Cherry Creek High School

Summer Assignment for students entering: Geometry Honors

Please have the following worksheets completed and ready to be handed in on the first day of class, August 18, 2021. Make sure you show your work where appropriate. Answers are provided for you to check; however, you will not be given credit if you don’t show work on problems that require it. Please neatly organize your work and use notebook paper when there is not enough room to show all of your work on these worksheets. It is expected that you have a good understanding of this material coming into Honor’s Geometry, as teachers will not be doing an extensive review of previously learned material. Have a great summer and we look forward to seeing you in the fall! The CCHS Math Department

Cherry Creek High School Name____________________________ Summer Assignment - Page 1 Exponents/Like Terms Review No Calculator. Simplify each with positive exponents only. 1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

Combine like terms. 13. 14. 15. 16. 17. 18. 19. 20. 21. ---------------------------------------------------------------------------------------------------------------------------------

Answers: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

11. 12. 13. 14. 15. 16.

17. 18. 19. 20. 21.

73( ) 711( ) x2x6

6x4 y5( ) 7x5 y( )

x7

x2

30x9 y5

−6x2 y

x−5 y3m2

x2 y−8m6

34( )5

x−2( )3 −2x5 y( )3

2x3

3y4

!

"#$

%&

2

6yx6

3y4x2

!

"#$

%&

4

2x2

m3

!

"#$

%&

−2

3x + x − 2y + 4y 7(x − 3) + 6(2x + 5y) −7x −12(x + 4) − x +13

x2 + 3x − 3x2 − x −2(x2 + 4x3) − x3 8xy + 2x + 9y −1

4w( p −1) − 2 pw + 4w − p −4r − 7r + 6r − 2r xy2 + x2 y + 5xy2 − 2xy2

714 x8 42x9 y6 x5

−5x7 y4

y11

x7m4 320

1x6 −8x15 y3

4x2

9y8

16x16

y12

m6

4x4 4x + 2y 19x + 30y − 21 −20x − 35 −2x2 + 2x

−9x3 − 2x2 8xy + 2x + 9y −1 2 pw − p −7r 4xy2 + x2 y

Cherry Creek High School Name____________________________ Summer Assignment - Page 2 - Lines No Calculator. Find the slope of the line that contains the points. 1. 2. 3. Find the equation of the line in slope-intercept form (y=mx + b) using the given information. #7-15 require work to be done on a separate sheet of paper. 4. Slope = 5, y-intercept = 2 5. m = -4, b = -9 6. m = 1/3, b = 1/4 7. m = 3, goes through (2, 5) 8. m = -2, goes through (-1, -4) 9. m = 1, goes through (0, 0) 10. goes through (1, 4) & (3, 10) 11. goes through (-3, -5) & (-1, -1) 12. goes through (5, 7) & (8, 1) 13. goes through (3, 6) & (6, 8) 14. goes through (-2, 2) & (-6, 4) 15. goes through (5, 5) & (10, 12) Find the equation of the line from the graph. 16. 17. Graph the lines on the same grid given the equations. 18. 19. 20. ---------------------------------------------------------------------------------------------------------------------------------

Answers: 1. 2. 3. 4. 5. 6. 7. 8.

9. 10. 11. 12. 13. 14.

15. 16. 17.

(2, 5) (7, 7) (−3, 2) (6, 5) (7, − 4) (8, − 3)

3x + 2y = 14

y = −4 x = −8

25

13 1 y = 5x + 2 y = −4x − 9

y =

13

x +14 y = 3x −1 y = −2x − 6

y = x y = 3x +1 y = 2x +1 y = −2x +17 y =

23

x + 4 y = −

12

x +1

y = 75x − 2

y = −

13

x − 2 y =

34

x +14

Cherry Creek High School Name____________________________ Summer Assignment – Page 3 Solving Linear Equations and Inequalities, Systems No Calculator. Solve for x. Show all work. 1. 2. 3.

4. 5. 6.

7. 8. 9.

Solve the inequality for x. Show all work.

10. 11. 12.

Solve the system for x and y. Show all work.

13. 14. 15.

16. 17. 18.

---------------------------------------------------------------------------------------------------------------------------------

Answers: 1. 2. 3. 4. 5. 6. 7. 8. 9.

10. 11. 12. 13. 14. 15. 16. 17.

18.

3x − 9 = 12 7(x + 2) −1= 48 6x − 3+ 4x + 8 = 105

5x − 7(x − 8) = 48

x7−12 = −19

x3+

25= 1

7x + 6 = 4(x − 9)

13

x −34= 2 +

12

x

6x − 23

+x − 3

2=

15

3+ 2x < 7x − 22 4(3− 2x) ≥ −x − 37 3x + 2(x −1) ≥

x2− 6

2x − y = 145x + y = 63

2x + 2y = 26x + 4y = −16

−3x − 5y = −31−7x + 2y = −45

x = 3+ y2(x − 4) − y = 1

y = 3(4 − 2x)−3y + 5x + x = −4x − 22

3x + 2y = 176x + 4y = 25

x = 7 x = 5 x = 10 x = 4 x = −49 x =

95 x = −14

x = −

332

x =

7175 x > 5 x ≤ 7

x ≥ −

89 (11, 8) (−10, 11) (7, 2) (6, 3)

(12

, 9)

∅

Cherry Creek High School Name____________________________ Summer Assignment – Page 4 Multiplying/Factoring Review No Calculator. Multiply. 1. 2. 3.

4. 5. 6. 7. 8. 9. Factor. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. --------------------------------------------------------------------------------------------------------------------------------- Answers: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.

4x(x + 6) (x − 4)(x − 3)

x + 8( ) x + 9( )

(x + 7)(x − 7) (x −10)(x −10)

x +11( )2

(3x −1)(4x + 3) (−5x + 4)(2x − 9) (7x + y)(x − 3y)

3x2 +15x −4x2 − 20x 5x3 + 35x2

x2 − 9 4x2 − 25 x2 + 36

x2 + 7x +12 x2 −12x + 20 x2 +14x − 32

x2 − x − 42 x2 + 2x − 63 x2 + x − 56

2x2 −11x − 21 12x2 + 5x − 2 26 15x x− −

x3 + 6x2 + 5x x3 −11x2 + 30x 2x4 + 9x3 − 5x2

4x2 + 24x x2 − 7x +12 x2 +17x + 72 x2 − 49 x2 − 20x +100 x2 + 22x +121 12x2 + 5x − 3 −10x2 + 53x − 36 7x2 − 20xy − 3y2

3x(x + 5) −4x(x + 5) 5x2 (x + 7)

(x + 3)(x − 3) (2x − 5)(2x + 5) x2 + 36 (x + 3)(x + 4) (x −10)(x − 2)

(x +16)(x − 2) (x − 7)(x + 6) (x + 9)(x − 7) (x + 8)(x − 7) (2x + 3)(x − 7)

(4x −1)(3x + 2) (3x − 5)(2x + 3) x(x + 5)(x +1) x(x − 6)(x − 5) x2 (2x −1)(x + 5)

Cherry Creek High School Name____________________________ Summer Assignment – Page 5 Solving Quadratics and Literal Equations No Calculator. Solve for x (using factoring). Show all work. 1. 2. 3. 4. 5. 6. 7. 8. 9. Solve for x (using the quadratic formula). Show all work. 10. 11. 12. Solve the literal equations for x. Show all work. 13. 14. 15. 16. 17. 18. ---------------------------------------------------------------------------------------------------------------------------------

Answers: 1. 2. 3. 4. 5. 6. 7.

8. 9. 10. 11. 12. 13. 14. 15.

16. 17. 18.

x2 −14x + 40 = 0 x2 +15x −100 = 0 x2 − 22 = 9x

x2 −121= 0 9x2 − 49 = 0 x2 +12x + 36 = 0

3x2 +14x − 5 = 0 6x2 − 5x − 6 = 0 x3 + 8x2 − 48x = 0

x2 − 4x + 2 = 0 x2 − 5x − 7 = 0 x2 + 5x + 7 = 0

5y + 3x = −4 9x − by = c 12ax − 36 = 6ax

5( y + 7) = −3(x + y) cx + 4c = 5x + 7c d2 − 4(x + 2) = d(x − 2)

x = 4,10 x = −20,5 x = −2,11 x = ±11 x = ±

73 x = −6

x = −5,

13

x = −

23

,32 x = −12,0,4 2 ± 2

5 ± 532

∅ −5y − 4

3 by + c

9 6a

8y + 35−3

3cc − 5 d − 2

Cherry Creek High School Name____________________________ Summer Assignment – Page 6 Simplifying Radicals No Calculator. Simplify. 1. 2. 3. 4. 5. 6. 7. 8. 9.

10. 11. 12.

Answers should not have radicals in the denominator so please rationalize.

13. 14. 15.

16. 17. 18.

--------------------------------------------------------------------------------------------------------------------------------- Answers: 1. 2. 3. 4. 5. 6. 7. 8. 9. 180

10. 11. 12. 13. 14. 15. 16. 17. 18.

8 27 40

4 45 + 2 20 −5 8 + 32 50 − 16 + 72

6 • 15 30 • 55 4 3 •5 27

3625

7525

4499

53

72

612

41+ 3

82 − 2

105− 5

2 2 3 3 2 10 16 5 −6 2 11 2 − 4 3 10 5 66

65 3

23

5 33

142

22 −2 + 2 3 8 + 4 2

5+ 52