SPM Form 5 Add Maths_Chapter 10 Linear Programming

In this chapter, it is important that students are able to understand the statements given in the question and able to interpret the problem. The mathematical expressions for different inequalities are as shown below:

Source: http://addmathssmkbs.files.wordpress.com/2010/12/module-20_linear-programing.pdf

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SPM Form 5 Add Maths_Chapter 09 Basic Motion along the straight line

Direction is very Important in Vector quantities:
(a) Displacement= change in position which includes both magnitude and direction
(b) Velocity = displacement/time
      V=dx/dt
(c) Acceleration= change in velocity = velocity/time;
     a= dv/dt = d/dt(dx/dt)

Direction is Not Important in Scalar quantities:
(a) Distance
(b) Speed= total distance/time which only describe how 'fast' is a particle moving without telling which direction


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SPM Form 5 Add Maths_Chapter 08 Probability Distributions

It is important for students to learn on how to read and use the standard normal distribution diagram in order to master this chapter. The video below shows a basic skill that students should have in solving these kind of questions.

Here is the second part of it which students will know how to solve the SPM type of questions.

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SPM Form 5 Add Maths_Chapter 07 Probability

Probability tells how likely of an event will happen or how likely a statement is true.
Suppose there are two events, A and B are independent to each other, the Probability will be calculated as: P(A and B) = P(A)P(B)

If the two events are dependent to each other, there are two cases as shown below:
Mutually Exclusive: P(A or B) =P(A)+ P(B)
Not Mutually Exclusive: P(A or B) = P(A) +P(B) - P(A and B)

The video below teaches students to use the tree diagram in solving the probability question besides categorizing the tree diagram for 1st time, 2nd time and the situation of "without replacement"

To enhance students understanding, the video below uses one of the famous type of probability question in Add Maths using tree diagram to solve.

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SPM Form 5 Add Maths_Chapter 06 Permutations and Combinations

In this chapter, students should know the difference between the Permutation and Combination in order to understand when to apply nPr or nCr.

Permutation is when the order is important in the arrangement.
Combination is when the order is not important in the arrangement.

The video below uses one of the famous question in SPM as an example.

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SPM Form 5 Add Maths_Chapter 05 Trigonometric Function

In this chapter, it is important for the students to learn about the shape and sketch the sin, cos and tan graph.

Sine Graph always started with a "∩" follow by a "∪"
Cos Graph always started with a "∪" follow by a "∩"

Tan Graph is a bit different with the other two graphs, however, once the concept is understood, students will find it easy.

Trigonometric does not only contain Sin Cos Tan but also the inverse of these three function, thus introducing Cot Sec and Cosec in the below video. Students will learn the basic formula in solving Paper 2 with the use of Past Year Questions as example.

The video below explains about the relationship between "pi" and "degree" besides teaching students on getting two answers from the value.

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SPM Form 5 Add Maths_Chapter 04 Vectors

Students should take note that Scalar is a quantity which only has the magnitude whereas, Vector is a mathematical object which comprises magnitude and direction.

Something EXTRA here!!!! Interesting knowledge about the relationship between hexagon and octagon with vectors.

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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 .=)

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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.

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