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Notes
Mathematics
Pure Mathematics 2
Mathematics 9709
Pure Mathematics 2 — Revision Notes
Hover a chapter to open it, then pick a topic to start reading.
1
Algebra
6 topics
1.1
The modulus function
1.2
Graphs of y = |f(x)|
1.3
Solving modulus inequalities
1.4
Division of polynomials
1.5
The factor theorem
1.6
The remainder theorem
2
Logarithmic and exponential functions
5 topics
2.1
Logs and the laws: the toolkit you apply everywhere
2.2
Solving ln / log equations (combine, then undo with e)
2.3
Unknown stuck in the power: a^x = b and the hidden quadratic
2.4
e^x and ln x: inverse twins, graphs, and the e/ln cancel
2.5
Straightening curves: turn y = kxⁿ or y = Ae^(bx) into Y = mX + c
3
Trigonometry
5 topics
3.1
Cosecant, secant and cotangent
3.2
Compound angle formulae
3.3
Double angle formulae
3.4
Further trigonometric identities
3.5
Expressing a sin θ + b cos θ as R sin(θ ± α) or R cos(θ ∓ α)
4
Differentiation
5 topics
4.1
Product and Quotient Rule
4.2
Differentiating e^x, a^x and ln x
4.3
Differentiating sin, cos and tan
4.4
Implicit Differentiation
4.5
Parametric Differentiation
5
Integration
6 topics
5.1
Integration of exponential functions
5.2
Integration of 1/(ax + b)
5.3
Integration of sin, cos and sec² of (ax + b)
5.4
Further integration of trigonometric functions
5.5
Definite integrals and the area under a curve
5.6
The trapezium rule
6
Numerical Solution of Equations
3 topics
6.1
Locating a Root: Sign Change and Sketching a Pair of Graphs
6.2
Rearranging f(x)=0 to x=F(x), and Proving It Converges to the Root
6.3
Running the Iteration to a Required Accuracy (and Confirming the Root)
Mathematics Pure Mathematics 2 — Revision Notes · Conquer Your A Levels