Transition to university

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

Questions to do with money.

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. 

Some questions to do with measures of distance and length.

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.

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.

Questions on geometric sequences.

Arithmetic operations involving fractions; converting between decimals and fractions; deciding if fractions are equivalent.

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. 

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.

This question tests the student's ability to identify the factors of some composite numbers and the highest common factors of two numbers. 

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

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

Questions asking you to find the equation of a line between two points, in Cartesian coordinates.

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

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

Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Work out the average percentage increase per year in price of an item, given two prices several years apart.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

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

Questions on the subtleties and pitfalls of methods of data collection.

Match up equations with the corresponding lines on a graph.

Some conceptual questions about parallel lines - fill in the gaps in some statements.

Identify the lines corresponding to given equations, and the lines parallel to lines with given equations.

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

Find the lowest common multiple and highest common factors of given numbers. Also a question on identifying prime numbers.

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

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