Y=mx+c: September 2013

Sunday, 29 September 2013

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"

Saturday, 28 September 2013

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"

Wednesday, 25 September 2013

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/ Q₀x 100

Q₀= Quantity at the base time

Q₁= Quantity at specific time

Price Index, I = P₁/ P₀x 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.

Monday, 23 September 2013

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.

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"

Friday, 20 September 2013

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.)

Wednesday, 18 September 2013

SPM Form 4 Add Maths_Chapter 07 Statistics

For the Statistic Chapter, students should understand and able to find out the "Mode", "Mean", "Median", "Variances" and "Standard Deviation" from a group data for both Paper 1 and Paper 2.

Students should understand about the formula of Median used in this chapter. The video below includes explanation of L, N, F, Fm and C in the formula.

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 06 Coordinate Geometry

Students should know how to find "Area", solving "Perpendicular" question by equations and also to find coordinate for ratio & y-intercept and the distance between 2 coordinate.

To fully enhance the students' understanding, the video below includes 5 different types of Past Year Question of Paper 1 related to this chapter.

As for Paper 2, there are 3 similar type of Past Year Questions included in the video below which also provides a step by step guidance and explanation.

"Locus" is one of the section included in this chapter which is important for students to fully understand it. The video below thus explains almost everything regarding to Locus with examples given.

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"

Monday, 16 September 2013

SPM Form 4 Add Maths_Chapter 05 Indices and Logarithms

It is very important for students to understand about the section of Indices first before going into detail to Logarithms. The video below therefore discuss about the basic law of indices besides provide a few examples from Past year Question in order to enhance the understanding of students.

Students should memorize and understand about the Law of Indices
Rule 1: a⁰ = 1

Rule 2: a^-m = 1/a^m

Rule 3: a^m x aⁿ = a^m+n

Rule 4: a^m÷ aⁿ = a^m-n
Rule 5: (a^m)ⁿ = a^mn

Rule 6: a^m/n = ⁿ√a^m =(ⁿ√a)^m

The video below teaches all the basic about logarithms where students will learn the important skills in solving this type of questions. A lot of examples are used in this video to ensure students fully understand about the fundamentals.

Similar to Indices, students should bear in mind about the Laws of Logarithms.

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 04 Simultaneous Equations

The video below uses SPM Add Maths, Paper 2 of Year 2012 to discuss on Simultaneous Equation, Quadratic Equation and Differentiation.

p/s Past Year Question is used to discuss this chapter, 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"

Friday, 13 September 2013

SPM Form 4 Add Maths_Chapter 03 Quadratic Functions

In this chapter, students should know how to determine the maximum point or minimum point by using the completing square method. Students should bear in mind that the general formula for completing square is "f(x) = a(x+p)² +q".

To determine the maximum and minimum point, students should derive the given equation into the general formula [f(x) = a(x+p)² +q]. When "a" is a positive value (aka "a >0"), the obtained graph "smile" such as "∪", thus is a minimum point. Whereas, when "a" is a negative value (aka "a<0"), the obtained graph will be a sad face such as "∩", thus students will get a maximum point.

The video below shows 2 Past Year Questions on Quadratic Functions. Students will have a clearer understanding in applying the general formula.

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"

Tuesday, 10 September 2013

SPM Form 4 Add Maths_Chapter 02 Quadratic Equations

The basic of this chapter is that students should understand about the Sum of Root (SOR) and Product of Root (POR) and know how to apply them in real case. The video below also brings out some of the common mistakes of students while solving questions involve this chapter.

One of the questions which is commonly come out in the Past Year Question is to ask students to form a new quadratic equation with the given roots as shown in the example in the video below. Students should bear in mind the equation of "x² –(SOR)x+(POR) =0" in which this formula is useful in solving a lot of questions involving quadratic equation. To avoid confusion, take α & β to represents the new root.

In order to enhance the understanding of students, the below video shows another 3 useful examples where students will get to learn about the difference between "two distinct (different) roots", "two equal roots" and "no roots (aka no intersect)". Students will then get to know when to use "b²- 4ac =0", "b²- 4ac >0" and "b²- 4ac <0".

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"

Sunday, 8 September 2013

SPM Form 4 Add Maths_Chapter 01 Functions

Students should know how to read the diagram and graph of the function including differentiating the different types of relation. The video below will explain about the basics including domain, co-domain, range, notation and etc.

The video below provides a simplest method for students to solve the questions involving composite function and inverse function.

There is another method in solving the composite function. Here is another one which is usually mention on the text book where some of the students may find it confusing. Examples are used in order to enhance the understanding of students.

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"

Monday, 2 September 2013

Complete List of Videos in "MsiaFreeEducation" Youtube Channel_ADD MATHS

SPM Mathematics Past Year Questions (by Chapter)

Form 4

Chapter 05 The Straight Lines
Paper 2

Chapter 07 Probability I

Form 5

Chapter 02 Graph Functions II

Chapter 09 Earth as a Sphere
Paper 2

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"

Sunday, 1 September 2013

SPM Form 5 Mathematics_Chapter 10 Planes and Elevations

In this chapter, students should know how to draw the planes of the combine solid. The video includes a full demo with some useful tips and explanation.

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 Mathematics_Chapter 09 Earth as a Sphere

Students should be able to know how to find the longitude and latitude of the earth, also understand the meaning and function of Greenwich Meridian and Equation after watching the video.

In the subsection "Distance of Earth", students should know how to find the distance of the earth and understand the difference between longitude and latitude distance in the earth. On the other hand, students should be able to apply the formula in calculating distance as shown in the video.

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 Mathematics_Chapter 08 Bearing

Students should bear in mind that bearing is an angle, which is measured in a clockwise direction from the North. In the video below, students will be able to learn all the basics in solving the bearing questions. In addition, 5 different past year questions are used as examples in order to enhance the understanding of students.

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 Mathematics_Chapter 07 Probability II

For easier understanding, Past Year Question is used to discuss on how to list out all the possible outcome and to find the probability with the use of number of event and number of sample.

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 Mathematics_Chapter 06 Gradient and Area under Graph

1. Speed-Time Graph
Students should understand about the uniform speed, rate of change of speed and average speed of the graph in this chapter. Two SPM past year questions are used in order to enhance the understanding of students.

2. Distance-Time Graph

The video below discuss a simple example of a distance time graph to give students a basic understanding on this question.

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 Mathematics_Chapter 05 Variations

In this chapter, students should first understand the relation between "a" and "b" in order to solve the question. The video below explains about the basic concept of variation and teaches how to find the constant value k with the use of past year example.

Another video here showing an example to help refresh students' memory =)

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 Mathematics_Chapter 04 Matrices

Matrices is one important chapter as it comes out in both Paper 1 and Paper 2 and therefore, this chapter is divided into two videos in which the first one explains all the basic skill of Matrices and students will be able to solve most of the questions in Paper 1 which involve matrices.

The second video here in this post (the video below) is about the meaning and function of the identity matrix, as well as inverse matrix. Students will have more understanding and will be able to solve the Matrices questions in SPM Maths Paper 2

Now, here is something extra. A short video about Inverse Matrices to refresh Students' mind in how to use the formula of Inverse Matrices.

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"