Lesson Notes 12-4
Investigation Normal Distribution
Collect data from around 50 students in your school for one of these categories: height,
weight, maximum hand span, length of foot, circumference of wrist.
1. Draw a histogram of the
Volume of Revolution
A solid of revolution is formed by rotating a plane figure about an axis of revolution.
First consider a rectangle perpendicular to the x-axis. Imagine rotating the rectangle 360
about the x-axis.
Draw the rotation of the
Derivatives of Trigonometric Functions
Lesson Notes 16-1
In Chapter 7 you met these properties of derivatives, where c is a constant real number.
[c ] = 0
Constant multiple rule:
[cf (x)] = cf '(x)
Sum or Difference rule:
[ f (x
Definite Integrals With Linear Motion
Lesson Notes 15-8
The displacement function tells us the distance and direction a particle is from an origin
at any time t. Recall that if displacement = s(t), then velocity = v(t) = s(t) and
acceleration = a(t) = v(t
Lesson Notes 12-5
Inverse Normal Distribution Part I
Here you need to find the value in the data that has a given cumulative probability. For
example, a company fills cartons of juice to a nominal value of 150 ml. 5% of cartons
are rejected for containing
Vector Basics Part II
Lesson Notes 13-2
Collinear points all lie in a straight line. To determine if the points are collinear, we
determine the vector joining any two of the points and repeat for two other points. If one
vector is a scalar multiple of the
Lesson Notes 15-4
Area & Definite Integrals
Investigation Area & the Definite Integral
1. Consider the area bounded by the function f(x) = x2 + 1, x = 0, x = 2, and the x-axis,
which is shaded in green in the graph.
a. i. Write down the width of each of t
Antiderivatives & Integrals
Lesson Notes 15-1
The process of integration is the opposite of differentiation. The symbol for integration
was introduced by Leibinz and it is called an integral sign.
If f(x) = x2 then f(x) =
Therefore, 2xdx =
Example 1: Dete
More on Indefinite Integrals
Lesson Notes 15-2
The power rule for integration doesnt work when n = -1 because it would result in
dividing by 0. We have seen that the derivative of lnx is x-1, so
x dx = ln x + C
Also, the derivative of ex is ex, so
Lesson Notes 13-1
Vector Basics Part I
If you travel 4 kilometers north and 3 kilometers east, how far have you traveled?
A vector is a quantity that has size (magnitude) and direction. Examples of vectors are
displacement and velocity.
A scalar is a quan