Median and Mean

Median is basically the middle number of a set of numbers, in either increasing or decreasing order. If there are odd number of numbers, there will only be one middle number. But if it even, you will have to take the sum of the 2 numbers and divide them by 2.

The picture shows how to find the largest possible value of x.

The other picture shows how to find the mean, which is the total date divided by the number of people.

Week 6

Completing the Square

The picture shows how to complete the square. Firstly, you have to focus on the first 2 terms(ax²+bx).

With that, you make the equation to

a²+2ab+b²

You will add a 'b²', and thus you will have to subtract a 'b²'.

The second picture shows how x²=2x. Since y=x² and y=2x, y=y, x²=2x

This picture shows how to solve the question, making the equation to ax² +bx + c=0

1. Factorise

2.Combine fractions(LCM)

3.Eliminate fractions(Multiply by denominators throughout)

Reminder:

1.When using the general formula, we must make sure that the right hand side of the equation is equal to 0, or you result will not be the correct answer.

2. Do not solve 2 equations separately, instead, combine these 2 equations together.

3. Keep improper fractions as it is a waste of time to keep switching from improper to proper fractions.

e.g. Find the sum of 3/2 and 2/4

3/2=1½

1½+ ²/₄

=3/2 + 2/4

=6/4 + 2/4

=8/4

=2

4. Keep fractions when solving the questions, or as the final answer; Decimals are confusing.

Math Recap 24-28/01/2011 Term 1

Done By: Tay Kun Yao (19) S2-05

This week, we've learnt about Quadratic Equations.

The General Formula of Quadratic

Equation is:

But first, we need to find out the value of "a, b and c".

To do so we have to rearrange the whole equation by making sure the equation is equals to 0. In other words, "3x - 1 = 6x^2 + 6x - 36" we've to deduct "3x - 1" and add "3x - 1" to the other side so that we would not change the equation. Thus, we would have an equation of "6x^2 + 3x - 35 = 0".

Therefore, we could figure out the values of "a, b and c" by using the formula:

where by a = 6, b = 3 and c = -35.

Now that we know the values of a, b and c. We can use the General Formula and solve for x by using the substituting method and get the answer of x which should look something like this:

Tips:

To check if your answer(s) is/are correct, use the substitution method.

The value of a cannot be equivalent to 0.

If "square root of [(b)^2 - 4(a)(c)]" in the General Formula is:

A POSITIVE number, there are 2 Solutions.

A NEGATIVE number, there are No Solutions.

A PERFECT SQUARE, it is factorable

Lastly, If it is ZERO, there's 1 solution.

This weeks recap (17/1/11 - 21/1/11)

This week, we learnt:

Completing the square!

As you can see, we subtracted both sides by 3, but wait. 5 does not have factors that add up/subtract to get 3! So. We have to do this equation using the "completing the square" method.

We can do this by subtracting the constant on both sides, giving you -3 in this case on the RHS. We then use the "a^2-b^b" method. Because of the 2ab part in the centre, we have to divide 5 by 2, giving us the "b" which is half of 5. BUT. To make both side equal, we have to ADD the "b" to both sides, which is 5/2 in this case. We then factorise and simplify the fractions, giving you the answer :)

(PRACTICE THIS! It is complicated BUT once you get it right, it would be easy for you :))

We can multiply a fraction by (-1)/(-1) and the fraction is still equal.

We also learnt that parabolas are always linked to quadratic equations.

One example of what we learnt:

x^2-5x=-6

(Note: Always make y=0)

x^2-5x+6=0

(Then we factorise)

(x-3)(x-2)=0

Therefore, x-3=0 OR x-2=0

Answer is x=3 OR x=2

(Note: We have to write both ORs down. Both of them are answers!)

Done by Kenneth Teh

Summary T1 W2 (10 January - 14 January)

For this week, we recapped that:

For expansion = 

a) (a+b)² = a²+2ab+b²

b) (a-b)² = a²-2ab+b²

c) (a+b)(a-b) = a²-b²

Note:
a²+b² is NOT equals to (a+b)² 
a²+b is equal to (a+b)²-2ab

For Factorization - 

c) via common factors

3a + 12 = 3(a+4)

b) via perfect square

a²+4a+4= (a)² + 2(a)(2)+(2)² = (a+2)²

a²-4a+4 = (a)² + 2(a)(-2)+(-2)²

  = (a)² - 2(a)(2)+(-2)²

   = (a-2)²

c) via trail and error

d) via grouping 

px+py+qx+qy = p(x+y) q(x+y)

For this week, we have done these examples:

Example 01:

Note: Find the Pattern - ½ - ⅓  same as 1/x - 1/x+1

Example 03:

Note: Factorize & Simplify each fraction independently 

*Take Note!

Steps for solving questions-

1. Factorize the denominator of the fraction independently
2. If there are two separate fractions, factorize each fraction it by itself 
3. Find the LCM of both the fractions 
4. Make the two fractions into one.