Basic indefinite integrals, Basic definite integrals, integration by substitution

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Integration by susbtitution, no hint given

A basic introduction to differentiation

As the title says

Simple Indefinite Integrals

Implicit differentiation.

Given $x^2+y^2+ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Quotient rule

Simple Indefinite Integrals

Real life problems with differentiation

Simple Indefinite Integrals

Real life problems with differentiation

Maximising the volume of a rectangular box

Implicit differentiation.

Given $x^2+y^2+ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Chain rule

Quotient rule

Questions of the form $f(x) = g(x)/h(x) $

Optimised for display of quotients using \displaystyle - see first part - otherwise difficult to read.

Questions about speed-time graphs

Questions about distance-time graphs

A basic introduction to differentiation

Solving quadratic equations using a formula,

Basic indefinite integrals, Basic definite integrals, integration by substitution

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Solve an exponential equation

Solve a logarithmic equation

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

Rolling a pair of dice. Find probability that at least one die shows a given number.

Manipulation of an exponential function

Sample of size $24$ is given in a table. Find sample mean, sample standard deviation, sample median and the interquartile range.

An experiment is performed twice, each with $5$ outcomes

$x_i,\;y_i,\;i=1,\dots 5$ . Find mean and s.d. of their differences $y_i-x_i,\;i=1,\dots 5$.

Critical points, absolute minimum, local maximum and minimum points, increasing and decreasing, concavity

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An experiment is performed twice, each with $5$ outcomes

$x_i,\;y_i,\;i=1,\dots 5$ . Find mean and s.d. of their differences $y_i-x_i,\;i=1,\dots 5$.