summer assignment for students entering: pre...
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Summer Assignment for students ENTERING: Pre-Calculus Honors
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 at the end of this packet; however, you will not be given credit if you don’t show work on
problems that require it. Please neatly organize your work, show all of your work, and place all of your work and answers ON these worksheets. It is expected that you have a good understanding of this
material coming into Pre-Calculus Honors, 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
0.1 -‐ Factoring and Operations with Rational Expressions Factor each expression in #1-‐10. 1. 4 2x 9x− 2. 2x 4x 32+ − 3. 4 2x 4x 32+ − 4. 6 3x 4x 32+ − 5. 26x x 2− − 6. 210x 31x 15− + 7. 3 2x 2x 7x 14− − + 8. ( ) ( ) ( ) ( )3 2 2x x 4 x 2 3 x 4 x 2− − − − −
9. ( ) ( ) ( )3 43x 1 x 8x 8 x 1+ + − + 10. ( ) ( ) ( )( )22 32 26x x 2 2x 1 2 2x 1 2 x− + + + −
Simplify each rational expression in #11-‐17.
11. 2
3
9 xx 27−−
12. 2
2
3x 17x 206x 7x 5
− +− −
13. 2
6
x x 1x 1+ +−
14. ( ) ( ) ( ) ( )( )
4 4 3 5
2
x 6 x 3 x 3 x 63 3 x
+ − − − +
− 15.
2 2
2
x 6x 9 2x 2xx 1 x 3− + −⋅
− −
16. 2 2
2 2
4x 9 4x 12x 13x 15 2x 11x 5
− −÷− + − +
17. 2 2
2 2
7 6x x 2x 3 1 x3x 2 x 8x 7 x 2x 1+ − − −⋅ ÷
− − + − +
Answers: 1. ( )( )2x x 3 x 3− + 2. ( )( )x 8 x 4+ − 3. ( )( )( )2x 8 x 2 x 2+ − + 4. ( )( )( )3 2x 4 x 2 x 2x 4− + − +
5. ( )( )3x 2 2x 1− + 6. ( )( )5x 3 2x 5− − 7. ( )( )2x 2 x 7− − 8. ( ) ( )( )( )2x 4 x 2 x 6 x 1− − − −
9. ( ) ( )( )3 2x 1 x 2 x 2x 4+ − + + 10. ( ) ( )( )2 2 34 x 2 2x 1 3x x 1− + + + 11. ( )2
3 xx 3x 9− ++ +
12. x 42x 1−+
13. ( )( )( )2
1x 1 x 1 x x 1− + − +
14. ( ) ( )43 x 6 x 3− + − 15. ( )2x x 3x 1
−+
16. 2x 32x 1
++
17. 2x 33x 2
−−
0.2 -‐ Simplifying Expressions and Solving Equations Simplify each expression.
1. ( ) ( )2 3
5 8 3x 1 x 1 x 1
+ −− − −
2. 3x 2 2 xx 1 1 x 1 x− + −− − −
3. 2
2
x x x3 x 3 x x 9
− −+ − −
4. 3 26x x 12x 12x 1+ −+ −−
5. 2 2 3
2
x 1 x 1 x x 4x 1x 1 1 x x 1+ − + +− + − +− − −
6. 2
6 1 3 x1 3x 2x 1 x 5x 6x 1
− + +− − − −
7. 2 2
x 3 x 2 3x 5x 6 x 8x 12 x 6
+ ++ −+ + + + +
8. 2 4
2
2 11x x2 11x x
+ +
+ + 9.
2 1xx
1x 1x
−
+ + 10.
2x h 1x h2x h 1x h
+ +++ −+
11.
2
141 x716
x 1
−−
+−
Solve for real values of x -‐ give answers in exact form.
12. 2 1 3 53 5x xx − −− = 13. ( ) ( )7 4 6 3 _8x x x− − =
14. 24 9 2 0x x− + = 15. 22 3 6x x+ = Answers:
1. ( )2
35x 2x 6x 1− −−
2. 4 3. ( )( )
2xx 3 x 3+ −
4. 23x− 5. ( )( )( )( )
22x 3 x 1
x 1 x 1
+ +
+ − 6.
( )( )22x 8x 3
x 2x 1 3x 1− +− −
7. ( )( )
x 2x 6 x 2
− ++ +
8. ( )( )
22
22
x 1
x x 1
+
+ 9. x 1− 10. 3x 2h
x+ 11. x 1
4x 3++
12. 5 13. All real numbers 14. 14, 2 15. 3 3
2±
0.3 -‐ Factoring, Simplifying, Operations with Rational Expressions, Linear Equations
Factor each expression completely. 1. 72x 128x− 2. 6 310x 17x 6+ + 3. 4 24x 37x 9− + 4. ( ) ( )4 3x x 3 4 3 x− + − 5. ( ) ( ) ( ) ( )4 3 23 25x x 5 2x 1 10x x 5 2x 1− + − − + Simplify each expression.
6. ( )
3 2
4x 6x 9x3 x− +−
7. ( )
3 2
3 4
x 8 x 4x 4x 162 x
+ − +⋅−−
8. 2
2 3
6 51x x1 5x x
− +
−
9. 2
2
21x 1
x xx x 2
+−
++ −
10.
2
1 1x 2 x 3
11x 5x 6
−− −
+− +
11. 2
x 2x 2 7x2 3x 3x 2 9x 4
−+ −− + −
12. 2 2
1 2x 9 2xx 2 6 x x x 2x 3
+− −+ + − − −
Give the equation of each line described in #13-‐21. 13. through ( )2, 8 and ( )7, 1 14. through ( )0, 7 and ( )4, 6−
15. through ( )8, 2 and the origin 16. through ( )5, 6 and horizontal
17. through ( )5, 6 and vertical 18. with x-‐intercept 3 and y-‐intercept 9
19. parallel to y 5x 6= − , through ( )8, 4 20. parallel to 5x y 13− = , through ( )6, 4−
21. perpendicular to y 5x 4= − , through ( )2, 2 Answers: 1. ( )( )( )( )2 22x x 2 x 2 x 2x 4 x 2x 4− + − + + + 2. ( )( )3 35x 6 2x 1+ + 3. ( )( )( )( )x 3 x 3 2x 1 2x 1− + + −
4. ( ) ( )( )3x 3 x 4 x 1− − + 5. ( ) ( )( )32 25x x 5 2x 1 x 9x 2− + − − 6. ( )2x
x 3− 7.
( )( ) ( )
2
2 2
x 2x 4
x 2 x 4
− − +
− +
8. ( )x x 1− 9. x 2x+ 10. 2
1x 5x 7
−− +
11. x 13x 2
++
12. ( )( )
x 3x 3 x 1
+− +
13. ( )7y 1 x 75
− = − − or ( )7y 8 x 25
− = − − or 7x 5y 54+ = 14. 13y 7 x4
− = − or ( )13y 6 x 44
+ = − − or
13x 4y 28+ = 15. ( )1y 2 x 84
− = − or 1y x4
= or x 4y 0− = 16. y = 6 17. x = 5 18. y 9 3x− = − or
( )y 3 x 3= − − or 3x y 9+ = 19. ( )y 4 5 x 8− = − or 5x y 36− = 20. ( )y 4 5 x 6+ = − or 5x y 34− =
21. ( )1y 2 x 25
− = − − or x 5y 12+ =
0.3.1 -‐ Logarithm and Exponential Expressions and Equations Simplify each expression. 1. 2log 16 2. 5ln e 3. 5log 1 4. 4log 34 5. 3log 27
6. 2log510 7. ln1 8. 31log81
⎛ ⎞⎜ ⎟⎝ ⎠
9. ln 4e 10. log10
11. ln e 12. 4log 4 13. ln e 14. 3
49log 7 15. 53log 3
16. 4 4log 2 log 8+ 17. 4 4log 128 log 8− Solve each equation for x.
18. 2log 5x = 19. 93log2
x = 20. ( )log log 3 1x x+ − =
21. 3 1 15 25x x− += 22. 2 1 34 8x
x− = 23. 2 5x = Answers:
1. 4 2. 5 3. 0 4. 3 5. 32 6. 25 7. 0
8. -‐4 9. 4 10. 1 11. 1 12. 1 13. 12 14. 1
6
15. 5 16. 2 17. 2 18. 32 19. 27 20. 5 21. 3
22. 23 23. ln 5
ln 2 or 2log 5
0.3.2 -‐ Trigonometric Expressions and Equations Determine the exact value of each expression.
1. ( )sin 60° 2. cos4π⎛ ⎞
⎜ ⎟⎝ ⎠ 3. ( )sec 30° 4. tan
4π⎛ ⎞
⎜ ⎟⎝ ⎠ 5. csc
6π⎛ ⎞
⎜ ⎟⎝ ⎠
6. 3cos4π⎛ ⎞
⎜ ⎟⎝ ⎠ 7. 7tan
6π⎛ ⎞
⎜ ⎟⎝ ⎠ 8. ( )sin 3π 9. ( )sec 270° 10. sin
6π⎛ ⎞−⎜ ⎟⎝ ⎠
Find the exact value of x for 0 360x≤ ≤ ° .
11. 3cos2
x = − 12. tan 1x = 13. 3sin2
x = 14. csc 2x = −
Find the exact value of x for 0 2x≤ ≤ π .
15. 1cot3
x = − 16. 1sin2
x = − 17. cos 0x = 18. 2sec3
x = −
Use a calculator to find the value, to three decimal places, of x for 0 360x≤ ≤ ° .
19. 1sin4
x = − 20. tan 0.65x = − 21. sec 3x = 22. 3cot2
x =
Answers:
1. 32
2. 12 3. 2
3 4. 1 5. 2 6. 1
2− 7. 1
3
8. 0 9. Undefined 10. 12
− 11. 210 , 330x = ° ° 12. 45 , 225x = ° °
13. 60 , 120x = ° ° 14. 225 , 315x = ° ° 15. 2 5,3 3
x π π= 16. 7 11,6 6
x π π=
17. 3,2 2
x π π= 18. 5 7,6 6
x π π= 19. 194.478 , 345.522x = ° °
20. 146.976 , 326.976x = ° ° 21. 70.529 , 289.471x = ° ° 22. 33.690 , 213.690x = ° °