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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?

Summary of Math Lesson (24/08/10)

1. With the given values in the questions (values of m, x, y and c), we can substitute to find out the part of the equation that we do not know.

2. Substitution is NOT the y intercept. The values of x and y given is a coordinate that lies on the line.

3. x/a + y/b=1. a is the y intercept, while b is the y intercept. Why?

when a=x intercept, y=0.

=x/a + 0/b=1

=1+0

=1

4. Parabola consists of 2 root/x-intercepts.

5. If 2 lines share the same x intercept as the parabola, with substitution of the equation, it causes one of the equation of the parabola to be 0, thus y=0 regardless of the 2nd equation

6. We only did one type of parabola today: We can only tell the min value and not the max.

7. Why is x/a + 0/b always 1? (Point 3)

8. Is it possible for the parabola to have not two equations, but one?

Yan Jin

Summary for the lesson (19/08/10)

Sorry that i posted at this late hour..... Just came back from YOG....
1) If (a,b) lies at y=mx+c, then b=m(a)+c
2) Gradient is = rise divided by run = change in y coordinate divided by change in the x coordinate.
THE ORDER IS IMPORTANT
3) y - 1x +c (Coordinates 1,5 and -3,1)
To find c, you have to find x. It can go two ways;
Either you substitute the coordinates (1,5) and get
5=1(1)+c
  =1+c
c = 4#
OR
1 = 1(-3)+c
   = -3+c
.: c = 4
4) To satisfy an equation means to balance both sides of an equation.

Summary of Linear Equations

Casandra Ong- 18Aug

1) Discuss if there is an equation, when c is not the y intercept.
2) At y-intercept, x is 0
3) c is not always the intercept. For example, y= 1÷x + c. Therefore, the value of y is undefined when x=0 and c would not be the y- intercept.
4) x= -c÷m
5) m= gradient
= (change in y-coordinate) ÷ (change in x-coordinate)

SUMMARY OF LINEAR EQUATIONS ...

ANONYMOUS - 17th August 2010

1. Today we reconsidered the linear equation & the general form of a linear equation is y = mx + c
2. where by the m refers to the GRADIENT
3. where c is the Y-INTERCEPT (or the value of y when x = 0)
4. m is POSITIVE when as x increases, y also increases
5. m is NEGATIVE when as x increases, y will decrease
6. m is ZERO when as x changes, y is constant (HORIZONTAL LINE)
7. m is undefined when x is constant and y changes (VERTICAL LINE)
8. X-INTERCEPT would be equal to -c / m ... (or the value of x when y = 0)

NOTE - c (or the constant in all the equation) is always the y-intercept, even for equations such as y = ax^2 + bx + c ...

Why do you think this is so? (HINT - look at point (3) above)

Prove point (8) for yourself ...

Question 1 by Iskandar B Dzulkarnain

A square has all of its sides equal, thus it is a rhombus. A rhombus, on the other hand, DOES NOT have perpendicular lines, hence, it is NOT a square.

Question 4 by Iskandar b Dzulkarnain

This square here, as indicated at BCD, has a 90º angle which is one of the characteristics of a square. But a parallelogram on the other hand, does not have any perpendicular lines, thus, it is not a square.

Question 5 by Iskandar B Dzulkarnain

ABCD, as it is a parallelogram, it will have all sides equal to the opposite's. Taking over from ABCD, BFDE will also have this characteristics thus proving that it is a parallelogram.

Question 5 by Niloy Faiyaz

It is a parallelogram since each side is parallel to the opposite side.

Question 4 by Niloy Faiyaz

I do not agree with the statement since for squares, its a must for every corner to have a 90 degree angle while a parallelogram can have any degree.

Question 2 by Niloy Faiyaz

The answer is D, all of the above.

The reason is that:

(a) a square and a parallelogram are quadrilaterals since they all have 4 sides.

(b) The opposite sides are parallel since they are facing the same direction.

(c) The trapezoid has one pair of parallel lines since one pair faces in different directions while the other pair faces at the same side.

so all are true.

Question 1,4,5

Question 1:

A square is a rombus as it has four equal lines,which two of them are parallel to each other but a rombus is not a square as the lines should be perpendicular to each other.

Question 4:

i disagree with the statement,as a parallelogram  does not have its sides perpendicular to each other.

Question 5:

Since E and F are midpoints,BF and ED should have the same distance,so BFDE should be a parallelogram.

 

Questions 1, 4 and 5 by Gavin Lim

5)If both e and f are midpoints, there is the same distance from AE and FC so BE and FD are parallel, which makes BEFD a parallelogram.

4)No. The sides of a square must all be perpendicular to each other while the sides of a parallelogram may not be perpendicular.

1) A square is a rhombus as it has 2 pairs of parallel lines of equal length but a rhombus is not a square as the sides of a square must all be perpendicular to each other while the sides of a rohmbus may not be perpendicular.

Problem with posts below

The images bay not be seen in my post below, as if i sent the text version, all my images would have ended up in the wrong question. Just try reloading, and it should work soon

Thanks,

Azeem Arshad Vasanwala
(Class S1 - 03)
School of Science and Technology, Singapore