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Quadratics

Factorising I

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Factorising II

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Parabolas

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Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Completing the square

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Finding the vertex

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

The quadratic formula

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

The discriminant

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Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Points of intersection

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Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

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Problem 10

Quadratic inequalities

Problem 1

Problem 2

Problem 3

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Problem 5

Problem 6

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Quadratics in disguise

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

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Coordinate Geometry

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Gradient

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Equation of a straight line

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Parallel and perpendicular

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Equation of a circle

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Partial sums

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Sigma notation

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Geometric series

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Sum to infinity

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Binomial expansion

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Generalised expansion

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Trigonometry

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Using identities

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Transformed equations

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Problem 7

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Problem 9

The sine rule

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Area of a triangle

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Problem 8

Problem 9

Problem 10

Double angle formulae

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Problem 7

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Problem 9

Harmonic Form

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Exponentials and Logarithms

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Problem 5

Problem 6

Problem 7

Logarithms

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Problem 3

Logarithms II

Problem 1

Problem 2

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Laws of logarithms I

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Laws of logarithms II

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Problem 5

Logarithm equations

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Problem 8

Problem 9

Equations with $e$

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Differentiation

Estimating Change

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First principles

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Problem 2

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Problem 6

Problem 7

Differentiating Polynomials (and beyond)

Problem 1

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Turning points

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Problem 6

Problem 7

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Optimisation

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Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Differentiation of sin and cos

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Differentiating $e^{kx}$

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

The Product Rule

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

The Chain Rule

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Problem 5

Problem 6

The quotient rule

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Implicit differentiation

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Parametric curves

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Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Related rates of change

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Convexity and concavity

Problem 1

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Problem 3

Problem 4

Problem 5

Problem 6

Numerical Methods

Change of sign rule

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Problem 2

Problem 3

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Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Iteration

Problem 1

Problem 2

Problem 3

Problem 4

Newton-Raphson

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The trapezium rule

Problem 1

Problem 2

Problem 3

Problem 4

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Problem 6

Problem 7

Problem 8

Riemann sums

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Problem 3

Problem 4

Problem 5

Problem 6

Integration

Geometric area

Integrating $\sin^2$ and $\cos^2$

Integration by parts

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Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Integration by substitution (indefinite)

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Integration by substitution (definite)

Parametric integration

Problem 1

Problem 2

Problem 3

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The function $f$ is defined by

f (x) = (x + 2) (x - 1)

Find all possible values of $x$ such that the sequence defined by

\begin{aligned} u_{1} & = x \\ u_{n + 1} & = f (u_{n}) \end{aligned}

is periodic of period $2$ .

We need $u_{1} = u_{3}$ , which implies

f (f (x)) = x

The equation

f (f (x)) = x

has $4$ solutions, but only two of these are valid.

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