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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

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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

Problem 1

Problem 2

Problem 3

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Problem 5

Problem 6

Problem 7

Parallel and perpendicular

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Problem 6

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Problem 8

Equation of a circle

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Problem 4

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Problem 6

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Tangent and normal to a circle

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Polynomials

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Long division

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Problem 5

Problem 6

Problem 7

Long division

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Modulus equations I

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Translation of graphs

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Sequences

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Partial sums

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Sigma notation

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Arithmetic Series

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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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Sin, cos and tan

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Using identities

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Transformed equations

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Problem 7

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The sine rule

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Area of a triangle

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Problem 7

Problem 8

Problem 9

Problem 10

Double angle formulae

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Problem 2

Problem 3

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Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Harmonic Form

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Problem 2

Problem 3

Problem 4

Reciprocal functions

Problem 1

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Problem 2

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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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

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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 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

u_{n} = p n + q

satisfies $u_{2} = - 10$ and $S_{2} = 14.$

Find the values of $p$ and $q .$

Since $u_{2} = - 10$ we know that

2 p + q = - 10

$S_{2} = 14$ so

(p + q) + (2 p + q) = 14

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