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

Home Forums A Level Tuition, O Level Tuition @ Kovan / Hougang A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor

This topic contains 132 replies, has 11 voices, and was last updated by  admin 2 years, 2 months ago.

Viewing 15 posts - 106 through 120 (of 133 total)
  • Author
    Posts
  • #3803

    admin
    Member

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

    Hi A-Level/H2 Math Students

    Binomial Expansion

    (1+x)^n = 1 + nx + [n(n-1)]/2!(x^2) + [n(n-1)(n-2)]/3!(x^3)……

    This formula is good to memorise as it very useful for all value of x.

    Note:
    1. n is a negative or rational number (not positive integer). For such n, the expansion must be of the form (1+x )^n
    2. The expansion has an infinite number of terms.
    3. The condition lxl < 1 is very important. This ensures that the expansion is valid.

    Binomial Expansion has two cases

    Case 1: Expansion in terms of ascending powers of x.

    Case 2: Expansion in terms of descending powers of x.

    Please contact Mr Ong @9863 9633 for more detail on Binomial Expansion

    #3861

    admin
    Member

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

    Hi A-Level/H2 Math Students

    Arithmetic Progression

    Definition

    An arithmetic progression (A.P.) is a sequence of numbers in which each term other than the first term is obtained from the preceding one by the addition of a constant number called the common difference.

    Therefore, if we let a be the first term and d be the common
    difference of the sequence, then the sequence is an A.P. of the form

    a, a + d, a + 2d, a + 3d, ……

    general nth term = Un = a + ( n – 1)d

    Sum of AP

    Sn = (n/2)[2a+(n-1)d]

    Sn = (n/2){First term + last term)

    Please contact Mr Ong @9863 9633 for more detail on Arithmetic Progression

    #3997

    admin
    Member

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

    Hi A-Level/H2 Math Students

    Geometric Progression

    A geometric progression is a sequence such that the ratio between every pair of consecutive terms is a constant number i.e. a sequence of the form

    a, ar, ar2, ar3, ……

    The constant r is called the common ratio.

    General nth term of a geometric progression

    Un = ar^(n-1)

    Sum of GP

    Sn = [a(1-r^n]/(1-r) lrl 1

    Sum to infinity = a/(1-r)

    Please contact Mr Ong @9863 9633 for more detail on Geometric Progression

    #4175

    admin
    Member

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

    Hi A-Level/H2 Math Students

    Arithmetic Progression – Practice Questions

    Question 1
    The sum of the first nine terms of an arithmetic progression is 75 and the twenty-fifth term is also 75. Find the common difference and the sum of the first hundred terms. [10/3,16000]

    Question 2
    The sum of the first n terms of a series is given by Sn = n^2 – 3n, n > 1. Show that the series is an arithmetic series. Hence, find the first term, a and the common difference, d. [-2,-2]

    Please contact Mr Ong @9863 9633 for more practice questions on Arithematic Progression

    #4253

    admin
    Member

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

    Hi A-Level/H2 Math Students

    Problem Students Encounter

    1. Do not understand the concept at all.
    2. Understand the concept but do not know how to apply especially complex questions
    3. Understand Lecture Notes and can do the tutorials but do badly in the exam
    4. How to memorized all formulae or concepts especially Vectors, Complex Number & Integration and Applications

    If these are the problems you encounter. Math tutor in One.Tution Place can help you. Please call Mr Ong @9863 9633

    #4337

    admin
    Member

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

    Hi A-Level/H2 Math Students

    J1 – Teaching Binomial Expansion and exam practice

    J2 – Teaching Permutations and Combinations and exam practice

    If you have problems in your tutorial. Math tutor in One.Tution Place can help you. Please call Mr Ong @9863 9633

    #4373

    admin
    Member

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

    Hi A-Level/H2 Math Students

    Permutations and Combinations

    Fundamental Principles of Counting

    Addition Principle
    If there are r choices for performing a particular task, and the number of ways to carry out the kth choice is ,nk for k = 1, 2, 3, …, r, then the total number of ways of performing the task is equal to the entire sum of the number of ways for all the r different choices i.e.

    n1+n2+n3…………nk

    Multiplication Principle
    If one task can be performed in m ways, and following this, a second task can be performed in n ways (regardless of which way the first task was performed), then the number of ways of performing the 2 tasks in succession is m × n.

    Permutations
    A permutation is an ordered arrangement of objects.

    Combinations
    A combination is a selection of objects in which the order of selection does not matter.

    If you have problems in your tutorial. Math tutor in One.Tution Place can help you. Please call Mr Ong @9863 9633

    #4438

    admin
    Member

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

    Hi A-Level/H2 Math Students

    Examination Skills

    DO
    1. Plan your timetable well so that you are able to allocate time to revise all the topics.

    2. Revise all tutorials, lecture tests, short quizzes given by your tutors, Common Test, and Past Years GCE ‘A’ Level Questions

    3. Optimise the use of Graphic Calculator whenever possible.

    4. Practice time management.

    DO NOT
    1. Practice questions without understanding – must grasp correct concepts
    learnt from every question.

    2. Skip topic(s).

    3. Be complacent.

    Important notes on accuracy of answers

    In general,
    1. Only if the final answer is not exact, then leave your answer to 3 significant figures unless otherwise stated.

    2. For angles, leave your answer to 1 decimal place(in degree) or
    3 significant figures(in radian) unless otherwise stated.

    3. In Statistics, intermediate values should be stated fully if it is exact. If not, an accuracy of 5 significant figures is recommended unless otherwise stated.

    If you have problems in your tutorial. Math tutor in One.Tution Place can help you. Please call Mr Ong @9863 9633

    #4478

    admin
    Member

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

    Hi A-Level/H2 Math Students

    Skill Set – Permutations and Combinations

    Skill Set 1

    Consider consecutive operations one after another and use multiplication principle

    Example
    A man has 10 different pieces of jewellery and wishes to give his
    three daughters one piece each as dowry. In how many ways can he
    do this?

    Consider each of the three daughters in sequence:
    1st daughter / 2nd daughter / 3rd daughter
    No. of ways = 10 x 9 x 8 = 720

    Skill Set 2

    Consider mutually exclusive cases and use addition principle

    A bag contains five red and three blue tokens, all of which are
    identical, apart from colour. Four tokens are taken out of the bag at
    random without replacement and arranged in a row. In how many ways can this be done?

    There are 4 possible cases:

    Tokens No. of ways
    Case 1 3 blue, 1 red
    No of ways = 4!/3!

    Case 2 2 blue, 2 red
    No of ways = 4!/(2!2!)

    Case 3 1 blue, 3 red
    No of ways = 4!/3!

    Case 4 4 red
    No of ways = 4!/4!

    Total = 15

    If you have problems in your tutorial. Math tutor in One.Tution Place can help you. Please call Mr Ong @9863 9633

    #4542

    admin
    Member

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

    Hi A-Level/H2 Math Students

    DO

    1. Plan your timetable well so that you are able to allocate time to revise all the topics.

    2. An overview of every topic is provided in the revision package, which
    highlights some of the important concepts. However, this is not to replace
    the lecture notes that contain more examples.

    4. Revise all lessons notes and examples given by One.Tuition Place, other JCs Prelim Papers and Past Years GCE ‘A’ Level Questions

    5. Optimise the use of Graphic Calculator whenever possible.

    6. Practice time management.

    If you have problems in your tutorial. Math tutor in One.Tution Place can help you. Please call Mr Ong @9863 9633

    #4629

    admin
    Member

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

    Hi A-Level/H2 Math Students

    Vectors 1

    Unit Vector
    A unit vector is a vector of magnitude 1.

    The unit vector in the direction of a^ is given by a^ = a/lal

    Parallel Vectors
    Two non zero vectors a and b are parallel if and only if a = kb for some k is element of real number.

    Collinear Points
    Three points A, B and C are collinear if and only if AB = k x BC for some k is element of real number

    Length of Projection
    Length of projection of a vector a on a vector b
    = | a . ^b |

    Angle Between 2 Vectors
    cos x = (a.b)/(lal x lbl)
    x = the angle between the 2 vectors

    Area of Parallelogram and Triangle

    Area of parallelogram = l a x b l
    Area of triangle = 1/2 l a x bl

    If you have problems in your tutorial. Math tutor in One.Tution Place can help you. Please call Mr Ong @9863 9633

    #4698

    admin
    Member

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

    Hi A-Level/H2 Math Students

    Vectors 2

    Scalar Product

    The scalar (or dot) product of two vectors a and b (denoted by a.b ) is defined as

    a.b = |a||b| cos ,

    where  is the angle between a and b.

    Vector Product

    The vector (or cross) product of two vectors a and b is defined by
    a x b = lal lbl sin nˆ
    where  is the angle between a and b, nˆ is the unit vector perpendicular to plane containing a and b

    If you have problems in your tutorial. Math tutor in One.Tution Place can help you. Please call Mr Ong @9863 9633

    #4736

    admin
    Member

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

    Hi A-Level/H2 Math Students

    Probability Part 1

    BASIC PROBABILITY CONCEPTS

    a) An experiment is a situation involving chance or probability that leads to results called outcomes.

    Tossing a fair die once.

    b) An outcome (sample point) of an experiment is the result of a single trial of the experiment.

    {1} or {2} or . . . or {6}

    c) The sample space, S, (or probability space) of an experiment is the set of all possible outcomes.

    S = {1, 2, 3, 4, 5, 6}

    d) An event, E, is one or more outcomes of an experiment and it is a subset of the sample space S. E = {set of even numbers}
    = {2, 4, 6}

    e) Probability is the measure of how likely an event is.

    P(E) = 3/6 = 1/2

    Experiment A: Tossing a fair coin and noting the outcome.
    Sample Space, = {H, T}
    P({H}) = P({T}) = 1/2 .

    Experiment B: Tossing a fair die and noting the outcome.
    Sample Space, = {1, 2, 3, 4, 5, 6}, and
    P({1}) = P({2}) = P({3}) = P({4}) = P({5}) = P({6}) = 1/6

    Experiments A and B each have a Uniform Space where each outcome is equally likely. A uniform space is a finite sample space with all outcomes equally likely, i.e. the probability of each outcome is 1/n where n is the number of outcomes.

    Experiment C: Selecting a coloured ball, at random, from a box containing 3 white balls, 2 black balls and 4 blue balls.

    Sample Space, = {white, black, blue}
    P({white}) = 3/9 = 1/3
    P({black}) = 2/9
    P({blue}) = 4/9

    As we can see, the outcomes in Experiment C are NOT equally likely to occur. We are more likely to choose a blue ball than any other colour. We are least likely to choose a black ball.

    Please contact Mr Ong @9863 9633 if you need help in Probability

    #4812

    admin
    Member

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

    Hi A-Level/H2 Math Students

    Binomial Distribution

    1. A Binomial situation arises when
    • there is a fixed number, n, of repeated & independent trials
    • each trial has only two mutually exclusive outcomes, namely ‘success’ or ‘failure’
    • the probability of success, p, is the same for each trial

    2. The binomial random variable X is the number of successes in the n trials carried out.
    It is denoted by X ~ B(n, p).

    3. If X ~ B(n, p), then
    • P(X = x) = nCx p^x (1-p)^n-x , where x = 0, 1, 2, … , n
    • use binompdf (n, p, x) to compute P(X = x)
    • use binomcdf (n, p, x) to compute P(X ≤ x)

    Please contact Mr Ong @9863 9633 if you need help in Binomial Distribution.

    #4871

    admin
    Member

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

    Hi A-Level/H2 Math Students

    Poisson Distribution

    A Poisson distribution is another special case of a discrete distribution.

    Characteristics / Assumptions of a Poisson Distribution:

     The outcomes occur singly and randomly.
     Whether an event occurs in a particular point in time or space is independent of what happens elsewhere.
     At all points in time (or space), the probability of one event occurring within a small fixed interval of time (or space) is the same.
     There is no (or negligible) chance of 2 events occurring simultaneously at precisely the same point in time (or space).
     The distribution is commonly used to model rare events (discrete).

    In a Poisson distribution, the random variable is a count of the number of occurrences of a random event in a given region of time and space when a mean number of occurrences, , is given for a particular interval of time and space.

    Real-Life examples in which the Poisson distribution is a good model: The number of
     particles emitted in a minute by a radioactive substance.
     typographical errors in a randomly chosen page of a book.
     accidents in a factory in a randomly chosen day.

    Please contact Mr Ong @9863 9633 if you need help in Poisson Distribution.

Viewing 15 posts - 106 through 120 (of 133 total)

You must be logged in to reply to this topic.

Comments are closed.