Table of Contents

 

 Unit 1 | Algebra

Page 1 | Expressions and Formulae

Page 2 | Index notation

Page 3| Solving Linear Equations

Page 4| Expanding and Factorising

Page 5| Factorising Quadratics and expanding double brackets

Page 6| Patterns and Sequences

Page 7| Simultaneous Equations

Page 8| Changing the subject of a Formula

Page 9| Adding , subtracting algebraic formulas

 Unit 2 |Graphs

Page 1 | Straight line graphs

Page 2 | Graphs of Quadratic functions

Unit 3 |Geometry and Measure

Page 1 | Transformations

Page 2 | Symmetry

Page 3 | Coordinates

Page 4 | Perimeter, Area, Volume

Page 5 | Circle geometry

Page 6 | Measurement

Page 7 | Trigonometry

Page 8 | Pythagoras

Page 9 | Angles

Page 10 | Shapes

Page 11| Time

Page 12 | Locus

Unit 4 | Numbers

Page 1 | Speed, Distance and time

Page 2 | Rounding and estimating

Page 3 | Ratio and proportion

Page 4 | Factors, Multiples and primes

Page 5 | Powers and roots

Page 6 | Decimals

Page 7 | Positive and negative numbers

Page 8 | Basic operations

Page 9 | Fractions

Page 10 | Percentages

Unit 5 | Statistics and Probability

Page 1 | Sampling data (MA)

Page 2 | Recording and representing data

Page 3 | Mean median range and mode

Page 4 | Standard deviation

Unit 4 | Calculus

Properties of Numbers


Differentiating between odd and even numbers is very simple.

All of the even numbers will end in 2, 4, 6, 8 or 0. Even numbers can all be divided by two.

All of the odd numbers will end in 1, 3, 5, 7 or 9.

People sometimes get confused between factors and multiples.

Factors of a specific number are the numbers that can fit into it exactly when multiplied.

For example, the factors of 20 would be 1, 2, 4, 5, 10 and 20. All of these numbers can be multiplied and fit exactly into 20.

When finding factors, you might find it easier to find them in pair. For 20, you could do this by realising that 2 x 10 = 20 so 2 and 10 are both factors.

Multiples are the numbers of a times table.

For example, the multiple of 6 would be 6, 12, 18, 24, 30 etc.

A prime number is a number that only has itself and 1 as its factors. 7 is a prime number because no number can multiply to make 7 other than 1 x 7.

A square number is a the answer when you multiply a number by itself. For example, 6 x 6 = 36 so, 36 is a square number.

A square root of a number is the number that needs to be multiplied by itself to get the number we have. So if we wanted find the square root of 36, it would be 6 because 6 multiplied by itself would become 36.

There are a few tricks in figuring out which numbers are in certain times tables.

Numbers divisible by 5 will end in 5 or 0

Numbers divisible by 3 will have digits that add up to a number divisible by 3 (eg 84 – 8 + 4 = 12 and 12is divisible by 3)

Numbers divisible by 9 will have digits that add up to a number divisible by 9 (eg 117 – 1 + 1 + 7 = 9 and 9 is divisible by 9)

Numbers divisible by 4 will have the last two digits divisible by 4 (eg 8724 – the last two digits are 24 and 24 is divisible by 4)

 

Properties of Numbers Exercise


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1) Complete this number so its a multiple of 8

5

 

 

2) Identify the number that are prime numbers.

11   6   14    19    41    77

 

 

3) Write a two digit odd number that a square number

 

 

4) Write down a number that has the factors 3 and

 

 

5) A shop marks 12732 pizzas every month.Pizzas are sold in packs of four.

a) Without dividing there will be no pizzas left over.
b) The shop decides to pack the pizzas into packs of five
Explain how you can check whether there will be any pizza left over.

 

 

6) Alex and kate count from 1 to 40. Alex jumps on every fourth number kate squals on every eight number. How many times will they jump and together ?

 

 

7) Circle all the number which are factors of 45.

5 7 11 10 3 8 9

 

 

8) Stephen says‘ I am thinking a number. My number is between 1 and 35. Its factors include 3 and 11. What’s Stephen’s number?

 

 

 

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