Additional Mathematics

 ADDITIONAL MATHEMATICS (0606/4037)

Checklist for Exam Preparation

SIMULTANEOUS EQUATION

1- Introduction of Simultaneous Equations
2. Exercise 2.1
3- Exercise 2.2 Qs 5 and 9
4. Exponential Equation and Logarithmic Equation (N17/ 22/q 4 and N18/ 22/ q5)

INDICES, SURDS AND LOGARITHM

1- Introduction of Indices & examples - video 1
2- Exponential equations - video 2
3- Surds - video 3
4- Laws of Log with examples to build the concepts
5. Sketch of Logarithmic and exponential function
6 - Solving logarithmic equation (Nov. 18/23/q6)
Exponential Equations -
7. Surds-Rationalizing the denominator-N16/23/q5
8. Solving logarithmic equation-J19/11/q7

QUADRATIC EQUATION AND EXPRESSION 

1- Introducation and concept building- Max, and Min. value and quadratic sketch
2- Quadratic - Discriminant and quadratic inequality 
3- Exercise 4.2 Qs. 14
4- Exercise 4.2 Qs. 21
5- Exercise 4.3 Qs. 7
6- Exercise 4.3 Qs 9
7- Misc. 4 Qs. 5
8-

Note: These exercises are from Additional Mathematics' book of Ho Soo Thong

EQUATIONS, INEQUALITIES AND GRAPH
1. Linear modulus equation with graphical explanation

2. solving modulus inequalities with a constant 

3. Solving two modulus linear function with inequalities

4. Sketching graphs of cubic polynomial and their moduli

REMAINDER AND FACTOR THEOREMS

1. Introduction of Polynomial Identities, Remainder and Factor Theorem
2. Long division and solving cubic equations

3. Challenging Qs. J18/21/Qs.4

COORDINATE GEOMETRY

1. Explanation of a Complete lesson-Coordinate Geometry

2. Challenging question N18/12/Q12

LINEAR LAW

Notes on Linear Law

1. Complete lesson on Linear Law (new) 

2. Complete introduction of Linear Law

2. Linear Law graph given. N16/13/q7

FUNCTIONS

1. Conceptual understanding Function video 1

2. Domain and Range of a function video 2

3. Composite function video 3

4. Inverse function and its sketch video 4

5.

6.

7.Sketch - Absolute valued function (quadratic)



TRIGONOMETRY 

Imp. Trigonometry notes

* video 1 Basic and general angle

** video 2 sketches of Trigonometric functions

*** Video 3 Trigonometric identities

**** video 4 Solving trigonometric equations

1. Introduction of basic angle and general angle.
2- Relationship between basic angle and general angle in the four quadrant & Identities
3- Solving trigonometric equations - various forms of equations part 1
4- Solving trigonometric equation and past paper questions
5- Sketching of trigonometric functions with paper paper questions
SKETCHES

 1- Trigonometric Sketch- Challenging Question
2- Exercise 10.4 - various questions
3- Exercise 10.3 Sketch of Sine graph
4- Exercise 10.3 Sketch of cos graph
5- Exercise 10.3 Sketch of tan graph
6- Exercise 10.3 Qs. 7,8,10

IDENTITIES
1 - Exercise 11.1 Identities
2. Identity and Express y in terms of x of trig. equation N17/13/q1 and J17/12/q6


CIRCULAR MEASURE
1. Area and perimeter of the sector. N18-13-q2 

2. good challenging Question J20/11/Q7

3. a good challenging question June 20/22/Q11


BINOMIAL THEOREM

1. Challenging Qs. N18-12-Q12

2. Binomial Theorem-Independent term Nov.19/11/qs.1

3. Coefficient of x square and independent termN11/11/Q7

4.A good Past Paper Qs. for revision J13/12/Q9

5. Getting the coefficient of a single term after binomial expansions multiplication

PERMUTATION AND COMBINATION

1- Introduction of basic counting principle, factorial and permutation with examples
2-Permutation with restriction and Combination.
3- P&C past paper questions part 1
4- P&C past paper questions part 2
5- P&C past paper questions part 3
6- P&C past paper questions part 4
7- P&C CAIE J17/12/8

8- P&C N16/13/Q9


SERIES

1.`Introduction of AP and GP
2. AP and GP past paper qs. J16/12/Q9
3.AP and GP past paper qs.J17/11/q4
4. AP and GP past paper qs.J17/12/q7

DIFFERENTIATION 

1. Differentiation of Product Rule of Polynomial function Ex. 15.3
2. Differentiation of Quotient Rule of Polynomial functions Ex. 15.4
3. Basic Differentiation of Polynomial and Trig. function Ex. 15.1 & 18.1
4. Basic Differentiation of Exponential and Logarithmic Functions
5.  Differentiation of trig functions Ex. 18.1
6. Rate of Change 
7.Equation of tangent and Rate of Change
8. Stationary point on the curve and its nature. 
9. Approximate change and rate of change N19/21/Q3 and Q7 

Note: video at point 6,7,8 have explanation of question from AS Level Maths but it covers the requirement of O Level Add Maths as well.

EXPONENTIAL AND LOGARITHMIC FUNCTION

1. Sketch - Logarithmic and Exponential functions

INTEGRATION

1. Integration - equation of normal and area N18/22/q9
2. Integration - Shaded area, Eq. of tangent, N17/22/Qs.11 (Challenging Qs.)

3.Integration- Shaded area, Equation of normalJ18/12/Q11


KINEMATICS (Chapter 22)

1- Kinematics Complete lesson video #1

2.Kinematics Complete lesson video #2

3. Kinematics Complete lesson video #3

4.Kinematics (exponential function.) Nov.19/13/q10b
5..Kinematics (trig. function) J17/12/q5

6.Kinematics (Logarithmic equation)J14/11/Q9

7.Kinematics (application of Integration and Differentiation both)N15/23/Q7

8. Kinematics (Exponential equation) N17-12-Q9

 Exercise 22.1 Qs. 3
 Interesting and Challenging Qs.
 Exercise 22.1 Qs. 18

VECTORS IN TWO DIMENSIONS

1. Complete lesson Vector video #1

2.Complete lesson Vector video #2

3.Vectors-compose and resolve velocity video 3

4.vectors-compose and resolve velocities-video 4 - Examination question

5 Express vectors in terms of required vectors. N18/13/q7

6.Vectors Challenging Qs. J16/21/Q7 & J18/22/Q7

7. Vectors Challenging Qs J19-22-Q10 and J19-23-Q9

8. vector and gradient relationship

Exercise 23.3 Qs. 7



RELATIVE VELOCITY (It is out of Syllabus NOW)

1- Exercise 24.2 Qs. 6
2- Exercise 24.2 Qs. 8a
3- Exercise 24.2 Qs. 8b