summerpacket.PreCalcTrigSummer2016

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 11, 2016. 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 − 2 y + 1)
(
) (
2. 4x 2 (7x + 5) − 3x 2 − 2(x 3 − x)
)
4. 4y ( 2 − y ) + 3y 2
3. 2y 3 + 2y 2 − y +16 − 5y 3 + 3y − 3
5.
2
30x 2 + 20 x − 10
−5
6.
6x 4 + 27x 5 + 3x 2 + 3x
3x 2
Evaluate each expression at the given value.
€
8. 6 4b − 5 − 3 2 − 2b when b = 2
7. −4x 2 + 6x − 5 when x = -3
Solve for x.
9. 5x − 7(x − 8) = 48
10.
x
− 12 = −19
7
11.
x 2
+ =1
3 5
12. 7x + 6 = 4(x − 9)
13.
1
3
1
x− = 2+ x
3
4
2
14.
6x − 2 x − 3 1
+
=
3
2
5
Solve the inequality for x. Show all work.
15. 3 + 2x < 7x − 22
17. 3x + 2(x − 1) ≥
16. 4(3 − 2x) ≥ −x − 37
x
−6
2
Solve the system for x and y. Show all work.
18.
2x − y = 14
19.
5x + y = 63
−3x − 5y = −31
20.
−7x + 2 y = −45
x = 3+ y
2(x − 4) − y = 1
--------------------------------------------------------------------------------------------------------------------------------Answers: 1. −7x + 13y − 4 2. 26x 3 + 17x 2 + 2x 3. −3y 3 + 2 y 2 − 4 y + 19 4. 4 y 3 −13y 2 + 16 y
5. −6x 2 − 4x + 2
12. x = −14
19. (7, 2)
6. 9x 3 + 2x 2 + 1+
13. x = −
20. (6, 3)
33
2
1
x
14. x =
7. -59
71
75
8. 12
15. x > 5
9. x = 4
16. x ≤ 7
10. x = −49
17. x ≥ −
8
9
11. x =
9
5
18. (11, 8)
Cherry Creek High School
Summer Assignment Worksheet 2
Multiplying/Factoring Review
Name____________________________
No Calculator.
Multiply.
2
1. (x + 7)(x − 7)
2. (3x − 1)(4x + 3)
3.
( x + 11)
4. (−5x + 4)(2x − 9)
5. (7x + y)(x − 3y)
6.
( x − 4) ( x
8. −4x 2 − 20x
9. 5x 3 + 35x 2
11. 4x 2 − 25y 2
12. x 2 + 36
13. x 2 + 7x + 12
14. x 2 + 14x − 32
15. 2x 2 + 7x − 4
16. 2x 2 − 11x − 21
17. 12x 2 + 5x − 2
18. 6 x 2 − x − 15
2
)
− 3x + 1
Factor using GCF.
7. 3x 2 + 15x
Factor using difference of squares.
10. x 2 − 9
Factor the trinomial.
Factor using grouping.
19. x 3 − 3x 2 − 2x + 6
20. x 3 + x 2 − 9x − 9
Factor using a combination of methods.
22. 3x 5 − 75x 3
21. x 3 + 6x 2 + 5x
23. x 5 − 7x 3 −18x
--------------------------------------------------------------------------------------------------------------------------------Answers: 1. x 2 − 49 2. 12x 2 + 5x − 3 3. x 2 + 22x + 121 4. −10x 2 + 53x − 36 5. 7x 2 − 20xy − 3y 2
6. x 3 − 7x 2 + 13x − 4
7. 3x(x + 5)
11. (2x − 5y)(2x + 5y)
16. (2x + 3)(x − 7)
12. x 2 + 36
8. −4x(x + 5)
10. (x + 3)(x − 3)
13. (x + 3)(x + 4) 14. (x + 16)(x − 2) 15. (2x −1)(x + 4)
17. (4x − 1)(3x + 2)
20. (x + 1)(x − 3)(x + 3)
9. 5x 2 (x + 7)
18. (3x − 5)(2x + 3)
21. x(x + 5)(x + 1)
19. (x − 3)(x 2 − 2)
22. 3x 3 (x + 5)(x − 5)
23. x(x − 3)(x + 3)(x 2 + 2)
Cherry Creek High School
Summer Assignment Worksheet 3
Solving Quadratics, Systems
No Calculator.
Name____________________________
Solve for x (using factoring). Show all work.
1. x 2 − 14x + 40 = 0
2. x 2 + 15x − 100 = 0
3. x 2 − 22 = 9x
4. x 2 − 121 = 0
5. 9x 2 − 49 = 0
6. x 2 + 12x + 36 = 0
7. 3x 2 + 14x − 5 = 0
8. 6x 2 − 5x − 6 = 0
9. x 3 + 8x 2 − 48x = 0
Solve for x (using the quadratic formula). Show all work.
10. x 2 − 4x + 2 = 0
11. x 2 − 5x − 7 = 0
12. x 2 + 5x + 7 = 0
Solve the system of equations for x and y. Show all work.
13.
16.
x 2 + 4 y 2 = 24
x 2 − y 2 = −1
y = x 3 + 4x
y = 2x 2 + 8
14.
17.
y = 2x + 3
15.
x 2 + y 2 − 26x = 0
y = x+6
y = x+4
18.
y = x4
y = 11x 2 −18
2x 2 + y 2 = 3
2x − y = 3
Using a graphing calculator, solve the system of equations for x and y.
19.
y = x 3 − 5x 2
y = −8x + 4
20.
y = 5x
21.
y = 32 x
y = 2x
y = 2x + 2
--------------------------------------------------------------------------------------------------------------------------------7
Answers: 1. x = 4,10 2. x = −20,5 3. x = −2,11 4. x = ±11 5. x = ±
6. x = −6
3
7. x = −5,
1
3
( ±2, ± 5 )
2 3
8. x = − ,
3 2
9. x = −12,0,4
10. 2 ± 2
(
11.
)
⎛ 9 33 ⎞
14. (1, 5 ) , ⎜ ,
⎟ 15. ( ±3, 81) , ± 2, 4
⎝5 5 ⎠
19. (1, − 4 ) , ( 2, − 12 ) 20. ( 0, 1) 21. (3, 8) , ( −0.690, 0.620 )
13.
5 ± 53
2
16.
( 2, 16)
12. no solution
17.
( −2, 2 )
18. (1, − 1)
Cherry Creek High School
Summer Assignment Worksheet 4
Name____________________________
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 + 2 y = 14
13. y = −4
14. x = −8
Graph the following:
15. y = ( x − 3) − 4
16. y = −2 ( x + 4) + 8
17. y = − x + 5
18. y = x − 5 + 2
19. y = −2 x + 3
20. y = x 3 − 2
21. x 2 + ( y + 3) = 25
22. y + 6 =
2
2
2
3
( x − 2)
4
23. x = −4
--------------------------------------------------------------------------------------------------------------------------------2
1
1
1
Answers: 1.
2.
3. undefined 4. y = 5x + 2 5. y = x +
6. y = −2x − 6 7. y = 3x + 1
5
3
3
4
1
3
1
8. y = 2x + 1 9. y = 7 10. y = − x − 2 11. y = x +
3
4
4
15.
16.
17.
18.
19.
20.
21.
22.
23.
Cherry Creek High School
Summer Assignment Worksheet 5
Simplifying Exponents, Radicals
Name____________________________
No Calculator.
Simplify each with positive exponents only.
(
1. x 2 x 6
4.
30x 9 y 5
−6x 2 y
(
)(
2. 6x 4 y 5 7x 5 y
5
7. −2x y
5.
x −5 y 3m2
x 2 y −8 m6
⎛ 6 yx 6 ⎞
8. ⎜ 4 −2 ⎟
⎝ 3y x ⎠
3
)
)
x7
x2
3.
3
( )
6. x −2
4
! 2x 2 $
9. # 3 &
" m %
−2
Simplify.
10.
27
11.
250
12. 4 45 + 2 20
13.
50 − 16 + 72
14.
6 • 15
15. 4 3 • 5 27
16.
75
17.
25
44
150
18.
99
2
Rationalize the denominator. Answers should not have radicals in the denominator.
19.
22.
5
20.
3
4
23.
1+ 3
7
6
21.
2
8
24.
2− 2
12
10
5− 5
--------------------------------------------------------------------------------------------------------------------------------1
y11
16x 32
Answers: 1. x 8 2. 42x 9 y 6 3. x 5 4. −5x 7 y 4 5. 7 4
6. 6
7. −8x15 y 3 8.
y12
x
x m
9.
m6
4x 4
18. 5 3
10. 3 3
19.
5 3
3
11. 5 10
20.
14
2
12. 16 5
21.
2
2
13. 11 2 − 4
14. 3 10
22. −2 + 2 3
23. 8 + 4 2
15. 180
24.
16.
5+ 5
2
3
17.
2
3