Summer Induction

Work

Deadline: Monday 11th

September

The Hazeley Academy

Further Maths

Further Mathematics

A Level Maths OCR (MEI): Further Pure Maths, Mechanics, Statistics

Objectives: To reinforce understanding of key GCSE algebraic skills in order to provide a firm foundation for

starting the A-Level Course.

Tasks

Solve the 12 questions in the Further Maths booklet.

You might not be able to do the questions immediately but don’t give up, think carefully about the

information given, writing simple algebraic expressions and formulae to represent it and then consider how

these expressions/formulae might be used to answer the question. If you still can’t do it after several

attempts, use the resources listed below to help you.

The deadline for completing and handing in this homework booklet is 11th September. The homework will be

marked and graded according the following scheme.

Grade A B C D E U

Grade threshold 80% 70% 60% 50% 40% Below 40%

Resources/Research

Use the notes provided in the A-level maths booklet along with resources such as www.mymaths.co.uk

(login: hazeley, password: angle), www.studymaths.co.uk, Mr Hegarty Maths and Mathswatch clips to

support your learning.

Wider Reading

If you are interested in some wider reading, the following books may be of interest:

Fermat’s Last Theorem – Simon Singh The Code Book – Simon Singh

Alex’s Adventures in Numberland – Alex Bellos Why Do Buses Come In Threes? – Rob Eastway

Submission Date

11th September 2017

Further Mathematics Summer Homework Question 1

Question 2

Prove that ( ) ( ) is a multiple of 4, for all positive integer values of (3 marks)

Further Mathematics Summer Homework

Question 3

Question 4

Prove algebraically that the difference between the squares of any two consecutive integers is equal to the sum of the two integers (4 marks)

Further Mathematics Summer Homework

Question 5

Further Mathematics Summer Homework

Question 6 The nth term of the so-called rectangle numbers is ( ) Prove that if you add two consecutive rectangle numbers and halve the answer, the result is always a square number (4 marks)

Question 7

AS Further Mathematics Summer Homework

Question 8

Further Mathematics Summer Homework

Question 9

Question 10

AS Further Mathematics Summer Homework

Question 11

By using the concept of the difference of two squares or otherwise, determine the smallest

value of n for which ( )( )( ) ( ) is a perfect square [3]

Question 12 I regularly travel a journey of 200 kilometres. When I travel by day, I average kilometres per hour. When I travel at night the traffic is not so bad so I can average 20 kilometres per hour faster. This means that I am able to complete the journey in 50minutes less time.

i) Write down expressions for the journey times during the day and at night [2]

ii) Hence form an equation in and show that it simplifies to [5]

(iii) Hence find the times it takes me to complete the journey during the day and at night [5]