Cambridge IGCSE and O Level
Additional Mathematics Coursebook

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Cambridge IGCSE and O Level
Additional Mathematics Coursebook Solutions

Topic 1. Functions

Ex. 1.1
Mappings

Ex. 1.2
Definition of a function

Ex. 1.3
Composite functions

Ex. 1.4
Modulus functions

Ex. 1.5
Graph of y = {f(x)| where f(x) is linear

Ex. 1.6
Inverse functions

Ex. 1.7
The graph of a function and its inverse

Topic 1.
Examination Questions

Topic 2. Simultaneous equations and quadratics

Ex 2.1
Simultaneous equations (one linear and one non-linear)

Ex 2.2
Maximum and minimum values of quadratic function

Ex 2.3
Graph of y = {f(x) | where f(x) is quadratic

Ex 2.4
Quadratic inequalities

Ex 2.5
Roots of a quadratic equations

Ex 2.6
Intersection of a line and a curve

Ex 2.7
Roots of a quadratic equations

Topic 2.
Examination Questions

Topic 3. Indices and surds

Ex 3.1
Simplifying expressions involving indices

Ex 3.2
Solving equations involving indices

Ex 3.3
Surds

Ex 3.4
Multiplication, division and simplification of surds

Ex 3.5
Rationalising the denominator of a fraction

Ex 3.6
Solving equations involving surds

Topic 3.
Examination Questions

Topic 4. Factors and Polynomials

Ex 4.1
Adding, subtracting and multiplying polynomials

Ex 4.2
Division of polynomials

Ex. 4.3
The factor theorem

Ex 4.4
Cubic expressions and equations

EX. 4.5
The remainder theorem

Topic 4.
Examination Questions

Topic 5. Equations, inequalities and graphs

Ex 5.1
Solving equations of the type |ax-b| = |cx-d|

Ex 5.2
Solving modulus inequalities

Ex. 5.3
Sketching graphs of cubic polynomials and their moduli

Ex 5.4
Solving cubic inequalities graphically

Ex 5.5
Solving more complex quadratic equations

Topic 5.
Examination Questions

Topic 6. Logarithmic and exponential functions

Ex 6.1
Logarithms of base 10

Ex 6.2
Logarithms of base a

Ex 6.3
The laws of logarithms

Ex 6.4
Solving logarithmic equations

Ex 6.5
Solving exponential equations

Ex 6.6
Change of base of logarithms

Ex 6.7
Natural logarithms

Ex 6.8
Practical applications of exponential equations

Ex 6.9
The graphs of simple logarithmic and exponential functions

Ex 6.10
The graphs of y =k(e^nx)+a and y=k ln(ax+b)n,k,a and b are integers

Ex 6.11
The inverse of logarithmic and exponential functions

Topic 6.
Examination Questions

Topic 7. Logarithmic and exponential functions

Ex 7.1
Problems involving length of a line and midpoint

Ex 7.2
Parallel and perpendicular lines

Ex 7.3
Equations of a straight lines

Ex 7.4
Areas of rectilinear figures

Ex 7.5
Converting from non-linear form to a linear form

Ex 7.6
Converting from linear form to a non-linear form

Ex 7.7
Finding relationship from data

Topic 7.
Examination Questions

Topic 8. Circular Measure

Ex 8.1
Circular Measure

Ex 8.2
Length of an arc

Ex 8.3
Area of a sector

Topic 8.
Examination Questions

Topic 9. Trigonometry

Ex. 9.1
Angles between 0 degree and 90 degrees

Ex 9.2
The general definition of an angle

Ex 9.3
Trigonometric ratios of general angles

Ex. 9.4
Graphs of trigonometric functions

Ex. 9.5
Graphs y = |f(x)| , where f(x) is a trigonometric functions

Ex. 9.6
Trigonometric equations

Ex. 9.7
Trigonometric identities

Ex. 9.8
Further trigonometric equations

Ex. 9.9
Further trigonometric identities

Topic 9.
Examination Questions

Topic 10. Permuations and combinations

Ex. 10.1
Factorial notations

Ex. 10.2
Arrangements

Ex. 10.3
Permutations

Ex. 10.4
Combinations

Topic 10.
Examination Questions

Topic 11. Series

Ex. 11.1
Pascal's triangle

Ex. 11.2
The binomial theorem

Ex. 11.3
Arithmetic progressions

Ex. 11.4
Geometric Progressions

Ex. 11.5
Infinite geometric series

Ex. 11.6
Further arithmetic and geometric series

Topic 11.
Examination Questions

Topic 12. Permuations and combinations

Ex. 12.1
The gradient function

Ex. 12.2
The chain rule

Ex. 12.3
The product rule

Ex. 12.4
The quotient rule

Ex. 12.5
Tangents and normals

Ex. 12.6
Small increments and approximations

Ex. 12.7
Rate of change

Ex. 12.8
Second derivatives

Ex. 12.9
Stationary points

Ex. 12.10
Practical maximum and minimum problems

Topic 12.
Examination Questions

Topic 13. Vectors

Ex. 13.1
Further vector notation

Ex. 13.2
Position vectors

Ex. 13.3
Vector geometry

Ex. 13.4
Constant velocity problems

Topic 13.
Examination Questions

Topic 14. Differentiation 2

Ex. 14.1
Derivatives of exponential functions

Ex. 14.2
Derivatives of logarithmic functions

Ex. 14.3
Derivatives of trigonometric functions

Ex. 14.4
Further applications of differentiation

Topic 14.
Examination Questions

Topic 15. Integration

Ex. 15.1
Differentiation reversed

Ex. 15.2
Indefinite Integral

Ex. 15.3
Integration of functions of the form (ax+b) n

Ex. 15.4
Integration of the exponential functions

Ex. 15.5
Integration of sine and cosine functions

Ex. 15.6
Integration of the functions of the form 1 divide by x and 1 divided by ax+b

Ex. 15.7
Further Indefinite Integration

Ex. 15.8
Definite Integration

Ex. 15.9
Further definite integration

Ex. 15.10
Area under a curve

Ex. 15.11
Area of a regions bounded by a line and curve

Topic 15.
Examination Questions

Topic 16. Kinematics

Ex. 16.1
Application of differentiation in kinematics

Ex. 16.2
Application of Integration in kinematics

Topic 16.
Examination Questions