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Gregory

FROM QUADRATIC FACTORISATION TO QUADRATIC FACTORISATION ...

Summary of today's maths lesson (14/9/10)

For today, we recapped that:

• (a+b)² = a²+2ab+b²
• (a-b)² = a²-2ab+b²
• (a+b)(a-b)=a²-b²
• x²+y² is NOT equals to (x+y)²
• x²+y² is equal to (x+y)²-2xy

As for today, we learnt that:

• 201² -402+1 = (201)² -2(201)(1)+(1)²

= (201-1)²

= 200²

=40 000

Note: Before you start doing anything, you need to look out for the relationship between each numbers, and make sure it follows exactly as the quadratic expressions that you learn by heart. In this case, 402 is twice of 201. Since you need to make it exactly the same, there has to be a squared for the 1. Hence, you can square the 1 as the result is still the same.

• 823² -177² = (800-23)² -(800-3)² Do not do this method.

Instead, do this method:

823² -177² = (800-+177)(800-177)

because it is easier to solve. The first method is not encouraged to do as it will take up a very long time to solve.

• All the above sums are called factorisation.
• In factorisation, there are four different methods (but we only learnt two of them today) — By common factors and perfect square.

An example for the common factors method is:

b²-3bc = b(b-3c)

Note: You are actually taking out the HIGHEST common factors, which means ALL the factors must have the same common factors. NOT only one or two of the factors.

Summary of Linear Equations

• What we had learnt from today's maths lesson (for the first 3, let p & q the x-intercepts)

1. The roots of a parabola are the x-intercepts and right them in the proper way like (p,0)
2. To find the y-intercept of the parabola, the person must find the result without the x in it such as from equation (x-p)(x-q) and the result from equation without the x in it is pq so the y-intercept would be (0,pq).
3. To find the line of symmetry of the parabola, we must find the centre of the x-intercepts and the equations would be p+q/2.
4. The way to expand equations, let the integer in a bracket multiply with the equation in the other bracket. eg. (2-k)(4+k)= 2x4, 2xk= -k(8+2k)=-kx4, -kxk= 8+2k-4k-k square= 8-2k-k square
5. Equations needed to remember

• (a+b)square=a square + 2ab+ b square
• (a-b)square= a square - 2ab +b square
• (a+b)(a-b)= a square - b square

Note: (a+b) square is not equal to a square + b square

Question: There are U & n shaped parabola going upwards or downwards so is there such thing as a C shaped parabola?

If there is such thing, is it called parabola or anything else?

REMEDIAL SESSION ...

Good morning everyone,

This is to confirm that we'll be having our remedial this THURSDAY (9th SEPTEMBER) at 0930 ... we'll meet in the LEARNING OASIS ... bring loads of writing paper and your calculator ... you would also need your LEARNING DEVICE in order to download the worksheet ...

Come prepared to work ... there is some issue with the notion of GRAPHS, its GRADIENT and the ALGEBRAIC PROBLEM SOLVING ...

JASON INGHAM

Summary of Maths Lesson(27 August 2010)

-Recap on linear graphs:

 We learnt that:

• convert all equations to y = mx + c
• Visualise the gradient; increasing/decreasing
• X-intercept= -c/m
• Y-intercept is when x=o
• Do working step-by-step to prevent error and careless mistakes
• Substitute the given values of x and y values into y = mx + c if two variables are unknown.
• Gradient

 = m 

 = rise/run

• It is the CHANGE IN Y-AXIS/ CHANGE IN X-AXIS
• Look at the slope; increasing or decreasing slope.
• Expansion of Quadratic Expressions:

We learnt that:

- expand a certain term

• write in alphabetical order
• convince that (a-b)2 = (a-b)(a-b) using expansion
• answers can leave in improper fraction unless state the co-efficient of the term.
• reduce to simpler form
• decimal is also possible
• did (a+b)2, (a+b)3 , (a+b)4 and so on as practice

Pascal Triangle:

• a shortcut way of attaining answers for quadratic expansion.
• Co-efficient of the number.

Question of the day:

How do you determine that the Pascal triangle is always correct and does it always give the exact co-efficient for all expansion of quadratic expressions? Is there a particular occasion when the Pascal triangle did not meet the co-efficient needed? In what circumstances? Examples is required.

new summary-tan kein shuen

1.we discovered that if x/a + y/b, then a and b CANNOT be zero.
2.the product of two linear factors will be the y intercept of its parabola.
3.we learnt that the line of symmetry is (a+b)/2.
4.question: why must both the two lines be parallel to each other to form a parabola?