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Cambridge IGCSE and O Level
Additional Mathematics Coursebook
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
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
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
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