Quiz on March 9th (10%)

A quiz will be posted on the blogs and the first person that answer my question correct will be required to put a similar question up for another person to answer. If you did not get 5 question scorrect on the blog, you are not allowed to sit the quiz in the classroom on March 9th.

Visualizing the scene

In 3-dimensional scene, one must be able to formulate the scene then draw.
Step 1 Use pens, pencils, rulers, etc
Step 2 Then draw

Formulate, draw then solve the following scenes:

1. A man standing on the beach looks up to the top of the cliff with an angle of elevation of 65 degrees. Ignoring his height and assuming he is standing on level ground with the base of the cliff and he is 15 metres from the base of the cliff, determine the height of the cliff.
2. From the question above, if the man walk 5 metres closer to the cliff and looks up to the top of the cliff, what will his angle of elevation be?
3. A man standing on the beach looks up to the top of the cliff with an angle of elevation of 70 degrees. Ignoring his height and assuming he is standing on level ground with the base of the cliff and he is 20 metres from the base of the cliff, determine the height of the cliff. A lady on the beach look up to the top of the same cliff with an angle of elevation of 40 degrees. Ignoring her height, determine the distance she stands from the base of the cliff.

Trigs

Trigs is based on ratios of line from a right angle triangle.

Draw the following

sin x = 3/5

cos m = 4/7

tan m = 3/ 4

sin m = 3 / 8

cos x = 5 / 8

tan x = 5 / 7

For each find all the angles and all the lengths

Expansion

From factorisation you can get back the original by expansion

Recall what is a term. A term is separated by + or - or =
A term consists of parts.
A book is on ething and consist of parts, toc, chapters, cover, pages, etc
Similarily, a term consists of parts, eg

2 + 3mn + 6twb -12 def + 1/2 mb = 120

This equation consists of 6 terms

• 2 is a number term and is a 1 part
• 3mn is a mn term and consists of 3 parts, a number, a m and a n
• 6twb is a twb term and consists of 4 terms, a number, a t, a w and a b
• 12def is a def term and consists of 4 parts, a number, a d, a e and a f
• 1/2 mb is a mb term and consists of 3 parts, anumber, a m and a b
• 120 is a number and is a 1 part

Identify how many terms are present in the equation, what are the trem, and what are the parts.

1. 12 mn + 3mds
2. 2m^2 + m
3. 6mn - 3mpd + 2 m^2
4. 20 m^2 - m
5. 6mnt - 3mn

For each of the above look for any common part in all the term.

This will go outside the bracket ( ) and inside the bracket put what reamins in each term

The y-intercept

What is the y-intercept?
What really does the y-intercept mean?

From the general equation of a straight line, the y-intercept is c.
Why is this true?

What is the y-intercept's of the following

1. y = 6x + 3
2. y = -12x + 5
3. y = 2x - 6
4. 2y = 5x + 3
5. 3y = - 4x + 1
6. 2y + x = 7
7. 3y + 5x = 11
8. 2y - 4x = 7
9. 4y + 3x + 2 = 0
10. 2y -3x + 5 = 0

Straight line

What is a straight line?
What does a straight line of distance against time mean?
What does a straight line of velocity against time mean?

A general equation for a straight line is
y = mx + c
Does all straight lines have to be written in this form?

From a straight line equation, the gradient is one of the most important thing
to determine. Explain how the gradient is determine form the following lines.

1. y = 6x + 3
2. y = -12x + 5
3. y = 2x - 6
4. 2y = 5x + 3
5. 3y = - 4x + 1
6. 2y + x = 7
7. 3y + 5x = 11
8. 2y - 4x = 7
9. 4y + 3x + 2 = 0
10. 2y -3x + 5 = 0

Graph

What is a graph?
Why are graphs necessary?
Give examples in real life where graphs are critical.
How are graphs used in these examples?

Factorisation Exercise

1) y^2 - 10y + 24 11) 3x^2 + 19x + 6
2) m^2 + 11m + 24 12) 6x^2 - 5x -4
3) x^2 + 7x + 12 13) 2x^2 + 5x -7
4) x^2 + 7x + 10 14) 5x^2 - x - 6
5) x^2 -3x -10 15) 12x^2 + 7x + 1
6) x^2 - 6x + 8 16) 3x^2 + 17x -6
7) 6x^2 + 7x + 2 17) 8x^2 + 6x + 1
8) 8x^2 - 6x + 1 18) 2x^2 + x - 15
9) 2x^2 + 11x + 5 19) 4x^2 + 23x + 15
10) 7x^2 - 6x - 1 20) 2x^2 -7x -4

Recall the approach ax^2 + bx + c ( ) ( )
3x^2 -10x - 8
Step 1 Multiply a by c ac 3 x -8 = -24
Step 2 Write all combinations to get ac __ x __ -1 x 24 1 x -24
-2 x 12 2 x -12
-3 x 8 3 x -8
-4 x 6 4 x -6
Step 3 For each in step2, add the number to get b (-10) 23 -23
10 -10 got it
Step 4 Rewrite question using the two terms for middle term
3x^2 + 2x - 12x - 8
Step 5 Factorize
3x^2 + 2x -12x - 8
x(3x + 2) - 4 (3x + 2)
(3x + 2) (x - 4)

Factorization of expression

An expression consists of terms, knotted terms and + or -.
A term consists of parts
eg 5mt consists of 3 parts, number, m and t and this term is called an mt term
235 consist of 1 part, a number and is called a number term
17bdcf consists of 5 parts, number, b, d, c, f and is called a bdcf term
A knotted term consists of bracket and it has to be untangled, expand to remove bracket

Factorization is taking out all common part in all terms

Factorise the following:

1) 4pm + 5md + 6mdp
2) 4mhd + 8mhdw

Factorisation versus expansion

What is factorisation?
What good is factorisation?
How can factorisation be demonstarted in the real world?

What is expansion?
What good is expansion?
How can expansion be demonstarted in the real world?

What is the use of ( )

What is ( )?
Why is ( ) necessary or what does it signify?
Show by example different uses of ( ).

Equation versus expression

What really is an expression?
Why are expression necessary?
What is an equation?
What is the difference between an equation and an expression?
Give an example in life where an expression is absolutely necessary.
Give an example in life where an equation is absolutely necessary.

An unknown number

Why are things unknown in our life?
Is there any quantity in your life that the quantity is unknown?
Are variables necessary in life?

What is a number

Why is numbers important?
Explain from life how number can be used to increase, decrease, group, share and compare.
What is a fraction?
How will the world be if it had no fractions?
How will the world be if it had no whole numbers?
How will the world be if it had no negative numbers?