Pre-Calculus 12
Unit 4 Send-In Assignment
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UNIT 4
Exponents & Logarithms
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All answers rounded to 2 decimal places unless otherwise stated.
Version 1 2012
Page 1 of 13
Unit 4
Pre-C
Lesson Notes 1-3
Venn Diagrams
Part A: Using the word not
The negation of the statement I am going to assign homework tonight would be: I am
not going to assign homework tonight. In Math the symbols for negations are: , , ,
<, >.
Show the following on a n
Lesson Notes 2-5
Combinations
It is important to know the difference between a permutation and a combination. The
two formulae are:
nP =
r
n!
(n r)!
n
n!
Cr = =
n
r r!(n r)!
A permutation is an arrangement of a set of objects where order is important.
A
Lesson Notes 2-3
Permutations of Distinguishable Objects
The number of permutations of n different objects taken r at a time is: nPr =
n!
(n r )!
Example 1: Matt has downloaded 10 new songs from an online music store. How many
different 6-song play lists
Lesson Notes 2-4
Permutations of Identical Objects
In lesson 1, we determined the number of arrangements of objects when the objects were
all different (ie. the letters in CLARINET were conveniently different).
Now, lets take any word that has two letters
Lesson Notes 1-2
Intersection & Union of Two Sets
The set of elements that are common to two or more sets is called the intersection. In set
notation, A I B denotes the intersection of sets A and B. For example, if A = cfw_1, 2, 3
and B = cfw_3, 4, 5 then
Lesson Notes 1-1
Types of Sets & Set Notation
QuickTime and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
How could we describe or organize the provinces and territories of Canada?
A set is a collection of distinguishable objects. For
Lesson Notes 2-1
Counting Principles
Counting was fun when you were little, but sometimes there were too many items to
count. In this chapter, you will learn some short cuts to counting. In other words, youll
be counting without actually counting!
Example
Lesson Notes 1-5
Inverses & Contrapositives
A statement that is formed by negating both the hypothesis and the conclusion of a
conditional statement is called an inverse. For example, for the statement If a number is
even, then it is divisible by 2 the in
Lesson Notes 1-4
Conditional Statements
Consider the following two statements:
If Adam is texting, then he is using a cellphone.
If Adam is using a cellphone, then he is texting.
How are the these statements relate to each other? Are they both true?
A c
Lesson Notes 2-2
Factorial Notation
Factorial notation is a concise representation of the product of consecutive descending
natural numbers: n! = n(n - 1)(n 2) (3)(2)(1). For example, 4! = (4)(3)(2)(1).
Example 1: Evaluate the following.
a) 6!
13!
(b) 4!9
Lesson 1: Writing Equations for Patterns
A banquet hall has small square tables that seat 1 person on each side. The tables can be
pushed together to form longer tables. At table one there is 4 people, at two tables there
are 6 people, at three tables the
Tangent Properties
A tangent line is a line that intersects a circle at one place.
A secant line is a line that intersects a circle at exactly two places.
A. Connect the radius and point of tangency.
B. Measure the an 19.
C. How big is it? 0
If a radius m
Lesson 2: Linear Relations
For any relationship between two sets of data can be represented by using words, a table
of values, a graph and an equation. To graph points the first number is the x coordinate
and the second number is the y coordinate. Graph t
Lesson 6: Using Graphs to Estimate Values
This graph shows how the distance traveled by a car on the highway changes over a 4
hour period. To draw the graph, we plotted the distance traveled every hour, then drew a
line through the points.
We can use inte
5
Circle Properties: Perpendicular Chord Theorem
Required equipment: Ruler and protractor
A. Draw a chord.
B. Bisect the chord.
C. Draw a radius through the bisection point.
D. Measure the angle.
How big is it? 610'
E. Draw another chord and repeat the
pr
Lesson 3: Another Form of the Equation for a Linear Relation
Recall, to graph an equation we can use a table of values. Make a table of values for the
following relations and draw the resulting graph.
y = 2x + 1
y = -2x + 3
y=4x
What do you notice about t
Mafh 9 H - Lesson Notes
Solving Money Problems
Example) Amrir has 16 more nickels than dimes. If he has $2.45 in Total, how many of
each coin does he have?
lerl X; of AIMS {OX +
4M WW; 0! molds W W 80 :m
X? l atle
X14677 nickek
Example) Smrufhi has a col
Math 9 Honours Lesson Notes
Factoring a Difference of Squares
Recall:
m2 3m 28 =
I call this a nice trinomial. The leading coefficient is 1.
p2 16 =
p2 0p 16 =
This isnt a trinomial, but it can be turned
into one by inserting 0p in the middle. It
now turn
Lesson 5: Matching Equations and Graphs
Megan and Jason are having a running race. As Megan is 5 years younger than Jason she
has a 10 m head start. The graphs and equations of both Megan and Jasons race are
given below. Match each graph with its equation
Lesson 5: Introduction to Linear Inequalities
We use an inequality to model a situation that can be described by a range of numbers
instead of a single number. When one quantity is less than or equal to another quantity,
we use this symbol: < . When one q
Math 9 Honours - Lesson Notes
Solvin Rational E nations with Variables in the Denominator
Example 1),] %0)=(15) n Because n is in the denominator, its value
_20 _ is restricted.
%- [Sn
:29"? n=
ExampleZ) I( 7? 3
24K: _
7% K
Example 3) %+%=% :1};
*3 95
Math 9 Honours Lesson Notes
_ Solving Equations - More than 1 Step .»
Example 1) Solve: 3x- 14 = 10
+lq l/Ll
3x=2#
VXZ5.
The biggest thing to remember when solving an equation is to maintain equality. Whatever
is done to one side, must be done to the othe
Lesson 1: Review of Solving Equations
From last year, solving an equation means to isolate for a variable or letter. To do this we
perform the opposite mathematical operation to both sides of the equal sign.
Mathematical Operation
Addition
Opposite Operat
Math 9H Lesson Notes
Multiplying Binomials
Example 1: (x + 5)(x + 2) = x(x + 2) + 5(x + 2)
This is what is known as FOIL (first, outside, inside, last). Its the distributive property
applied twice.
Example 2: (m + 3)(m 7)
Example 3: (2y 5)(y 3)
Example 4:
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FIX[IIR XLI JSPPS[MRK RYQFIVW
i
i
[MXL ER MRXIKIV RYQIVEXSV
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Lesson 3: Adding and Subtracting Polynomials
A. Review of Like and Unlike Terms
Simplify by collecting like terms.
1. 5x2 5 + 7x 3x + 2x 3x2 + 1
2. -8x + 4x2 + 4x 2x2 + 5
B. Adding Polynomials
To add or subtract polynomials, we combine the algebra tiles t
Lesson 3: Exponent Rules
There are some special properties that can applied when the bases of exponents are the
same. Simplify the following using the properties that were learned in lesson one.
24 x 23
42 x 43
5 x 52
26
22
35
33
77
75
(22)3
(34)2
(44)3
1