WJEC Mathematics for A2 Level: Pure
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Language
English
ISBN
9781398387836
Cover
Title Page
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Contents
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Topic 1 Proof
1.1 Real, imaginary, rational and irrational numbers
1.2 Proof by contradiction
1.3 Proof of the irrationality of √2
1.4 Proof of the infinity of primes
1.5 Application of proof by contradiction to unfamiliar proofs
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Topic 2 Algebra and functions
2.1 Simplifying algebraic expressions
2.2 Partial fractions
2.3 Definition of a function
2.4 Domain and range of functions
2.5 The graphical representation of functions, with input x and the outputs y
2.6 Composition of functions
2.7 Inverse functions and their graphs
2.8 The graphs of inverse functions
2.9 The modulus function
2.10 Graphs of modulus functions
2.11 Combinations of the transformations on the graph of y = f(x)
2.12 Exponential and logarithmic functions
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Topic 3 Sequences and series
3.1 Binomial expansion for positive integral indices
3.2 The binomial expansion of (a + bx)n for any rational value of n
3.3 Using Pascal’s triangle to work out the coefficients of the terms in the binomial expansion
3.4 The binomial expansion where a = 1
3.5 The binomial theorem for other values of n
3.6 The difference between a series and a sequence
3.7 Arithmetic sequences and series
3.8 Proof of the formula for the sum of an arithmetic series
3.9 The summation sign and its use
3.10 Geometric sequences and series
3.11 The difference between a convergent and a divergent sequence and series
3.12 Proof of the formula for the sum of a geometric series
3.13 The sum to infinity of a convergent geometric series
3.14 Sequences generated by a simple recurrence relation of the form xn+1 = f(xn)
3.15 Increasing sequences
3.16 Decreasing sequences
3.17 Periodic sequences
3.18 Using sequences and series in modelling
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Topic 4 Trigonometry
4.1 Radian measure (arc length, area of sector and area of segment)
4.2 Use of small angle approximation for sine, cosine and tangent
4.3 Secant, cosecant and cotangent and their graphs
4.4 Inverse trigonometric functions sin-1, cos-1 and tan-1 and their graphs and domains
4.5 The trigonometric identities sec2 θ = 1 + tan2 θ and cosec2 θ = 1 + cot2 θ
4.6 Knowledge and use of the addition formulae sin (A ± B), cos (A ± B), tan (A ± B) and geometric proofs of these addition formulae
4.7 Expressions for a cos θ + b sin θ in the equivalent forms R cos (θ ± α) or R sin (θ ± α)
4.8 Constructing proofs involving trigonometric functions and identities
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Topic 5 Differentiation
5.1 Differentiation from first principles for sin x and cos x
5.2 Using the second derivative to find stationary points and points of inflection
5.3 Differentiation of ekx, akx, sin kx, cos kx and tan kx and related sums, differences and multiples
5.4 The derivative of ln x
5.5 Differentiation using the Chain, Product and Quotient rules
5.6 Differentiation of inverse functions sin-1 x, cos-1 x, tan-1 x
5.7 Connected rates of change and inverse functions
5.8 Differentiation of simple functions defined implicitly
5.9 Differentiation of simple functions and relations defined parametrically
5.10 Constructing simple differential equations
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Topic 6 Coordinate geometry in the (x, y) plane
6.1 Parametric equations
6.2 Using the Chain rule to find the first derivative in terms of a parameter
6.3 Implicit differentiation
6.4 Using parametric equations in modelling in a variety of contexts
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Topic 7 Integration
7.1 Integration of xn(n . -1), ekx, 1x, sin kx, cos kx
7.2 Integration of (ax + b)n (n ≠ −1), eax + b, 1ax + b, sin (ax + b), cos (ax + b)
7.3 Using definite integration to find the area between two curves
7.4 Using integration as the limit of a sum
7.5 Integration by substitution and integration by parts
7.6 Integration using partial fractions
7.7 Analytical solution of first order differential equations with separable variables
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Topic 8 Numerical methods
8.1 Location of roots of f(x) = 0 considering changes of sign of f(x)
8.2 Sequences generated by a simply recurrence relation of the form xn + 1 = f(xn)
8.3 Solving equations approximately using simple iterative methods
8.4 Solving equations using the Newton–Raphson method and other recurrence relations of the form xn + 1 = g (xn)
8.5 Numerical integration of functions using the Trapezium rule
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