Advanced Placement Calculus A/B
2015-2016 Summer Assignment from Mr. Grubis @ WVHS
Expectations are one hour of homework after each class period. Students with weak
algebra skills will need to spend even more time on homework. There will be a quiz on
this summer assignment during/after the first week of school. I strongly recommend a
TI-89, TI-Spire, or TI-84 for calculus.
Expectations are one hour of homework after each class period. Students with weak
algebra skills will need to spend even more time on homework. There will be a quiz on
this summer assignment during/after the first week of school. I have provided links
to websites for Algebra review http://www.purplemath.com/index.htm
A Find the domain, range, and zeros for the 12 basic function (practice so that you can
graph the function and list the domain, range, and zeros without a calculator)
You should know how to graph all 12 functions without a calculator. (See the last page)
B Simplifying complex fractions (write as one simplified fraction)
http://www.purplemath.com/modules/compfrac.htm
1
2+x
1.
1
2+x
2.
5x
7
x -4 x-2
2
1
x
3.
1
1x
1+
4.
b -2 - x -2
b -1 + x -1
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AP Calculus A/B
2015-2016
C Writing equations of lines use the point slope form: y = m(x –x1) + y1
http://www.purplemath.com/modules/strtlneq2.htm
1. Find the equation of the line perpendicular to 2x +3y = 4 that goes through the
point (1, -3)
2. Find the equation of the line parallel to 2x + 2y = 7 through the point (3, ½)
D. Use functional notation. Help at: http://www.purplemath.com/modules/fcnnot.htm
1. f(x) = 3x + 2. Find f(7) =
f(a+1) =
f(x2) =
f(x + h) – f(x) =
Find the average rate of change of f(x)
f (3) - f (2)
=
3- 2
f (4) - f (-1)
=
4 - (-1)
2. A car travels 360 miles in a period of 180 minutes. Find the average velocity of the car
in miles per hour over this time period.
3. g(x) = x2 – 2x + 1 Find
g(2) - g(1)
=
2 -1
g(-3) - g(0)
=
-3 - 0
4. Find the composition of functions f(x) = 3x + 2 and g(x) = x2 – 2x + 1
http://www.purplemath.com/modules/fcncomp.htm
a. f(g(x)) =
b. g(f(x)) =
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AP Calculus A/B
2015-2016
E. State the domain and range of the function and find the zeros
http://www.purplemath.com/modules/fcns2.htm (domain & range)
1. f(x) = x Domain: all reals
Range: all reals
Zeros: at x = 0
2. f(x) =x2 – x – 2 Domain:
Range:
Zeros:
x2 - x - 2
Domain:
Range:
Zeros:
x +1
F Solving Trigonometric Functions (you will need to know the 6 basic functions)
Example: compute exact value for cos-1(1/2). Answer is π/3
Example: evaluate to three decimal places sin-1(0.453). Answer is approx. 0.470
Example: solve sin(x) = ½ (There are an infinite set of solutions) {π/6 +2nπ, 5π/6 +2nπ
where π is an integer}. http://www.purplemath.com/modules/basirati.htm
http://www.purplemath.com/modules/invratio.htm
More detailed Trig is at: http://math.com/homeworkhelp/Trigonometry.html
3. f(x) =
1. Compute exact values
- 2
a. cos-1(
)
2
b. tan-1(-1)
- 2
c. sin-1(
)
2
2. Evaluate to 3 decimal places or write DNE (Does not exist)
The domain of the inverse function is range of the original function
a. cos-1(0.873)
b. tan-1(2.4)
c. sin-1(-0.671)
d. sec-1(0.511)
3. Write all solutions – there will be infinite solutions – describe the pattern.
a. cos(x) = ½
b. sin(x) = -1
c. tan(x) =
- 3
3
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AP Calculus A/B
2015-2016
G. Sketch the graph of the piecewise function
http://www.purplemath.com/modules/graphing3.htm#piecewise
1. f(x) = x+1,
x≥1
-2x+4,
x< 1
Find the domain and range
and be able to graph all 12 of
these functions and their
basic transformations without
a calculator.
1.
f(x) = x
2.
f(x) = x2
Domain:
Range:
Zeros:
Domain:
3.
f(x) = x3
Domain:
Range:
Zeros:
Domain:
4.
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Range:
Zeros:
f(x) = 1/x
Range:
Zeros:
AP Calculus A/B
2015-2016
5.
f(x) = x
Domain:
Range:
6.
Zeros:
Domain:
7.
f(x) = lnx
Domain:
Range:
8.
Zeros:
Domain:
9.
f(x) = sinx
Domain:
Range:
Zeros:
Domain:
10.
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f(x) = ex
Range:
Zeros:
f(x) = cosx
Range:
Zeros:
f(x) = |x|
Range:
Zeros:
AP Calculus A/B
2015-2016
11.
f(x) = intx
This is greatest integer function
12.
Domain:
Range:
Zeros:
Domain:
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f(x) = 52 x 2
Range:
Zeros:
AP Calculus A/B
2015-2016