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.

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.

A bag contains balls of three different colours. You're told how many there are of each, and asked the probability of picking a ball of a particular colour.

Choose the probability of getting a tails, from four options.

First part asks for the probability of rolling an even number. Second part asks for the probability of not rolling either of two given numbers.

Given the first four terms of a quadratic sequence, write down the formula for the $n^\text{th}$ term.

Given a formula for a sequence, calculate a given term.

Given the first three terms of a sequence, give a formula for the $n^\text{th}$ term.

In the first sequence, $d$ is positive. In the second sequence, $d$ is negative.

Given the common difference and first term of an arithmetic sequence, work out the index of the nth term of the sequence.

Framed as a word problem with ticket numbers in an ice cream shop.

The amount of money a person gets on their birthday follows an arithmetic sequence.

Calculate the amount on a given birthday, then calculate the sum up to that point.

Given the first and last terms of a finite arithmetic sequence, calculate the number of elements and then the sum of the sequence.

Each part is broken into steps, with the formula given.

Factorise a quadratic expression of the form $x^2+akx+bk^2$ for $x$, in terms of $k$. $a$ and $b$ are constants.

Given sequences with missing terms, find the common difference between terms.

Given arithmetic sequences with some terms missing, fill in the missing terms.

Given the first few terms of an arithmetic sequence, write down its formula, then find a couple of particular terms.

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

Find the inverse of a composite function by finding the inverses of two functions and then the composite of these; and by finding the composite of two functions then finding the inverse. The question then concludes by asking students to compare their two answers and verify they're equivalent.

Decide whether statements about square and cube numbers are always true, sometimes true or never true.

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

Calculate outcomes for different configurations of rolling two dice. 

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

In the first three parts, rearrange linear inequalities to make $x$ the subject.

In the last four parts, correctly give the direction of the inequality sign after rearranging an inequality.

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

Use a piecewise linear graph of speed against time to find the distance travelled by a car.

Finally, use the total distance travelled to find the average speed.

Apply and combine logarithm laws in a given equation to find the value of $x$.

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

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

Inequality involving a single absolute value, question solution uses the piecewise nature of the absolute value function.

Unit circle definition of sin, cos, tan using degrees

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