Elliott Fletcher

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.

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.

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.

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

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.

This question aims to test understanding and ability to use the laws of indices.

This question aims to assess the student's understanding of the difference between biased and unbiased events and also to assess the student's understanding of the fact that the experimental probability tends towards the theoretical probability as the number of trials increases.

Calculate outcomes for different configurations of rolling two dice. 

Apply the factor theorem to check which of a list of linear polynomials are factors of another polynomial.

Calculate relative frequencies in a variety of scenarios.

Given results from a survey about what people eat for breakfast, where some people eat one or both of cereal and toast. Student is asked to pick the probability of eating either one or the other from a list. Distractors pick out common errors.

Represent a given probability to a decimal, fraction or percentage.

Determine whether outcomes are impossible or certain to occur.

Given descriptions of some pairs of random events, pick the ones which are mutually exclusive.

This question assesses the students understanding of what it means for two events to be independent or dependent. Specifically, if two events are independent then the outcomes of one event do not affect the outcomes of the other event.

This question tests the student's knowledge of the remainder theorem and the ways in which it can be applied.

Given a factor of a cubic polynomial, factorise it fully by first dividing by the given factor, then factorising the remaining quadratic.

Use a given factor of a polynomial to find the full factorisation of the polynomial through long division.

This question tests the student's ability to find remainders using the remainder theorem. 

Find the remainder when dividing two polynomials, by algebraic long division.

Present some given data in a frequency table.

This question assesses the student's ability to use some given information involving two different units of measurement to rewrite the information as a compound measure.

This question assesses the students ability to find the expected number of times an event occurs given the probability of the event occurring for a single trial and the total number of trials.

Calculate the density of an object given its mass and volume.

Basic probability skills involving coins, dice and other events with equally likely outcomes.