**Table of Contents**

** Unit 1 | Algebra**

Page 1 | Expressions and Formulae

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 2 | Symmetry

Page 3 | Coordinates

Page 4 | Perimeter, Area, Volume

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 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 **

*Simultaneous Equations *

**L.O To be able to solve equations with 2 different variables by satisfying both equations in the problem **

When we looked at Linear Equations we were simply working the value of the term in the problem. Notice they were all something like 4p + 10 = 5p – 2 both containing “p” so we could easily solve the problem. What if you received a problem like 4x + y = 15 & 2x + 3y = 10 . How would you tackle this when you would still have the variables “x” and “y” left at the end? This is where simultaneous equations come in.

**Example 1:** Solve the simultaneous equations

**Example 2 : **Solve the simultaneous equations

**Example 3 : **Solve the simultaneous equations

**Example 4 : **Solve the simultaneous equations

__Writing Simultaneous Equations__

In many problems you will also have to write out the simultaneous equations out themselves. These can be more challenging at the start but is simply algebraic equations with a context.

__Word Problems__

a) Alison goes stationary shopping before university. She buys 7 sharpeners and 4 rubbers that cost her £5.00, and then she buys 3 sharpeners and 2 rubbers that cost her £2.00. Work out the cost of a sharpener and rubber each and calculate how much it would be to buy 5 sharpeners and 6 rubbers.

b) Billy is going to university and is taking large boxes (x) and small boxes (y) . He wants to know if they will all fit on his wall. When he **takes away the length of a small box from a large box** he gets 2m. However when **he stacks 2 large boxes and 1 small **box he gets a total of 10m. Work out the length of a small box and a large box and how many of each he could fit on an **8 m wall**.

**He can fit 4 small boxes and 2 large boxes**

c) Ellie is collecting stamps and coins. She places them all on a page in her book. She rearranges one of the lines by **taking off 2 coins**, so she is only left with **6 stamps** which comes to a total of **33 cm**. On another line she places **4 stamps and 3 coins** ; and this comes to **9 cm**. Work out the theoretical length of a stamp and a coin. If the length of a page in her book is **50 cm** how many of stamps could she stick on the page.

**She can fit 11 stamps**

c)Mark is playing video games. His characters is collecting gold and silver which his character sells for money. On level 1 he sold **4 gold coins and 3 silver** coins for **3 dollars**. On level 2 however he sold **6 gold coins and 5 silver coins** for **7 dollars**. Work out the gamin value of each silver coin and gold coin. How much can he earn if on level 3 he gains **3 gold coins and 6 silver coins**?

**27 dollars**