers are in the set? 7

8 VII. Perimeter, Area, Surface Area and Volume 1. Find the area of a square that has a perimeter of 24 cm. 2. Find the area of the triangle. 7 in. Find the area of the circle. (nearest hundredth) 15 in d = 12 m 4. Find the area of the trapezoid. 24 cm 10 cm 6 cm 10 cm 8 cm 5. Find x. 8 m 15 m 6. Given a rectangle with a side of 10 m and a diagonal of 26 m. Find the perimeter of the rectangle. 26 m 10 m 7. Find the volume and surface area of each of the following. (nearest hundredth) a) b) radius = 25 ft c) m 7 cm 7. cm 5 m m 55 ft 4 cm 4 cm 8

9 IX. Simplifying Expressions with Polynomials Find the sum or difference. 1. x 2 10x 26 x 2 12x r 2 4r 2 6r 2 17r 2. 7m 2 15m 4 2m 2 14m g 7g 22 4g 2 9g 5. 1m 524m 9 5m b b b b 2 b 2 b Find the product. 7. 7c2c 2 4c 9 8. w 5 w a b 4a 12b 10. 2y 4 y 2 17y 24 9

10 X. Factoring Factor completely. 1. x 2 7x c 2 8c 12. z 2 6z 5 4. a 6 1a 6 5. g 2 2g h 2 h 7. 6e 2 24e 8. m 5 n 27m n 7 12m 4 n 4 9. k 2 6k d f r 11r 2 24r 1. 12p 2 7p c 2 c b 2 0b 25 10

11 Answer Key I Operations with Integers II Fractions Practice III Order of Operations IV Solving Equations 1. x 6 2. y 5 1. k 5 4. d f 0 6. m 2 7. r w = all real numbers 9. p n h 12. v 1 V Rates, Ratios and Proportions 1. 6 gallons per minute people per table. $0.5 per apple miles per hour 5. a c 9 7. a

12 8. y apples minutes miles yds gallons VI Linear Equations 1. m 7 2. m 9 and y-int y 2 5 x 2 5. y 2 x 8 (-, -) (0,-2) (, -1) 6. y 1 x 5 7. parallel 8 VII Statistics 1. 9 minutes minutes. 9 o F mph tornadoes 6. mode = 2, median =, mean = VIII Perimeter, Area, Surface Area and Volume 1. 6 cm in m cm m m 7a. S.A. = 78 m 2 V = 45 m 7b. S.A. = 12,566.7 ft 2 V = 107, ft 7c. S.A. = 74.4 cm 2 V = 7. cm 12

13 IX Simplifying Expressions with Polynomials 1. 4x 2 2x r 2 21r 4. 5m 2 29m y 4y 2 16y m b 2 2b 7. 14c 28c 2 6c 8. w 2 w a 2 60ab 6b y 46y 2 116y 96 X Factoring 1. x x 4 2. c 6c 2. z 1z 5 4. a 4 a 9 5. g 5g 6. hh ee 4 8. m n m 2 9n 4 4mn 9. k 10k d 2 d f 710 f r r p 1p c 7c 15. b 5 2 r 1