Foundations & Pre-Calculus Math 10
Goal: To use trigonometry to solve problems modeled by more than one
right triangle.
Three Examples:
Ex 1: Solve for the missing side x.
Ex 2: Solve for WZX.
Ex 3: Find the height of the taller building.
A person is lyin
Foundations & Pre-Calculus Math 10
3.6 Polynomials of the form ax2 + bx +c
Factor the trinomial:
1.
4 x 2+11 x+ 6
2.
7 m+6 m 210
3.
8 p 2 1 8 p5
(where a
1
)
Foundations & Pre-Calculus Math 10
4.
187 x+ x 2
5.
12+14 g+ 6 g 2
6.
3 x +10 x+ 3
2
Foundations
Foundations & Pre-Calculus Math 10
4.3 Mixed and Entire Radicals
Extra Practice
1. Simplify each radical:
a.
99
b.
72
c.
3
72
d.
3
56
2. Write as an entire radical:
a. 2 7
b. 53 3
c. 3 11
d. 23 5
3. Arrange the following radicals from smallest to greatest
Foundations & Pre-Calculus Math 10
Use your mad Trigonometry skills to solve the following triangles:
1.
2.
3.7cm
3. Determine the perimeter of this rhombus to the nearest tenth of a centimetre.
65
Assignment: p. 111 # 4 a,c, 6 13,
math 10 FPC
Goal: To use Algebra Tiles to factor polynomials.
Use Algebra Tiles to model each polynomial. Write the factored and expanded form for each:
2
1. 2x 4 x + 2
2. 4 x 6
3. 2x 4
2
4. 4 x + 6x 4
2
5. x + 5x + 6
math 10 FPC
Now lets write out some p
Foundations & Pre-Calculus Math 10
3.3 Common Factors of a Polynomial
Remember a Factor is:
Ex. 1 Factor the binomial
_
3 g +6
Step one:
Ex. 2 Factor the binomial 8 y +16 y 2
Step two:
2
Ex. 3 Factor the trinomial
48 x + 12 x 66
Ex. 4 Factor the trinomial
3.2 Perfect Squares, Cubes
And Their Roots
Math 10 FMP
Perfect Squares are called squares because
Ex. 1 Determine the square root of 1296
Step 1: write 1296 as a product of its prime factors
Step 2: Re-order the prime factors into two identical groups (if
FMP 10
4.3 Mixed and Entire Radicals
21
4
5
3 27
2 3
Mixed Radicals are:
Entire Radicals are:
What is 43
?
Four forms
Entire
n
ab= a
n
Multiplication
Mixed
n
* b
You will need to be able to switch between Entire and Mixed forms!
1. Mixed Entire
Write 3
FMP 10
3.8 Factoring Special Polynomials!
Since there is a
number in front
2
of the x term,
we must use the
4 Step
Method to
factor.
2
Factor: 36x + 12x + 1
If the first
term and last
term are
perfect
squares, and
the middle
term is twice
the product of
t
2.1 The Tangent Ratio
Recall that the three sides of a Right Triangle have special names. They are:
Angles are important in Trigonometry. Angles are always our Starting Point.
Angle of Inclination or elevation is defined
as:
Angle of declination or depres
FMP 10
4. 4 F r ac t i o n al Ex p o n en t s an d R ad i c al s
2
4 = 16
and
Q: How do you write
16 = 4
16 = 4 as a power?
Ex 1: Evaluate each:
1
a. 81
b.
2
1
16 2
c. 27
1
3
1
d. 64
3
e. 250.5
16
f. 81
In General, the DENOMINATOR of the fraction tells us
3.1 GCF and LCM
Math10 FMP
Prime number:
Composite number:
Prime factorization:
Ex.1.
Write the prime factorization for each of the composite numbers:
a) 3
b) 6
c) 45
d) 47
The GCF stands for:
Ex 2: Find the GCF of 120 and 288.
Method 1
list all the fact
FMP 10
4.2 Number Systems
Natural numbers Whole numbers Integers Rational numbers Irrational numbers Real numbers -
To which number system do the following belong?
cfw_2, 0, 4, 53 , 5 ,
Natural:
Whole:
Integers:
Rational:
Irrational:
Real:
Q: Label the f
Foundations & Pre-Calculus Math 10
3.5 Polynomials of the Form: x2 + bx + c
Definitions:
Descending order: _
Ascending order: _
Expanding and simplify the binomial:
( x1 ) ( x 7 )
Expanding and
Factor are
opposites the
UNDO each
other!
Factor the trinomia
Trigonometry Quiz #2
Name_
For each of the following questions you must NEATLY draw a sketch of the situation
(2 marks). Then you have to label the sketch properly (OAH) (1 mark). Then you
must pick and set up the correct trig ratio (SohCahToa) (1 mark) a
Name _
Reach for the Top Trig
The Task - In this project, you will work with a partner to calculate the
height of an inaccessible object in your community. Partners MUST hand in
their own project, but you may work together. You will both play the role of
Math 10 Foundations & Pre-Calculus
3.4 Modelling Trinomials as Binomial Products
Q: How can we
multiply 14 by 13
easily?
Nowrepresent the following trinomials by creating a rectangle using
algebra tiles.
a.
b.
c.
d.
2
y
2
d
2
p
2
x
+
+
+
4y
7d
2p
3x
+
+
3
2.2 Calculating lengths using the
Tangent ratio
Review of Yesterday:
Find the measure of B.
The Second type of Trigonometry problem has
to do with solving for missing sides. Here the
given angle is our Starting Angle.
Ex 1: Find the length of JG.
3 Step P
2.4/2.5 Sine and Cosine Ratios
Recall our typical Right Triangle
From our starting angle , name the
sides.
We know that tan =
What about sine and cosine?
Sine of an Angle
Cosine of an Angle
There is one useful word that helps us remember all the Trigonome
FPC Math 10
3.7 Multiplying Polynomials.
Goal: To extend our knowledge of multiplying binomials to multiplying polynomials
Remember some definitions:
Polynomial:
Monomial:
Binomial:
Trinomial:
Remember: when multiplying powers with the same base, you add
FMP 10
4. 3 Ra d i c a l s
Product Rule for Radicals :
1. 12 x 3
2.
32=
3.
3 40
a x b= axb
Mixed and Entire Radicals
21
4
5
2 3
3 27
Mixed Radicals are:
Entire Radicals are:
You will need to be able to switch between Entire and Mixed forms!
entire mixe
1. A league cf the scccer teams has numercus games pcstpcned because ct bad weather. On
1 February. the teams are 42%, 5 s. 51%, and 2 cf the way mrcugh their scheduled games.
Which list shcws the ccmpleticn rates in crder trcm least tc greatest?
a] 215,4