WJEC Mathematics for AS Level: Pure
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Description
Contents
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Language
English
ISBN
9781398387805
Cover
Title Page
Copyright
Contents
How to use this book
Topic 1 Proof
1.1 Real and imaginary numbers
1.2 Rational and irrational numbers
1.3 Proof by exhaustion
1.4 Disproof by counter-example
1.5 Proof by deduction
Test yourself
Summary
Topic 2 Algebra and functions
2.1 Laws of indices
2.2 Use and manipulation of surds
2.3 Completing the square
2.4 Solution of quadratic equations
2.5 The discriminant of a quadratic function
2.6 Sketching the graph of a quadratic function
2.7 Simultaneous equations
2.8 Solving linear and quadratic inequalities
2.9 Using set notation for solutions of inequalities
2.10 Algebraic manipulation of polynomials
(expanding brackets, factorisation, algebraic division, the remainder theorem, the factor theorem, factorising a polynomial)
2.11 Sketching curves of functions
2.12 Interpreting algebraic solutions of equations graphically
2.13 Using intersection points of graphs of curves to solve equations
2.14 Proportional relationships and their graphs
2.15 Transformations of the graph of y = f(x)
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Summary
Topic 3 Coordinate geometry in the (x, y) plane
3.1 Finding the gradient, length, mid-point and equation, of a line joining two points
3.2 Conditions for two straight lines to be parallel or perpendicular to each other
3.3 The equation of a circle
3.4 Circle properties
3.5 Finding the equation of a tangent to a circle
3.6 Finding where a circle and straight line intersect or meet
3.7 Using the discriminant to identify whether a line and circle intersect and, if so, how many times
3.8 Condition for two circles to touch internally or externally
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Summary
Topic 4 Sequences and series – the Binomial Theorem
4.1 The binomial expansion
4.2 Pascal’s triangle
4.3 The binomial expansion where a = 1
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Summary
Topic 5 Trigonometry
5.1 Sine, cosine and tangent functions and their exact values
5.2 Obtaining angles given a trigonometric ratio
5.3 The sine and cosine rules
5.4 The area of a triangle
5.5 Sine, cosine and tangent: their graph, symmetries and periodicity
5.6 Use tan θ = sin θ/cos θ and sin^2 θ + cos^2 θ = 1
5.7 Solving trigonometric equations
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Summary
Topic 6 Exponentials and logarithms
6.1 y = a^x and its graph
6.2 y = e^x and its graph
6.3 The graph of y = e^kx and the gradient = ke^kx
6.4 The definition of log_a x as the inverse of a^x
6.5 ln x and its graph
6.6 Proof and use of the laws of logarithms
6.7 Solving equations in the form a^x = b
6.8 Using exponential growth and decay in modelling
6.9 Limitations and refinements of exponential models
6.10 Using logarithmic graphs to reduce exponential equations to linear form
Test yourself
Summary
Topic 7 Differentiation
7.1 What is differentiation?
7.2 Differentiation from first principles
7.3 Differentiation of x^n and related sums and differences
7.4 Stationary points
7.5 The second order derivative
7.6 Increasing and decreasing functions
7.7 Simple optimisation problems
7.8 Gradients of tangents and normals, and their equations
7.9 Simple curve sketching
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Summary
Topic 8 Integration
8.1 Indefinite integration as the reverse process of differentiation
8.2 Interpretation of the definite integral as the area under a curve
8.3 Evaluation of definite integrals
8.4 Finding the area bound by a straight line and a curve
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Summary
Topic 9 Vectors
9.1 Scalars and vectors
9.2 Vectors in two dimensions
9.3 The magnitude of a vector
9.4 Algebraic operations of vector addition, subtraction and multiplication by scalars, and their geometrical interpretations
9.5 Position vectors
9.6 Coordinate geometry and vectors
9.7 Position vector of a point dividing a line in a given ratio
9.8 Using vectors to solve problems in pure mathematics
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Summary
Formulae
Formula booklet
Formulae to be remembered
Test yourself answers
Backcover
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