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Quadratics

Factorising I

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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

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Problem 2

Problem 3

Problem 4

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Problem 6

Problem 7

Problem 8

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Problem 10

Quadratic inequalities

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Problem 2

Problem 3

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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 4

Problem 5

Problem 6

Midpoints

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Gradient

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Equation of a straight line

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Problem 2

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Problem 5

Problem 6

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Parallel and perpendicular

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Equation of a circle

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Problem 6

Problem 7

Tangent and normal to a circle

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Problem 3

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Polynomials

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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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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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Using identities

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Transformed equations

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Problem 2

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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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Arcs and sectors

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Addition formulae

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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 6

Problem 7

Problem 8

Problem 9

Harmonic Form

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Problem 2

Problem 3

Problem 4

Reciprocal functions

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Small angle approximations

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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

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Problem 4

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 6

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Problem 8

Problem 9

Equations with $e$

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Problem 3

Problem 4

Problem 5

Differentiation

Estimating Change

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First principles

Problem 1

Problem 2

Problem 3

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Problem 6

Problem 7

Differentiating Polynomials (and beyond)

Problem 1

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Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Turning points

Problem 1

Problem 2

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Problem 6

Problem 7

Problem 8

Optimisation

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Problem 4

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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 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

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Problem 3

Problem 4

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Problem 6

Numerical Methods

Change of sign rule

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Problem 2

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Problem 7

Problem 8

Problem 9

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Iteration

Problem 1

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Newton-Raphson

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The trapezium rule

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Riemann sums

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Problem 6

Integration

Geometric area

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

Integration by parts

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Problem 2

Problem 3

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Problem 6

Integration by substitution (indefinite)

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Problem 2

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Problem 4

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Integration by substitution (definite)

Parametric integration

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Problem 2

Problem 3

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The kinetic energy, $E,$ of a mass $m$ moving with velocity $v$ is

E = \frac{1}{2} m v^{2}

Find the rate of change of the kinetic energy of a car of mass $800 kg$ when it is accelerating at $5 {m s}^{- 2} .$

Acceleration means $\frac{d v}{d t} .$

\frac{d E}{d t} = \frac{d E}{d v} \frac{d v}{d t}

The answer is $λ v$ .

Give the value of $λ$ .

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