1a)
2
a)
b)
b)
d)
e)
c) 3a)
b)
c)
4a)b)
c)
5)6)
6b)
7a)
b)
xy-20.062510.25011426
Thisisgrowth
xy-216140110.2520.06
25
ThisisDecay
Similarities:
NoXintercept
Horizontalasymptotey=0
yinterceptisx=0
NoMinorMaxpoints
Domainisrealnumbers
Rangeisrealnumbersove
MCR3U-C
3
UNIT
Trigonometric Functions
Copyright 2012 The Ontario Educational Communications Authority. All rights reserved. No part
of these materials may be reproduced, in whole or in part, in any form or by any means, electronic
or mechanical, includin
MCR3U-C
13
Lesson
Periodic and Trigonometric Functions
Lesson 13
Functions MCR3U-C
Introduction
Imagine you are sailing with the explorer John Cabot in the year 1497. You are about to become
one of the first explorers to sail to North America from Europe.
There are two special triangles, which are both right-angled triangles.
The first includes two 45 angles, and the second includes a 30 and a
60 angle. The three angles (30, 45, and 60), and a combination of
these angles, are frequently used in trigonometr
This is to compare
exponential and
logarithmic function
y=log 3 (4 )=
log (4 ) not exist
=
=undefined
log 3
0.4771
A parent function is the simplest form that an
equation can take, before any transformations
have been applied.
As you can see, when the val
Typing your assignment
When you type your assignment, it is important to keep in mind that your teacher will be
marking your work based on communication and presentation, as well as correct
answers. Later, in the Assessments of Learning, where your assign
Komal Patel
ILC no: -16295012
MHF4UC
Unit 1
Task 1: Knowledge/Understanding Questions
1.
Expand and simplify the following powers. Give all of the answers in terms
of positive exponents. Make sure that you type your solutions using Equation
Editor in MS W
Komal Patel
ILC no: -16295012
MHF4UC
Unit 2
Task 1: Knowledge/Understanding Questions
1.
Simplify each of the following expressions. Express all answers in terms of positive
exponents. (10 marks)
4a
9 a
a) ( 5)
( 3)
36 a(3 +5)
36 a8
9 x 3 y 8 z 17
b)
3 x
Alissia Castelo
Lesson 5: Exponential and logarithmic equations
Task 1
3
5
1. a) (4 a )(9 a )
(36 a3+5 )
36 a8
b)
9 x 3 y 8 z 17
3 x 5 y 5 z10
2
3 x
3
y z
7
8 3
c)
7 k
(7 k 8 ) (7 k 8 ) (7 k 8 )
21 k
d)
24
2 a3 b6 5
3 a 4 b4 2
5
15
30
2 a b
( 32 ) a 8 b
7.1 Lesson Handout
sin
sin
6
cos
cos
3
sin
cos
2
9
sin
5
18
cos
4
9
cos
7
18
sin
7
18
sin
4
9
5
18
sin
2
9
cos
sin
6
cos
2
3
cos
cos
18
7
9
cos
7
18
sin
8
9
cos
cos
cos
sin
cos
17
18
5
18
sin
5
6
sin
9
9
3
4
9
sin
cos
6
sin
sin
18
3
2
9
13
18
Conje
2.3
Various Forms of Exponential
Functions
SETTING THE STAGE
Now you have seen several examples of exponential growth. In grade 11, you
used exponential growth formulas to describe compound interest, growth of
bacterial populations, and geometric sequence
1 .3 Creating New Polynomial
III-0.
to Composition
SETTING THE STAGE
Functions: An Introduction
Can you combine polynomial functions using the basic mathematical
operations? If so, what is the result?
Rhona is a licensed plumber and Bill is an apprentice
7.6 Homework
Knowledge
1. Prove the following identities:
(a) tan x cos x = sin x
(b) cos x sec x = 1
(c) (tan x)/(sec x) = sin x
2. Prove the identity:
(a) sin2x(cot x + 1)2 = cos2x(tan x + 1)2
(b) sin2x tan2x = -sin2xtan2x
(c) (cos2x 1)(tan2x + 1) = -ta
6.5 Homework
Knowledge
Find each function value:
1.
csc , if
2
4
2.
cos , if sec = 2.5
3.
sin , if csc = 3
4.
sin , if csc = 15
5.
sec , if cos =
6.
sec , if cos =
7.
csc , if sin =
8.
cos , if sec =
9.
sin , if csc
10.
sin =
1
7
11
6
3
=
3
sec , if cos
5
NUMB3RS Activity
Student Page 1
Episode: Counterfeit Reality
Name: _
Date: _
NUMB3RS Activity: Lets Add Some Trig
When Charlie explains how to crack a counterfeiting ring, he talks about the intricate
engraving used in banknotes, called guilloche (pronoun
Asymptotes
Rational Functions, h ( x ) =
f( x)
g( x )
, have asymptotes which may be vertical, horizontal,
oblique, or curved.
Horizontal Asymptote
Horizontal asymptotes occur if the degree of f ( x ) degree of g ( x ) .
Ex: h ( x ) =
2 x 2 +1
x2 +2
y
Pro
1. Graph the composite trigonometric curve y = x2/10 sin x
Answer
First, we draw the two curves y = x2/10 and y = -sin x on the same set of axes. We
recognise y = x2/10 as a parabola, that we met before.
The sum of the two curves is shown:
Expanding the d
MPM1D-A
Lesson
10
Converting Among Representations
Copyright 2012 The Ontario Educational Communications Authority. All rights reserved. No part of these
materials may be reproduced, in whole or in part, in any form or by any means, electronic or mechanic
MPM1D-A
4
UNIT
Measurement and
Geometry
Copyright 2012 The Ontario Educational Communications Authority. All rights reserved. No part of these
materials may be reproduced, in whole or in part, in any form or by any means, electronic or mechanical,
includi
MPM1D-A
Lesson
19
Optimization and Measurement
Copyright 2012 The Ontario Educational Communications Authority. All rights reserved. No part of these
materials may be reproduced, in whole or in part, in any form or by any means, electronic or mechanical,
MPM1D-A
5
Lesson
Manipulating Formulas
Copyright 2012 The Ontario Educational Communications Authority. All rights reserved. No part of these
materials may be reproduced, in whole or in part, in any form or by any means, electronic or mechanical,
includin
MPM1D-A
Lesson
3
Simplifying Algebraic Equations
Copyright 2012 The Ontario Educational Communications Authority. All rights reserved. No part of these
materials may be reproduced, in whole or in part, in any form or by any means, electronic or mechanical
MPM1D-A
18
Lesson
Volume and Surface Area of
Cones and Spheres
Copyright 2012 The Ontario Educational Communications Authority. All rights reserved. No part of these
materials may be reproduced, in whole or in part, in any form or by any means, electronic
MPM1D-A
Lesson
2
More Algebra and Exponent Rules
Copyright 2012 The Ontario Educational Communications Authority. All rights reserved. No part of these
materials may be reproduced, in whole or in part, in any form or by any means, electronic or mechanical