A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor

A-Level Tuition Singapore/A-Level Maths Tutition/H2 Maths Tuition/JC Maths Tuition/Maths Tutor

Hi JC Mathematics/A-level Mathematics students,

We intend to complete the A-level Mathematics syllabus by end May and in the month of June we will practise 2011 prelim questions from top 5 JCs.

Wishing you and your family a Blessed and Joyful Chinese New Year

• This reply was modified 123 days ago by  admin.
• This reply was modified 118 days ago by  admin.

A-Level Mathematics Tuition Singapore/H2 Mathematics Tuition/JC Mathematics Tuition/Mathematics Tutor

Probability : Learning outcomes

1. P(A) = (number of successes)/(number of trial)
= p
= probability of success

2. P(A or B or both)
= P(A u B)
= P(A)+P(B)-P(A n B)

3. Conditional Probability of A occuring given B has occured
= P(A/B)
= P(A n B)/P(B)

4. Two events A and B are mutually exclusive if they cannot occur simultaneously. ie P(A n B) = 0
P(A u B) = P(A) + P(B)

5. An event A is said to be independent of an event B if the progability that A occur is not affected by the occurrance of B.
P(A n B) = P(A) x P(B)
P(A/B) = P(A)
P(B/A) = P(B)

Note that point (4) and (5) are tests to check if the 2 events A and B ae mutually exclusive or independent respectively.

6. Problem Solving Techiaues in Probability

A. Sample Space Diagrams or Tables

Commonly used when the sample space is finite and all outcomes can be listed out easily. This techniques is useful for questions involving outcomes of 2 tossed dice and so on.

B. Venn Diagrams

Commonly used when questions involve sets

C. Tree Diagram

Commonly used when the problem involves one experiment repeated many times or a sequence of processess.

D. Selection (Without Replacement) and Arrangements

Commonly used when the questions have some “element” of selection and /or arrangements

P(such arrangement) = (Number of such arrangements)/( Total number of arrangements)

P(such selection) = (Number of scush selections)/(Total number of of selections)

Note that this method is NOT APPLICABLE when questions involve selections WITH REPLACEMENT AND/OR ARRANGEMENTS

E. Reduced sample space for finding conditional probabilities if the outcome can be counted.

Practise questions will be given during the lesson.

Cheers!

A Level Mathematics Tuition Singapore/H2 Maths Tuition/JC Maths Tutor

How do you do this P&C question: N85/I/3 (about the placing of 4 objects)?

i) You need to consider cases in this part of question
Case 1 : a is in the right box A and the rest wrong
Nos of ways = 1 (a in box A) x 2 (c or d in box B) x 1 (d in box C) x 1 (b in box D) = 2
Case 2 : b is in the right box B and the rest wrong
Nos of ways = 2
Case 3 : c is in the right box C and the rest wrong
Nos of ways = 2
Case 4 : d is in the right box D and the rest wrong
Nos of ways = 2
Total nos way = 8

A-Level/JC Mathematics Tuition Singapore by JC Maths Tutor

Hi Jeremy,

If possible please post the question.

Thanks

A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor

Treat z and w as a variable,
From eqn (1) make z = (1-2w)/i
Sub this into the second eqn.
let w = x+iy and conj w = x-iy
Solve the eqn as usual

From JC Maths Tutor

A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor

Hi Wei Kiat

Q8 solution

To show coefficient
C3 = (−1)(−1) + (−2)(1) + 3(4) =11
Cr = (-1)(-1)^r + (-2)(1)+3(r+1)
= (-1)^r+1 +3r + 1
C3 =11, Cr = (-1)^r+1 +3r + 1

From A-Level Tutor Singapore

How to solve for e^6=-64? (Complex Numbers)

Should it be Z^6 = 64
= 64e^2kpie
Therefore z = 2e^(kpie/3) k=0, +-1, +-2, 3

From A-level Mathematics Tuition Tutor Singapore