IGCSE

IGCSE Additional Mathematics

Learn About The Subject

IGCSE Additional Mathematics (Add Maths) is an advanced course specifically designed for students with strong mathematical abilities who wish to delve deeper into knowledge beyond the regular IGCSE Mathematics curriculum. The subject introduces important concepts in Calculus (Differentiation and Integration), advanced Algebra, and Trigonometry, aiming to cultivate rigorous logical thinking, complex problem-solving skills, and build a solid foundation for higher-level mathematics programs such as IB HL or A-Level.

Common Challenges When Learning IGCSE Additional Mathematics

Difficulty with advanced concepts: Needing to quickly and deeply grasp new, more complex topics such as Calculus, advanced Trigonometry, and extended Algebra.
Challenge in algebraic manipulation skills: Requiring proficiency, precision, and high speed in complex algebraic manipulations.
Requirement for logical thinking & problem-solving: Needing to flexibly apply multiple concepts and skills to solve multi-step, non-routine problems.
Pressure regarding speed and accuracy: Needing the ability to work quickly and achieve high accuracy under the time pressure of the examination.

Course Content

Unit 1: Functions

1.1: Understand the terms: function, domain, range (image set), one-one function, inverse function and composition of functions

1.2: Use the notation f(x)=sinx, f:x↦logx, (g(x)>0), f−1(x) and f2(x) [$ = f(f(x))$]

1.3: Understand the relationship between y=f(x) and y=∣f(x)∣, where f(x) may be linear, quadratic or trigonometric

1.4: Explain in words why a given function is a function or why it does not have an inverse

1.5: Find the inverse of a one-one function and form composite functions

1.6: Use sketch graphs to show the relationship between a function and its inverse

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Unit 2: Quadratic functions

2.1: Find the maximum or minimum value of the quadratic function f:x↦ax2+bx+c by any method

2.2: Use the maximum or minimum value of f(x) to sketch the graph or determine the range for a given domain

2.3: Know the conditions for f(x)=0 to have: (i) two real roots, (ii) two equal roots, (iii) no real roots and the related conditions for a given line to (i) intersect a given curve, (ii) be a tangent to a given curve, (iii) not intersect a given curve

2.4: Solve quadratic equations for real roots and find the solution set for quadratic inequalities

Unit 3: Equations, inequalities and graphs

3.1: Solve graphically or algebraically equations of the type ∣ax+b∣=c (c≥0) and ∣ax+b∣=∣cx+d∣

3.2: Solve graphically or algebraically inequalities of the type ∣ax+b∣>c (c≥0), ∣ax+b∣<c (c>0) and ∣ax+b∣≤∣cx+d∣

3.3: Use substitution to form and solve a quadratic equation in order to solve a related equation

3.4: Sketch the graphs of cubic polynomials and their moduli, when given in factorised form y=k(x−a)(x−b)(x−c)

3.5: Solve cubic inequalities in the form k(x−a)(x−b)(x−c)≤d graphically

Unit 4: Indices and surds

4.1: Perform simple operations with indices and with surds, including rationalising the denominator

Unit 5: Factors of polynomials

5.1: Know and use the remainder and factor theorems

5.2: Find factors of polynomials

5.3: Solve cubic equations

Unit 6: Simultaneous equations

6.1: Solve simple simultaneous equations in two unknowns by elimination or substitution

Unit 7: Logarithmic and exponential functions

7.1: Know simple properties and graphs of the logarithmic and exponential functions including lnx and ex (series expansions are not required) and graphs of kenx+a and kln(ax+b) where n,k,a and b are integers

7.2: Know and use the laws of logarithms (including change of base of logarithms)

7.3: Solve equations of the form ax=b

Unit 8: Straight line graphs

8.1: Interpret the equation of a straight line graph in the form y=mx+c

8.2: Transform given relationships, including y=axn and y=Abx, to straight line form and hence determine unknown constants by calculating the gradient or intercept of the transformed graph

8.3: Solve questions involving mid-point and length of a line

8.4: Know and use the condition for two lines to be parallel or perpendicular, including finding the equation of perpendicular bisectors

Unit 9: Circular measure

9.1: Solve problems involving the arc length and sector area of a circle, including knowledge and use of radian measure

Unit 10: Trigonometry

10.1: Know the six trigonometric functions of angles of any magnitude (sine, cosine, tangent, secant, cosecant, cotangent)

10.2: Understand amplitude and periodicity and the relationship between graphs of related trigonometric functions, e.g. sinx and sin2x

10.3: Draw and use the graphs of y=asin(bx)+c, y=acos(bx)+c and y=atan(<13>bx)+c where a is a positive integer, b is a simple fraction or integer (fractions will have a denominator of 2, 3, 4, 6 or 8 only), and c is an integer

10.4: Use the relationships sin2A+cos2A=1, sec2A=1+tan2A, csc2A=1+cot2A, tanA=cosAsinA, cotA=sinAcosA

10.5: Solve simple trigonometric equations involving the six trigonometric functions and the above relationships (not including general solution of trigonometric equations)

10.6: Prove simple trigonometric identities

Unit 11: Permutations and combinations

11.1: Recognise and distinguish between a permutation case and a combination case

11.2: Know and use the notation n! (with 0!=1), and the expressions for permutations and combinations of n items taken r at a time

11.3: Answer simple problems on arrangement and selection (cases with repetition of objects, or with objects arranged in a circle, or involving both permutations and combinations, are excluded)

Unit 12: Series

12.1: Use the Binomial Theorem for expansion of (a+b)n for positive integer n

12.2: Use the general term (rn)an−rbr (knowledge of the greatest term and properties of the coefficients is not required)

12.3: Recognise arithmetic and geometric progressions

12.4: Use the formulae for the $n$th term and for the sum of the first n terms to solve problems involving arithmetic or geometric progressions

12.5: Use the condition for the convergence of a geometric progression, and the formula for the sum to infinity of a convergent geometric progression

Unit 13: Vectors in two dimensions

13.1: Use vectors in any form

13.2: Know and use position vectors and unit vectors

13.3: Find the magnitude of a vector; add and subtract vectors and multiply vectors by scalars

13.4: Compose and resolve velocities

Unit 14: Differentiation and integration

14.1: Understand the idea of a derived function

14.2: Use the notations dxdy, f′(x), f′′(x), dx2d2y [$ = \frac{d}{dx}(\frac{dy}{dx})$]

14.3: Use the derivatives of the standard functions xn (for any rational n), sinx, cosx, tanx, ex, lnx, together with constant multiples, sums and composite functions of these

14.4: Differentiate products and quotients of functions

14.5: Apply differentiation to gradients, tangents and normals, stationary points, connected rates of change, small increments and approximations and practical maxima and minima problems

14.6: Use the first and second derivative tests to discriminate between maxima and minima

14.7: Understand integration as the reverse process of differentiation

14.8: Integrate sums of terms in powers of x including ∫(ax+b)ndx (for any rational n, except n=−1), ∫eax+bdx, ∫sin(ax+b)dx, ∫cos(ax+b)dx

14.9: Evaluate definite integrals and apply integration to the evaluation of plane areas

14.10: Apply differentiation and integration to kinematics problems that involve displacement, velocity and acceleration of a particle moving in a straight line with variable or constant acceleration, and the use of x–t and v–t graphs

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IGCSE Additional Mathematics

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Frequently Asked Questions

Frequently Asked Questions About

IGCSE Additional Mathematics

How does IGCSE Additional Mathematics (often Cambridge code 0606) differ from IGCSE Mathematics (0580)?

IGCSE Additional Mathematics is a separate and significantly more advanced subject than IGCSE Mathematics (0580). Add Maths includes many topics not found in 0580, especially substantial content on Calculus (Differentiation, Integration), advanced Trigonometry, and more complex Algebra sections. It is designed for students with stronger mathematical abilities.

Which students are suitable for studying Add Maths?

This subject is suitable for students who have achieved high grades (usually A* or A) in IGCSE Mathematics (Extended - 0580), have a passion for Mathematics, possess good logical thinking skills, and particularly those who intend to study Mathematics at higher levels (such as IB Math AA HL, IB Math AI HL, A-Level Mathematics, A-Level Further Mathematics) or university majors requiring a very strong mathematical foundation (e.g., Engineering, Physics, Computer Science, Econometrics...).

How does Add Maths prepare students for studying Mathematics at the IB or A-Level?

Add Maths provides extremely good preparation. It covers many important foundational topics and skills that will be studied in the first year of IB Higher Level Mathematics programs or A-Level Mathematics/Further Mathematics. Successfully completing Add Maths gives students a significant advantage, greater confidence, and an easier transition to new knowledge when moving to higher levels.

Are calculators allowed in the IGCSE Add Maths examination?

Yes, students are usually allowed to use a scientific calculator in IGCSE Add Maths papers to assist with complex calculations. However, a clear understanding of the solution steps and underlying theory remains the decisive factor.

How difficult is IGCSE Add Maths compared to other IGCSE subjects?

IGCSE Additional Mathematics is widely recognized as one of the most challenging subjects at the IGCSE level. It demands a high level of abstract thinking, proficient algebraic skills, the ability to solve complex problems, and considerable diligence and effort in practice.

Does Intertu Education offer trial classes for IGCSE Additional Mathematics?

Yes. Intertu Education offers Trial Classes for IGCSE Additional Mathematics. This is an excellent opportunity for you and your parents to directly experience our teaching methods, meet the teacher, and assess suitability before deciding to enroll in a full course. Please contact our counseling department for more information.

How is the tuition fee for the IGCSE Additional Mathematics course at Intertu calculated?

The tuition fee for IGCSE Additional Mathematics at Intertu Education depends on the study hour package and the level of support service (Standard, Premium, Platinum) that parents choose, to best meet specific learning needs and goals. To receive a detailed fee schedule and advice on the most suitable study package, please contact Intertu's counseling team directly.

IGCSE

IGCSE Additional Mathematics

Learn About The Subject

Common Challenges When Learning IGCSE Additional Mathematics

Course Content

Register For A Consultation With Our Experts

Personalized Learning Approach

Academic Pathway

Competency Assessment

Set Learning Objectives

Create A Learning Path

Implement And Optimize

MEET THE TEACHING TEAM

Dedicated Team Of Teachers Ready To Support Your Learning Journey

Tuan Nguyen

Duy Nguyen

Thuy Nguyen

Tra Nguyen

Tin Nguyen

Hieu Pham

Uyen Vu

Carolina Rondon

Choosing the right study package

Find The Optimal Academic Support Solution For You

Learn About Another Subject

Frequently Asked Questions

Frequently Asked Questions About

IGCSE Additional Mathematics

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