A box contains $m$ white balls and $n$ black balls. A ball is drawn out of the box at random. What is the probability that the ball is black/white?

Converting a length in m to mm, cm and km.

Addition, multiplication and division of fractions.

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A variety of worded fraction questions.

The simplest case. Divisor is single digit. There is no remainder. 

Solve a quadratic equation by completing the square. The roots are not pretty!

The simplest case. Divisor is single digit. There is no remainder. 

Simple Percentages

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 Basics, percentage of an amount, converting to fractions and decimals.

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6 questions which introduce the user to the Numbas system.

Practice with adding, subtracting and dividing basic algebraic fractions

Several problems involving dividing fractions, with increasingly difficult examples, including mixed numbers and complex fractions. 

Several problems involving the multiplication of fractions, with increasingly difficult examples, including a mixed fraction and a squared fraction. The final part is a word problem. 

One-way ANOVA example

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

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Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

It is estimated that 30% of all CIT students cycle to college. If a random sample of eight CIT students is chosen, calculate the probability that...

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This is the question for Lent Term week 10 of the MA100 course at the LSE. It looks at material from chapters 39.

This is the question for Lent Term week 9 of the MA100 course at the LSE. It looks at material from chapters 37 and 38.

This is the question for Lent Term week 8 of the MA100 course at the LSE. It looks at material from chapters 35 and 36.

This is the question for Lent Term week 7 of the MA100 course at the LSE. It looks at material from chapters 33 and 34.

The following is a description of parts a and b. In particular it describes the varaibles used for those parts.

This question (parts a and b) looks at optimisation problems using the langrangian method. parts a and b of the question we will ask the student to optimise the objective function f(x,y) = y + (a/b)x subject to the constraint function r^2 = (x-centre_x)^2 + (y-centre_y)^2.

The variables centre_x and centre_y take values randomly chosen from {6,7,...,10} and r takes values randomly chosen from {1,2,...,5}.

We have the ordered set of variables (a,b,c) defined to be randomly chosen from one of the following pythagorean triplets: (3,4,5) , (5,12,13) , (8,15,17) , (7,24,25) , (20,21,29). The a and b variables here are the same as those in the objective function. They are defined in this way because the minimum will occur at (centre_x - (a/c)*r , centre_y - (b/c)*r) with value centre_y - (b/c)r + (a/b) * centre_x - (a^2/bc)*r , and the maximum will occur at (centre_x + (a/c)*r , centre_y + (b/c)*r) with value centre_y + (b/c)r + (a/b) *centre_x + (a^2/bc)r. The minimisation problem has lambda = -c/(2br) and the maximation problem has lambda* = c/(2br).

We can see that all possible max/min points and values are nice rational numbers, yet we still have good randomisation in this question. :)

This is the question for Lent Term week 6 of the MA100 course at the LSE. It looks at material from chapters 31 and 32.

This is the question for Lent Term week 5 of the MA100 course at the LSE. It looks at material from chapters 29 and 30.

This is the question for Lent Term week 4 of the MA100 course at the LSE. It looks at material from chapters 27 and 28.

This is the question for Lent Term week 3 of the MA100 course at the LSE. It looks at material from chapters 25 and 26.

This is the question for Lent Term week 2 of the MA100 course at the LSE. It looks at material from chapters 23 and 24.

This is the question for Lent Term week 1 of the MA100 course at the LSE. It looks at material from chapters 21 and 22.