Summer 2017 Math Packet

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1 Summer 017 Math Packet for Rising Geometry Students This packet is designed to help you review your Algebra Skills and help you prepare for your Geometry class. Your Geometry teacher will expect you to be proficient in these skills and will collect your work on the first day of class. Directions: 1. Do ALL the exercises on separate paper. Please do not complete your work on the packet pages themselves. Label each topic clearly and compile your work in order.. Each topic has an explanation and example problems at the top of the page. Some of the more difficult topics have embedded videos that you can watch. Be sure to read the example problems and watch the video before attempting the problems.. Check your work with the answers provided at the end of the packet. If your answer is incorrect, go back and rework the problems until it is correct.. If you need additional help, the following resources are available online: Explanations and Example Problems: Videos and Tutorials: de&wcprefix=ate&wcsuffix=0775 0

2 Topic 1: Order of Operations Topic 1 Exercises: Evaluate each expression [ ] 9. Evaluate each expression when,,,, and

3 ( ) ( ) 0. ( ) ( ) Topic : Distributive Property and Combining Like Terms Topic Exercises: Simplify each expression. If not possible, write simplified Write an algebraic expression for each verbal expression, then simplify.

4 15. Six times the difference of and, increased by. 16. Two times the sum of squared and squared, increased by three times the sum of squared and squared. Topic : Writing Equations Topic Exercises: Translate each sentence into an equation or formula. 1. Three times a number minus twelve equals forty.. One-half of the difference of and is 5.. Three times the sum of and is.. The area of a circle is the product of and the radius,, squared. 5. WEIGHT LOSS Lou wants to lose weight to audition for a part in a play. He weighs 160 pounds now. He wants to weigh 150 pounds. a. If represents the number of pounds he wants to lose, write and equation to represent this situation. b. How many pounds does he need to lose to reach his goal?

5 Translate each equation into a sentence Topic : Solving Equations, Ratios and Proportions Topic Exercises: Solve each Equation. It is possible for the equation to be an identity or have no solution

6 [ ] Topic Exercises continued: Solve each equation or formula for the variable indicated Topic Exercises continued: Evaluate each expression. 5

7 Josh finished math problems in one hour. At that rate, how many hours will it take him to complete 7 problems? Topic 5: Graphing Linear Equations, Slope, and Direct Variation Topic 5 Exercises: 6

8 Topic 5 Exercises continued: Find the slope that passes through each pair of points. 7

9 Find the value of so that the line passing through the given points has the given slope Topic 5 Exercises continued: Suppose varies directly as. Write a direct variation equation that relates to. Then solve. 8

10 16. If when, find when. 17. If when, find when. 18. If when, find when. 19. If when, find when. Topic 6: Writing Equations of Lines Standard Form Standard Form, where A and B are coefficients and C is a constant ** After finding point-slope form, manipulate the equation to put the equation in slope-intercept form and standard form Watch this Video! Topic 6 Exercises: Write the equation of the line passing through the given points in: a.) Point-slope form b.) Slope-intercept form c.) Standard form using integers (follow the example in the video. Each problem has solutions) 9

11 Topic 6 Exercises continued: Write the equation of the line in slope-intercept form that passes through the given point and is parallel to the given line. 10

12 Write the equation of the line in slope-intercept form that passes through the given point and is perpendicular to the given line Topic 7: Solving and Graphing Inequalities Topic 7 Exercises: Solve each inequality and graph the solution on a number line

13 Topic 7 Exercises Continued: 1

14 Topic 8: Solving Systems of Linear Equations 1

15 Topic 8 Exercises: 1

16 Topic 8 Exercises continued: Use substitution to solve each system of equations. 7. { 8. { 9. { 10. { 11. { 1. { 15

17 Watch this Video! Topic 8 Exercises continued: Use elimination to solve each system of equations. 1. { 1. { 15. { 16. { 17. { 18. { 19. The length of Sally s garden is meters longer than times the width. The perimeter of her garden is 7 meters. What are the dimensions of Sally s garden? 16

18 Topic 9: Polynomials Topic 9 Exercises: Simplify ( ) ( )

19 Topic 9 Exercises Continued: Simplify ( ) 15. ( ) 16. ( ) ( ) 19. ( ) 0. [ ] 1. ( ) 18

20 Remember to distribute the negative! Topic 9 Exercises Continued: Add or Subtract

21 FOIL First - Outer - Inner - Last Example: Topic 9 Exercises Continued: Multiply

22 Topic 10: Factoring Factoring Guide Type of Factoring 1. Greatest Common Factor When to Use It Method Example Anytime, ALL THE TIME, if Possible. You should always look for the GCF before you do any other type of factoring. Find the greatest common multiple of each term and factor it out. Factored: 1x 1x 7x(x ). Difference of Two Squares Two Terms. A perfect square minus another perfect square. Factored: a b (a b) a b Factored: x (x ) x. Standard Form when a 1 Three Terms. Trinomial in the form x bx c. Grouping Four Terms. This is the only type of factoring you can try when there are terms. Look for factors of c that add up to b. Group the first two and the second two terms. Find GCF of each group. Factored: x 7x 1 (x ) x x x 6x 8 Factored: (x x)( 6x 8) x(x ) (x ) (x )(x ) 5. Perfect Square Trinomial 6. Standard Form when a 1 Three Terms. Trinomial in the form a ab b or a ab b Three Terms. Trinomial in the form ax bx c a ab b Factored: (a b) a ab b Factored: (a b) 1. Multiply a c. Look for factors of a c that add up to b.. Separate b term into those factors.. Grouping x 1x 9 Factored: (x ) x 5x Factored: (x 6x) (x ) x(x ) 1(x ) (x 1)(x ) 1

23 Topic 10 Exercises: Factor Completely Topic 11: Solving Quadratic Equations

24 Topic 11 Exercises: Solve by Factoring and the Zero Product Property Solve by using the Quadratic formula

25 Topic 1: Radical Expressions Topic 1 Exercises: Simplify

26 Topic 1: Rational Expressions Topic 1 Exercises: Find each product. USE FACTORING! 5

27 Topic 1: Relations and Functions Topic 1 Exercises: Determine whether each relation is a function. Write yes or no. 6

28 Summer 01 Math Packet Answers For Rising Geometry Students Topic 1 Answers: , Topic Answers: 1. 0x x. 6x y. 6x y z 5. xy y 6. 5x-y 7. 11a 8. Simplified 9. 5x p 11. 9a + 8b 1. x 1. xy 6x x 5y 15. 1a b 16. 5x 5y Topic Answers: 1. t ( ) 5 a b. ( d ). 5. A r a.) 160 p 150 b.) 10 pounds 6. Four times a minus six equals twenty-three. 7. The sum of x squared and y y squared is eight. 8. One-third of the difference between the h and 1 equals b. 9. The area, A of a triangle is one-half the product of the height, h and the base, b. Topic Answers: 1. x. x. b. p x 5 a y identity 9. y 10. x 11. identity 1. f 7 1. t 1. no solution 15. x 16. w y 18. a 19. x 0 0. y y = c b x a. k = t 1 r z x 1 y or - y 16w x A h a b 9 F C 5 P w l x p y 6. No solution. a w 6 6. hours Topic 5 Answers: 1. 7

29 m 1. m. undefined. 5. m m 7 m r r r r r r k m k m k m y y y y 8 Topic 6 Answers: y ( x 0) 1. a.) or y 7 ( x 1) b.) y x c.) x y y 1( x 6). a.) or y 5 1( x ). a.) b.) y x c.) x y 1 y ( x ) 1 or y ( x ) b.) 1 y x c.) x y 9 y 11( x 1). a.) or y 7 11( x ) b.) y 11x 15 c.) 11x y 15 7 y ( x ) 5. a.) 7 or y 5 ( x 0) 7 b.) y x 5 6. a.) c.) 7x y 15 b.) 6 y ( x ) 5 6 or y 8 ( x 9) y x 5 5 c.) 6x 5y 1 7. y x y x y x 1 y x 1 y x x 1. 0 Topic 7 Answers: 1. t 5 8

30 . x. No solution. m k 6. 1 n 7. w 1 or w y 5 or y 9. n or n a 1 or a Topic 8 Answers: 1, 1..,.,1. 1, 5. no solution 6. infinitely many solutions 7. 1, 8. no solution 9. infinitely many solutions 10. infinitely many solutions 11. no solution 1.,1 1., 1. 1,1 9

31 15., 16., ,0 1, width 9m length 8m Topic 9 Answers: y 16a x y 10 0x 7 a b c 6 0x y z 8 a b 9 51x y j k a b f 6 8x y x y z y a b 15. pr rn ab b a 0. 6 x 1 8x 1. 6 y. a 6. 15xy y x p 9p 6p 8p q 6x x h j k 8. 5a 1b z 5z x 5x xy x y x x x 5x x x x 9x 5 x x 6x y x y 10x y x 9 0a 16 ab x 11x 8 Topic 10 Answers: 1. xx ( ). x x 1. x. x x 5. x x 6. x x 1 7. x 9x 1 8. x 7x 9. 5x x xy x y 11. y y 5 1. x yx y 1. a 9a a 1. 5x 15. x x 7x y 5 y x x 18. x x 1 x 0. a 1a 6 Topic 11 Answers: 1. x 8,1. m 0,1. x. 1 x 0, 5. 5 k,1 6. x 5, 1 7. x,1 8. x 9, 1 9. x 0,1 10. x, c, 1 x, x 1 1. x, x, 1 x 5 x, 8 6 p 5 89 Topic 1 Answers:

32 x a a 8a 15 a a a 0 10b 10x 1b Topic 1 Answers: 1. yes. yes. no. no 5. no 6. yes 7. yes 8. no 9. yes 10. yes 11. no 1. no Topic 1 Answers: 6a b p x x x 8 x 16 x 1 a a 10 x x m 1 m m 1 n 1 n 6 pr p r 1

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