Transition to university

Rationalise the denominator with increasingly difficult examples involving compound denominators. 

Calculate the time taken for a certain distance to be travelled given the average speed and the distance travelled.

Small, simple question.

Manipulate surds and rationalise the denominator of a fraction when it is a surd.

Given the cost of hiring a room for a given number of hours, compare with competing prices given per hour and per minute.

Calculate a rate of pay (in pounds per week) given the total pay over a given period of time.

Given the probabilities that each of four out of five friends will win a round of mini-golf, work out the probability that the fifth friend won't win, then use that to find the probability that they will win.

Given a description in words of the costs of some items in terms of an unknown cost, write down an expression for the total cost of a selection of items. Then simplify the expression, and finally evaluate it at a given point.

The word problem is about the costs of sweets in a sweet shop.

Given a student discount, calculate a discounted price.

This question assesses

• the students ability to apply both theoretical and experimental probability to calculate expected values 
• the students understanding of how to calculate the relative frequency of an outcome

The question also helps to show students how using experimental probability and theoretical probability results in different expected values of an outcome.

Calculate the volume of different 3D shapes, given the units and measurements required. The formulae for the volume of each shape are available as steps if required.

This question assesses the students ability to calculate and convert between different types of compound units, including rates of pay, speed and unit pricing.

Find the original price before a discount by dividing the new price by the percentage discount.

Compute the experimental probability of a particular score on a die given a sample of throws, and compare it with the theoretical probability.

The last part asks what you expect to happen to the experimental probability as the sample size increases.

Substitute values into formulae for the area or volume of various geometric objects.

Given a table of data, calculate the mean, mode and median, and complete a frequency table.

An applied example of the use of two points on a graph to develop a straight line function, then use the t estimate and predict. MCQ's are also used to develop student understanding of the uses of gradient and intercepts as well as the limitations of prediction.

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function, which allows the student to check their answer against the graph before submitting.

This particular example has a 0 gradient.

Drag points on a graph to the given Cartesian coordinates. There are points in each of the four quadrants and on each axis.

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a negative gradient.

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

Differentiate between linear and quadratic sequences and arithmetic and geometric sequences through a series of multiple choice questions. Spot different patterns in sequences like the triangle sequence, square sequence and cubic sequence and then use this pattern to find the next three terms in each of the sequences.

Find the common ratio of a given geometric sequence, write down the formula for the nth term and use it to calculate a given term in the sequence.

Sort a list of numbers into "prime" or "composite".

Two trains arrive at the same platform with different periods. Compute the LCM of the two periods to find the time they clash.

This is a context question testing the student's ability to identify the lowest common multiple of two integer values which are not multiples of each other. 

This question introduces base vectors i and j and asks the student to interpret a JSXGraph diagram to write four vectors in terms of the base vectors. Further parts ask the student to add vectors and find a magnitude.

This question asks the student to interpret a JSXGraph diagram to write three vectors in terms of the base vectors. Each vector has both a horizontal and vertical component. Further parts ask the student to add vectors and find a magnitude. 

Fill in a frequency table for grouped data, then estimate the mean and identify the modal class.

Describe a given linear transformation as a vector in Cartesian coordinates.

Substitute values into formulae for the area or volume of various geometric objects.