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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

Problem 1

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

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Points of intersection

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Quadratic inequalities

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

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Quadratics in disguise

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Coordinate Geometry

Distance between points

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Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Midpoints

Problem 1

Problem 2

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Problem 4

Problem 5

Gradient

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Problem 2

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Equation of a straight line

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Problem 2

Problem 3

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Problem 5

Problem 6

Problem 7

Parallel and perpendicular

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Problem 6

Problem 7

Problem 8

Equation of a circle

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Problem 2

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Problem 4

Problem 5

Problem 6

Problem 7

Tangent and normal to a circle

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Problem 2

Problem 3

Problem 4

Problem 5

Polynomials

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Cubic functions

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Long division

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Problem 2

Problem 3

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Problem 5

Problem 6

Problem 7

Long division

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Problem 3

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Problem 7

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Problem 2

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Partial sums

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Sigma notation

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Arithmetic Sequences

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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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Problem 7

Problem 8

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Problem 7

Using identities

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Transformed equations

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Problem 2

Problem 3

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Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

The sine rule

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Problem 2

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Problem 4

Problem 5

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Area of a triangle

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Problem 2

Problem 3

Problem 4

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Radians

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Arcs and sectors

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Addition formulae

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Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Double angle formulae

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Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Harmonic Form

Problem 1

Problem 2

Problem 3

Problem 4

Reciprocal functions

Problem 1

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Small angle approximations

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Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Exponentials and Logarithms

Exponential functions

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Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Logarithms

Problem 1

Problem 2

Problem 3

Logarithms II

Problem 1

Problem 2

Problem 3

Problem 4

Laws of logarithms I

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Problem 2

Laws of logarithms II

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Logarithm equations

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Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Equations with $e$

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Differentiation

Estimating Change

Estimating Gradients

First principles

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Differentiating Polynomials (and beyond)

Problem 1

Problem 2

Tangents and Normals

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Turning points

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Optimisation

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

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

Problem 1

Problem 2

Problem 3

Problem 4

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

Problem 1

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

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Numerical Methods

Change of sign rule

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Iteration

Problem 1

Problem 2

Problem 3

Problem 4

Newton-Raphson

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

The trapezium rule

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Riemann sums

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Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Integration

Geometric area

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

Integration by parts

Problem 1

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 sequence $p_{n}$ is defined by

\begin{aligned} p_{1} & = 1 \\ p_{n + 1} & = k (p_{n} - n - 1) \end{aligned}

Given that $p_{3} = - 40,$ find the two possible values of the constant $k .$

Substitute $n = 1$ into the recursive formula to get

p_{2} = k (p_{1} - 1 - 1)

and simplify as much as possible.

Can you do similar for $p_{3}$ ?

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