SPM Form 5 Add Maths_Chapter 03 Integration

Integration is the opposite of Differentiation where list of integration formula can be obtained here.

Students should be able to understand on getting the equation of curve from the gradient through integration and find the value of C with the use of given coordinate after watching the video below.

Another important application of integration is, to find the area and volume of the graph.

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SPM Form 5 Add Maths_Chapter 02 Linear Law

For this chapter, again, Past Year Question and examples will be used for explanation. What is important in this chapter is the formula of "Y= mX + c" where m is the gradient and c is the y-intercept.

p/s If any of the students feel that they need a more detail or further explanation on this chapter please do not hesitate to let me know .=)

Any doubts or suggestion, please do not hesitate to contact me by  leaving a comment or you can join our facebook page at "y=mx+c"

SPM Form 5 Add Maths_Chapter 01 Progressions

There are generally two types of Progressions which are Arithmetic Progression (AP) and Geometry Progression (GP).

For AP, there are two formulas which one is to find the Nth Term and the other is to find out the Sum of N terms.

"T_n = a +(n-1)d" is used to find the Nth term in a arithmetic series. For example, a series is given as shown below:

1, 3, 5, 7, 9, x, y, z,...........n

a is the first term in the series.

d is the common difference which can be find by subtraction. 

i.e 2nd term - 1st term = 3-1 = 2; 3rd term-2nd term = 5-3 = 2 and so on..

Thus, a = 1, d = 2

Students should be able to find out the value of "x", "y" & "z" immediately by adding the common difference to the number before these terms in the series.

x= 9+2 = 11; y= 11+2 = 13; z = 13+2 = 15

However, if there is a situation that required students to find the 100th term by providing the series above, it is impossible for students to add up in this way up till the 100th term, thus this is the application of the formula where students can easily find the 100th term by doing the below calculation.

T₁₀₀ =1 +(100-1)(2) = 199

"S_n = n/2 [2a+(n-1)d]" applies when students were asked to find the Sum up to nth term. For example, the sum up to 5th term,

Method without applying the formula will be: 1+3+5+7+9 = 25

Method with formula applies: S₅ = 5/2 [2(1)+(5-1)(2)] = 25

The video below shows a more complex example relating to AP and also introducing another formula relate to the 'Last' term.
S_n = n/2 [a+L]

The video below is made to enhance the understanding of students towards the whole concept of AP with the use of Past Year Question as examples.

In AP, we talk about common difference which is basically just subtraction. Now, in GP a new term known as "common ratio" is introduced. When the word "Ratio" is seen, students should now know that it involves dividing. Similar to AP, formulas are developed to find the Nth term and the Sum up to Nth term. What students should bear in mind is that:
To find a common difference: Subtraction involves~ d= 2nd term - 1st term
To find a common ratio: Division involves~ r= 2nd term/ 1st term

Infinite Sum is one of the topic include in GP which means if "n" approaches infinity, what will be the Sum?

The videos below are using Past Year Question as further examples to enhance students' understanding.

Any doubts or suggestion, please do not hesitate to contact me by  leaving a comment or you can join our facebook page at "y=mx+c"

SPM Form 4 Add Maths_Chapter 11 Index Number

There are two formulas in this chapter where students will be able to find the quantity or price at a specific time if an Index Number is given.

Formulas:
Index Number, I = Q₁/ Q₀ x 100

Q₀ = Quantity at the base time

Q₁ = Quantity at specific time

Price Index, I = P₁/ P₀ x 100

P₀ = Price of item at the base time

P₁ = Price of item at specific time

As time goes, price or value of an item might fluctuates thus Index Number is important in calculating the value of an item in a specific year, i.e future year or past year. 

Any doubts or suggestion, please do not hesitate to contact me by  leaving a comment or you can join our facebook page at "y=mx+c"

SPM Form 4 Add Maths_Chapter 10 Solution of Triangles

This chapter uses one of the past year question from Pelangi Publisher as an example for illustration. Students should know how to find the 'Length' with the use of Cosine and Sine formula and understand how to find the area of triangle with the Sine formula after watching the video below.

Students should bear in mind the formula of 'SOH', 'CAH' & 'TOA' which expresses the following:

Sin A = Opposite side/ Hypotenuse
Cos A = Adjacent side/ Hypotenuse
Tan A = Opposite side/ Adjacent side

In trigonometry, the Law of Sines (Sine Law) relates the length of the sides to the Sines of its Angle where 'a' is the length opposite to angle 'A' and etc.

a/ sin A = b/ sin B = c/ sin C

One important note is that the sum of the angle in a triangle is always 180 degree.

p/s If any of the students feel that they need a more detail or further explanation on this chapter please do not hesitate to let me know .=)

Any doubts or suggestion, please do not hesitate to contact me by  leaving a comment or you can join our facebook page at "y=mx+c"

SPM Form 4 Add Maths_Chapter 09 Differentiation

In this chapter, students should know how to apply differentiation to the given equation including second differentiation.

ie:
Given equation: y= mxⁿ +c

First differentiation: dy/dx = m(n)(x^n-1)

Second differentiation: d²y/dx²=m(n)(n-1)(x^n-2)

One thing that students should look out in this differentiation chapter is that.. There is a Product Rule and Quotient Rule that students should apply when differentiating equations that involve a product and quotient, ie. y = uv and y = u/v

Product Rule:  dy/dx = u dv/dx + v du/dx
Quotient Rule: dy/dx = [v du/dx - u dv/dx]/ (v²)

There is another section in differentiation involving the Rate of Change. Students should know that, when talking about Rate, it is about Time. Thus, Chain Rule is introduced here.

dx/dt = dx/dy x dy/dt ; where dx/dy = 1/ (dy/dx)

Approximate Small Change is the last section in this chapter, which the video below will teach 2 types of questions regarding this section.

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SPM Form 4 Add Maths_Chapter 08 Circular Measure

The videos below discuss the examples related to this chapter where students need to take note that there is some mistakes made in the first video but has been corrected in the second video. (The second video continues the example from the first video.)

p/s If any of the students feel that they need a more detail or further explanation on this chapter please do not hesitate to let me know .=)

Any doubts or suggestion, please do not hesitate to contact me by  leaving a comment or you can join our facebook page at "y=mx+c"