Transition to university

Solve a linear equation of the form $ax+b = c$, where $a$, $b$ and $c$ are integers.

The answer is always an integer.

This question tests the students ability to factorise simple quadratic equations (where the coefficient of the x^2 term is 1) and use the factorised equation to solve the equation when it is equal to 0.

Solve a simple linear equation algebraically. The unknown appears on both sides of the equation.

Calculate the interest accrued in a savings account, given the initial balance and annual interest rate.

Given five fractions, identify the one which is not equivalent to the others by reducing to lowest terms.

Given five fractions, identify the odd fraction out. The denominators are mainly two or three digits long.

Work with lower and upper bounds for estimates of weight.

Round numbers to a given number of significant figures.

Estimate the result of an arithmetic operation by first rounding numbers to given significant figures

Students are asked to estimate values in possible real-life scenarios.

Round numbers to a given number of decimal places.

Round some large integers to the a given power of ten.

Estimate whether you can afford an extra item in a shop by rounding prices to the nearest 10p.

Estimate the number of buckets of paint to buy, by rounding measurements of a room up to the nearest metre and estimating the total area.

Calculate relative frequencies in a variety of scenarios.

Given some coordinates, recognise which quadrant a point lies in, or which axis a point lies upon.

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

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.

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

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.

Given the probability that a basketball shot misses the hoop, find the probability that it's on target - use the law of total probability.

Determine whether outcomes are impossible or certain to occur.

A simple situational question about a box of chocolates, asking how many of each type there are, what percentage of the box they represent, the probability of picking one and ratios of different types.

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

This question involves matching images of graphings to descriptions of the relationships between variables.

This is a simple question testing the student on their ability to calculate the lowest common multiple of two integers which are: 

Part a) - coprime;

Part b) - where the greatest common divisor between the two integers is greater than one and not equal to either given number; and

Part c) - where one of the integer is a multiple of the other. 

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.

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.

Given a geometric sequence, find the common ratio (negative in this question), write down the formula for the nth term and use it to calculate a given term.