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.
A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor
Hi A-Level/H2 Math Students
J1 – 30 min Modular Differentiation and Applications
J2 – 30 min Modular Revision Vectors
From A Level Math Tutors
A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor
Hi A-Level/H2 Math Students
J1 – 30 min Modular Graphing Technique
J2 – 30 min Modular Revision Complex Numbers
From A Level Math Tutors
A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor
Hi A-Level/H2 Math Students
J1 – Exam Practice focusing on Differentiation and Graphing Technique
J2 – Concept review on the selected questions from 2007 to 2012 A level questions. Solution posted on the math resource.
From A Level Math Tutors
A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor
Hi A-Level/H2 Math Students
J1 – Exam Practice focusing on Functions and MOD and Teaching Integration Part 2
J2 – Concept review on stats and practice prelim questions
From A Level Math Tutors
A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor
Hi A-Level/H2 Math Students
J1 – Exam Practice focusing on Graphical Technique and Teaching Integration Part 3
J2 – Concept review on Differential Equations and practice prelim questions
From A Level Math Tutors
A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor
Hi A-Level/H2 Math Students
J1 – Exam Practice focusing on Differentiation & Applications and Teaching Differential Equations
J2 – Concept review on statistics and practice prelim questions
From A Level Math Tutors
A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor
Hi A-Level/H2 Math Students
J1 – Exam Practice using top JCs promo questions
J2 – Concept review on statistics and practice top JCs prelim questions
From A Level Math Tutors
A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor
Hi A-Level/H2 Math Students
J1 – Exam Practice using top JCs promo questions
J2 – Concept review on pure math and practice top JCs prelim questions
From A Level Math Tutors
A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor
Hi A-Level/H2 Math Students
J1 – Teach Maclaurin Series and Exam Practice
J2 – Concept review on Statistics and practice top JCs prelim questions
From A Level Math Tutors
A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor
Hi A-Level/H2 Math Students
A Level Mathematics – Final Lap
Date Day Time Remark
26-Oct Sat 5.30pm to 7.30pm Pure Math Preparation
2-Nov Sat 5.30pm to 7.30pm Pure Math Preparation
9-Nov Sat 5.30pm to 7.30pm Statistics Preparation
Please contact Hp 98639633 for Exam Based Questions
A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor
Hi A-Level/H2 Math Students
Power Revision
A Level Mathematics – 2 hrs Each Lesson
1. Function – 2 lessons
2. AP & GP – 2 lessons
3. Series and Sequences – 2 lessons
4. Graphing Technique – 2 lessons
5. Differentiation and Applications – 3 lessons
6. Maclaurin’s Series 2
7. Integration and Applications – 4 lessons
8. Differential Equations – 2 lessons
9. Vectors – 4 lessons
10. Complex Numbers – 4 lessons
11. Permutations & Combinations – 2 lessons
12. Probability – 2 lessons
Any Enquirers Please contact Hp 98639633 or Hp 96790479
A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor
Hi A-Level/H2 Math Students
2013 A Level H2 Math topics not tested in Paper 1.
(1) Functions
(2) Maclaurin Series + Binomial Expansion
(3) Maxima/Minima + Rate of Change (but seldom tested)
(4) Transformations/Further Curves Sketching
(5) Recurrence Sequences
(6) Vectors (questions on lines, though they usually involve planes with column vectors given)
(7) Integration – by parts and volume of revolution
All the best for P2
For information, Please contact Hp 98639633 or Hp 96790479
A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor
Hi A-Level/H2 Math Students
2013 J1 – Teaching integration by parts
The success of doing integration by parts often depends on the choice of u and v. Notice that we need to choose one term to differentiate and one term to integrate.
There are 3 types
Type 1: If only one of the two parts of the integrand is integrable, then integrate the one that is integrable.
Example
(a) ∫ x^3 ln xdx (b) ∫ x tan-1 xdx
Type 2: If both parts of the integrand are integrable separately, then choose the one that will ultimately give zero if differentiated a sufficient number of times as the function u for differentiation.
Example
(a) ∫ x cos x dx (b) ∫ x^2 e^3x dx
Type 3: If both parts of the integrand are integrable separately and neither gives zero on repeated differentiation, then it does not matter which function we choose to differentiate.
Example
Find ∫ e^x cos x dx .
Any Enquirers Please contact Hp 98639633 or Hp 96790479
A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor
Hi A-Level/H2 Math Students
Common Techniques complementing the Process of Integration
1. Partial Fractions
For integrals of the form ∫ f(x)/g(x) dx
where f (x) and g(x) are polynomials and g(x) can be factorised,
we can express f(x)/g(x) as partial fractions before applying the relevant integration results.
2. Factor Formulae and Double-Angle Formulae
As we often CANNOT INTEGRATE PRODUCTS and MULTIPLE POWERS of
trigonometric expressions directly, we have to use Factor Formulae, Double-Angle Formulae and other trigonometric identities to simplify them before integrating.
3. Completing the Square in Denominator
There are two type
Type 1
Non–Factorisable Quadratic Expression in Denominator with Constant Numerator
Type 2
Non-Factorisable Quadratic Expression in Denominator with Linear Numerator
4. Integration by Substitution
Many expressions may be simplified by means of a suitable substitution i.e. change of variable to recognisable forms ie. one of the standard forms.
Please contact Mr Ong @9863 9633 for more detail on integration technique
A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor
Hi A-Level/H2 Math Students
Integration by Substitution
Many expressions may be simplified by means of a suitable substitution i.e. change of variable to recognisable forms ie. one of the standard forms.
The following example illustrates the steps involved in the substitution method.
Explanation of Steps:
Step 1: Using the substitution provided, differentiate with respect to x.
Step 2: Replace terms in the integrand involving x with terms involving new variable,u. The operator dx has to be changed to du accordingly. Simplify if necessary.
Step 3: Integrate the integrand with respect to u.
Note that the new integrand should be easier to integrate (if not, it defeats the purpose of carrying out the substitution). Otherwise, check steps 1 and/or 2 for mistakes.
Step 4: Replace all the terms in u with that in x.
Note: Under the syllabus, the substitution to be used will be given to you in the question if you are expected to integrate using a substitution.
However, even if the substitution is not given, you may still use the substitution method if you know the appropriate substitution to use. (But there will usually be another method of doing it.)
Example
By using the substitution u = ln x , find
∫[(ln x )^6 + 1]/x dx
Step 1:
Let u = ln x
du/dx = 1/x
dx/x = du
Step 2: ∫[(ln x )^6 + 1]/x dx
= ∫ (u^6 + 1)du
Step 3: = u^7/7 + u + c
Step 4: = (ln x)^7/7 = ln x +c
Please contact Mr Ong @9863 9633 for more detail on integration integration by Substitution.
You must be logged in to reply to this topic.