Honors Calculus Summer
Assignment(s) 2015
1. Complete the packet to hand in the 1st day (1/3 of a grade).
Directions below
2. Complete the following IXL assignments from the following
courses (1/3 of a grade). Please make sure you login for it to
count.
Under the Pre-Calculus section, please complete:
1.
A.5Evaluate functions
2.
A.6Add, subtract, multiply, and divide functions
3.
A.7Composition of functions
4.
B.4 Transformations of functions
5.
C.6Solve a quadratic equation by factoring
6.
E.2 Solve rational equations
7.
F.10Solve exponential equations using logarithms
8.
L.9Solve trigonometric equations
9.
N.3Trigonometric identities I
10.
N.4Trigonometric identities II
3. You will have an assessment on the 3rd day of class
based on the CONCEPTS from this packet and IXL for
(1/3 of a grade).
Directions for packet:
 Complete either on a separate piece of paper, or print this out with spaces
 Show all work (no credit otherwise)
 Neat and Organized (questions in order, and labeled) (if I cannot follow it,
you do not get credit for it)
 Persevere though the more difficult problems (you have the prior knowledge
to do so)
 Collected 1st day of class at the start of the school year.
 Looking for effort and the ability to look up material you may have
forgotten.
 It is very important that you complete this assignment by yourself.
 If you don’t practice these skills and concepts you will be at a big
disadvantage at the start of the year.
 Pace yourself (Don’t wait until the last minute). It should take you about 6
hours to complete.
 Have a great summer!
 *There is a formula page on my website for reference
 *There are notes for the first chapter on my website that may help
Mr. Ruhle’s Email: ruhlep@lincolnps.org
Website: http://home.comcast.net/~ruhlep/
Suggested Pace (with most topics identified):
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Week 1: July 9th-15th

Linear Functions

Parallel and Perpendicular Lines

Equations of conic sections (circles), tangent lines, secant

Completing the square

Absolute Value/Piecewise functions
Week 2: July 16th – 22nd

Rational Functions

Domain and Range

Inverse functions

Odd/even

Transformations of functions
Week 3: July 23rd-29th
o
Conic Section- Parabola
o
Solving higher order polynomials
o
Inverse Functions
o
Exponential Growth/Decay
o
Solving Log and base e functions
Week 4: July 30th – August 5th
o
Solving Trig Equations
o
Knowing the Unit Circle
o
Graphing Trig functions
Week 5: August 6th – 12th

o
Factoring to simplify
o
Reading graphs
o
Solving systems of equations
o
Simplifying rational expressions
o
Function notation
o
Adding and subtraction rational expressions
Week 6: August 13th – 19th
o
Transformations
o
Geometric area
o
Basic algebra
o
Rationalize
Week1:
1. Given AB with A(6, 8) and B(-2, -4), find the equation of the perpendicular bisector of AB .
Put answer in slope intercept.
2.
3. Find an equation for the line passing through the point (4, -1) and
perpendicular to the line 2x – 3y = 3.
4. Find the equation of the secant line: if (a, f(a)) => (1,2) and (b, f(b)) => (2,1)
This video may help
https://youtu.be/wLtBPvMv6kw
5.
6. Convert the function
f ( x)  5 x  4
to a piecewise function.
7. Graph the piecewise function. Draw a graph of the function.
8.
a) Find f(3)
b) Find f(-4)
c) Find f(0)
(No calculator)
9. Write the equation of the piecewise function below.
Week2
2 x2  x  2
10. Given the function f ( x) 
x2  4
(No Calculator)
a) Write the equation of the horizontal asymptote.
b) Write the equation of any vertical asymptotes.
c) Find the x and y coordinate of any holes.
d) Find the x and y-intercepts
e) Find the domain.
11. Find the domain of the following functions without a calculator.
a) f ( x)   x 2  6 x  4
b) f ( x)   3  x  5
c) f ( x)   log 2 ( x  4)  1
d) f ( x)  tan x on [0,2pi]
4 x 1
e) f ( x)  e
f) f ( x)  csc x on [0,2pi]
12. Is the function f ( x ) 
13. solve: ( no calculator)
14. Solve the equation
x
even, odd or neither. Show all work to prove.
x 5
2
2x  32  4 x( x  3)  0
2log 2 ( x  3)  log 2 ( x  1)  3
(No Calc)
15. Solve the equation 2e2 x 1  6  10 . Find the exact answer (no calculator)
16. Solve the equation for y. ln( y  1)  ln 2  x  ln x
17. No calc: Mult. Choice.
Week 4:
18. Unit Circle Values: (no calc, and try to do at a good pace)
a) sin
3
2
e) tan 
i) sec
3
4
7
4

3
c) tan 4  tan 4
7
6
g) csc
b) cos
f) sec
j) cot
11
3
5
3
k)
d) tan
h) cot
sin
3
2
5
5
 cos
3
6
19. Solve the following trig equations over the given domain (no calculator)
a)
1
 sin x  0 on 0, 2 
2
b)
c) sin x  cos x on 0, 2 
d) sin(2x) = cosx on 0, 2 
e) 2 – 2sin2x = -5cosx –2 on 0, 2 
f)
3
 cos x  0 on (0,2 )
2
g)
2 cos x  sin 2 x  0 on [0,2 ]
5
6
20. No Calc: Mult. Choice
Week 5:
21. Factor and simplify the following
a) 3x  1 ( x  2) 4  4( x  1)3 ( x  2)3
2
2
2
3
c) 3( x  2) ( x  3)  ( x  2) (2)( x  3)
( x  3) 4
b) 2 x  1( x  1) 2  2( x  1) 2 ( x  1) 3
d)
3( x  2) 2  6 x( x  2)
x2
22. Solve the equation:
23. Multiple Choice
24. multiple choice
25.
 2 x  4  3  5  11
2
(no calculator)
Week 6:
26.
27. Multiple Choice.
28. Multiple Choice
29. (use your calculator)
30.
a)
b)
c)
d)
e)