Lesson 15-7
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.
Constant rule:
d
[c ] = 0
dx
Constant multiple rule:
d
[cf (x)] = cf '(x)
dx
Sum or Difference rule:
d
[ 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
Lesson Notes 12-4
Normal Distribution
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
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
1
x dx = ln x + C
Also, the derivative of ex is ex, so
e d
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
Lesson Notes 8-5
The Cosine Rule
We found the sine rule useful when
there was not a 90 angle, and
we knew one angle and its opposite side
Now, we will find the cosine rule useful when:
there is not a 90 angle, and
either
a) we know all three sides and
Lesson Notes 9-3
Trigonometric Identities
Identities are special kinds of equations that are true for ALL values of x. You are
already familiar with two identities:
sin2 + cos2 = 1
tan =
There are also some double-angle identities:
cos(2) = 1 2sin2
= 2cos
Lesson Notes 9-2
Solving Equations Using the Unit Circle
To solve for angles given their sine, cosine, or tangent values:
Step 1: Determine which quadrants the solution(s) will be in by looking at the
sign (+ or -) of the given ratio.
Step 2: Solve for th
Lesson Notes 8-4
The Sine Rule
Determine h in the following triangle
The Sine Rule
sin A sin B sinC
=
=
a
b
c
a
b
c
=
=
sin A sin B sinC
Example 1: Determine b.
C
A
B
D
b
13m
71
A
29
17m
B
Example 2: Determine angle A.
4)
C
8m
11 m
45
A
B
Example 3: A shi
Lesson Notes 8-7
Radians, Arcs, and Sectors
Angles can be measured in radians instead of degrees. One radian is defined as the size
of the central angle subtended by an arc which is the same length as the radius of the
circle.
Two radians is the size of t
Lesson Notes 8-1
Right-Angled Triangle Trigonometry
Angles can be described in various ways. The following triangle could be called ABC
and the angle at A could be called A, BAC, CAB, BAC, or CAB. Angles can also be
labeled with Greek letters like (theta)
Lesson Notes 8-2
Applications of Right-Angled Trigonometry
In this lesson, you will see how to apply these trigonometric ratios to solve problems in
real-life situations. Lets begin with some terminology
The angle of elevation is
The angle of depression i
Lesson Notes 8-3
Using the Coordinate Axes in Trigonometry
The angle in a Cartesian coordinate system has its vertex at the origin, as shown in the
diagram. A positive angle is measured anticlockwise from the x-axis.
The following diagram shows a circle w
Lesson Notes 9-1
Using the Unit Circle
On a Cartesian plane, you can generate an angle by rotating a ray about the origin. The
starting position of the ray, along the positive x-axis, is the initial arm of the angle. The
final position, after a rotation a
Pascals Triangle & the Binomial Expansion
Lesson Notes 7-9
Now we will look at a famous mathematical pattern know as Pascals triangles.
1
1
1
1
1
1
2
3
4
1
3
6
1
4
1
These numbers can also be found using combinations, or the nCr function on the GDC.
4C0
=