honors geometry summer packet 2021
TRANSCRIPT
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