Cherry Creek High School

Summer Assignment for students entering: PreCalculus/Trigonometry

Please have the following worksheets completed and ready to be handed in on the first day of class, August 14, 2017. 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. It is expected that you have a good understanding of this material coming into these courses 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 Worksheet 1 Simplifying and Evaluating Expressions, Solving Linear Equations and Inequalities, Systems No Calculator. Simplify each expression. 1. 5(x + y) − 4(3x − 2y +1) 2. 4x2 (7x + 5) − 3x2 − 2(x3 − x) 3. 2y3 + 2y2 − y +16( )− 5y3 + 3y − 3( ) 4. 4y 2 − y( )2 + 3y2

5.

€

30x2 +20x −10−5

6. 6x4 + 27x5 + 3x2 + 3x

3x2

Evaluate each expression at the given value. 7. −4x2 + 6x − 5 when x = -3 8. 6 4b − 5 − 3 2 − 2b when b = 2 Solve for x.

9. 5x − 7(x −8) = 48 10.

x7−12 = −19 11.

x3+

25= 1

12. 7x + 6 = 4(x − 9) 13.

13

x −34= 2 +

12

x 14.

6x − 23

+x − 3

2=

15

Solve the inequality for x. Show all work.

15. 3+ 2x < 7x − 22 16. 4(3− 2x) ≥ −x − 37 17. 3x + 2(x −1) ≥

x2− 6

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

18.

2x − y = 145x + y = 63

19.

−3x − 5y = −31−7x + 2y = −45

20.

x = 3+ y2(x − 4) − y = 1

--------------------------------------------------------------------------------------------------------------------------------- Answers: 1. −7x +13y − 4 2. 26x3 +17x2 + 2x 3. −3y3 + 2y2 − 4y +19 4. 4y3 −13y2 +16y

5. −6x2 − 4x + 2 6. 9x3 + 2x2 +1+ 1x

7. -59 8. 12 9. x = 4 10. x = −49 11. x =

95

12. x = −14 13. x = −

332

14. x =

7175

15. x > 5 16. x ≤ 7 17. x ≥ −

89

18. (11, 8)

19. (7, 2) 20. (6, 3)

Cherry Creek High School Name____________________________ Summer Assignment Worksheet 2 Multiplying/Factoring Review No Calculator. Multiply.

1. (x + 7)(x − 7) 2. (3x −1)(4x + 3) 3.

x +11( )2

4. (−5x + 4)(2x − 9) 5. (7x + y)(x − 3y) 6. x − 4( ) x2 − 3x +1( )

Factor using GCF. 7. 3x2 +15x 8. −4x2 − 20x 9. 5x3 + 35x2 Factor using difference of squares. 10. x2 − 9 11. 4x2 − 25y2 12. x2 + 36 Factor the trinomial. 13. x2 + 7x +12 14. x2 +14x − 32 15. 2x2 + 7x − 4 16. 2x2 −11x − 21 17. 12x2 + 5x − 2 18. 26 15x x− − Factor using grouping. 19. x3 − 3x2 − 2x + 6 20. x3 + x2 − 9x − 9 Factor using a combination of methods. 21. x3 + 6x2 + 5x 22. 3x5 − 75x3 23. x5 − 7x3 −18x --------------------------------------------------------------------------------------------------------------------------------- Answers: 1. x2 − 49 2. 12x2 + 5x − 3 3. x2 + 22x +121 4. −10x2 + 53x − 36 5. 7x2 − 20xy − 3y2 6. x3 − 7x2 +13x − 4 7. 3x(x + 5) 8. −4x(x + 5) 9. 5x2 (x + 7) 10. (x + 3)(x − 3) 11. (2x −5y)(2x + 5y) 12. x2 + 36 13. (x + 3)(x + 4) 14. (x +16)(x − 2) 15. (2x −1)(x + 4) 16. (2x + 3)(x − 7) 17. (4x −1)(3x + 2) 18. (3x − 5)(2x + 3) 19. (x − 3)(x2 − 2) 20. (x +1)(x − 3)(x + 3) 21. x(x + 5)(x +1) 22. 3x3(x + 5)(x −5) 23. x(x − 3)(x + 3)(x2 + 2)

Cherry Creek High School Name____________________________ Summer Assignment Worksheet 3 Solving Quadratics, Systems No Calculator. Solve for x (using factoring). Show all work. 1. x2 −14x + 40 = 0 2. x2 +15x −100 = 0 3. x2 − 22 = 9x 4. x2 −121= 0 5. 9x2 − 49 = 0 6. x2 +12x + 36 = 0 7. 3x2 +14x − 5 = 0 8. 6x2 − 5x − 6 = 0 9. x3 + 8x2 − 48x = 0 Solve for x (using the quadratic formula). Show all work. 10. x2 − 4x + 2 = 0 11. x2 − 5x − 7 = 0 12. x2 + 5x + 7 = 0 Solve the system of equations for x and y. Show all work.

13. x2 + 4y2 = 24x2 − y2 = −1

14. y = 2x + 3x2 + y2 − 26x = 0

15. y = x4

y =11x2 −18

16. y = x3 + 4xy = 2x2 +8

17. y = x + 6y = x + 4

18. 2x2 + y2 = 3

2x − y = 3

Using a graphing calculator, solve the system of equations for x and y.

19. y = x3 −5x2

y = −8x + 4 20.

y = 5x

y = 32x 21. y = 2

x

y = 2x + 2

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

Answers: 1. x = 4,10 2. x = −20,5 3. x = −2,11 4. x = ±11 5. x = ±

73

6. x = −6

7. x = −5,

13

8. x = −

23

,32

9. x = −12,0,4 10. 2 ± 2 11.

5 ± 532

12. no solution

13. ( )2, 5± ± 14. ( ) 9 331, 5 , ,5 5

⎛ ⎞⎜ ⎟⎝ ⎠

15. ( ) ( )3, 81 , 2, 4± ± 16. ( )2, 16 17. ( )2, 2− 18. ( )1, 1−

19. ( ) ( )1, 4 , 2, 12− − 20. ( )0, 1 21. ( ) ( )3, 8 , 0.690, 0.620−

Cherry Creek High School Name____________________________ Summer Assignment Worksheet 4 Graphing No Calculator. Find the slope of the line that contains the points. 1. (2, 5) (7, 7) 2. (−3, 2) (6, 5) 3. (7, − 4) (7, − 3) Find the equation of the line in slope-intercept form (y=mx + b) using the given information. 4. Slope = 5, y-intercept = 2 5. m = 1/3, b = ¼ 6. m = -2, goes through (-1, -4) 7. goes through (1, 4) & (3, 10) 8. goes through (-3, -5) & (-1, -1) 9. goes through (5, 7) & (-8, 7) Find the equation of the line from the graph. 10. 11. Graph the lines on the same grid given the equations. 12. 3x + 2y = 14 13. y = −4 14. x = −8

Graph the following: 15. ( )23 4y x= − − 16. ( )22 4 8y x= − + + 17. 5y x= − + 18. 5 2y x= − + 19. 2 3y x= − + 20. 3 2y x= −

21. ( )22 3 25x y+ + = 22. ( )36 24

y x+ = − 23. 4x = −

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

Answers: 1.

25

2.

13

3. undefined 4. y = 5x + 2 5. y =

13

x +14

6. y = −2x − 6 7. y = 3x +1

8. y = 2x +1 9. y = 7 10. y = −

13

x − 2 11. y =

34

x +14

15. 16. 17. 18. 19. 20.

21. 22. 23.

Cherry Creek High School Name____________________________ Summer Assignment Worksheet 5 Simplifying Exponents, Radicals No Calculator. Simplify each with positive exponents only.

1. x2x6 2. 6x4 y5( ) 7x5 y( ) 3.

x7

x2

4.

30x9 y5

−6x2 y 5.

x−5 y3m2

x2 y−8m6 6.

x−2( )3

7. −2x5 y( )3 8. 6yx6

3y4x−2⎛⎝⎜

⎞⎠⎟

4

9.

2x2

m3

!

"#$

%&

−2

Simplify. 10. 27 11. 250 12. 4 45 + 2 20 13. 50 − 16 + 72 14. 6 • 15 15. 4 3 •5 27

16.

7525

17.

4499

18. 1502

Rationalize the denominator. Answers should not have radicals in the denominator.

19.

53

20.

72

21.

612

22.

41+ 3

23.

82 − 2

24.

105− 5

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

Answers: 1. x8 2. 42x9 y6 3. x5 4. −5x7 y4 5.

y11

x7m4 6.

1x6 7. −8x15y3 8. 16x

32

y12

9.

m6

4x4 10. 3 3 11. 5 10 12. 16 5 13. 11 2 − 4 14. 3 10 15. 180 16. 3 17.

23

18. 5 3 19.

5 33

20.

142

21.

22

22. −2 + 2 3 23. 8 + 4 2 24.

5+ 52