## Maths GCSE: ALGEBRA Private tuition and homework help online anywhere in the world! http://schoolsuccess.co.uk

by Bob Foster
## 1. the language

### 1.1. term, equation, expression, formula

### 1.2. 4 rules

1.2.1. Add

1.2.2. Subtract

1.2.3. Multiply

1.2.4. Divide

### 1.3. brackets

1.3.1. factorising

1.3.1.1. linear

1.3.1.2. quadratic

## 2. simplifying expressions

## 3. Creating expressions

### 3.1. P pencils at 50p, plus R rulers at £1.2 cost £x

### 3.2. Perimeter of shape

### 3.3. Angle sum

## 4. formulae

### 4.1. substitution

4.1.1. Put brackets around each letter and substitute the number along with its sign if it is negative

4.1.2. Use BIDMAS when working out the answer

4.1.3. Be careful if you are substituting a negative number for a letter with a negative sign

### 4.2. rearranging

4.2.1. x appears twice

4.2.1.1. alone or with a coefficient

4.2.1.2. multiplied with another letter

4.2.2. squares & roots

4.2.3. complex fractions

## 5. solving linear equations

### 5.1. views

5.1.1. same to both sides

5.1.2. moving over

### 5.2. one x

### 5.3. two x

### 5.4. algebraic fractions

### 5.5. brackets

### 5.6. graphs

## 6. simultaneous equations

### 6.1. two linear

6.1.1. substitution

6.1.2. subtraction

6.1.3. addition

6.1.4. graphical

### 6.2. linear and quadratic

6.2.1. regular quadratic

6.2.2. graphical

6.2.3. circle equation

6.2.3.1. points of intersection

## 7. inequalities

### 7.1. simple

### 7.2. complex

### 7.3. number line

### 7.4. graphs

## 8. quadratics

### 8.1. graphs

8.1.1. simple plotting

8.1.2. using a graph to solve a different equation

### 8.2. definition

8.2.1. general formula

8.2.2. types

8.2.2.1. a, b, c

8.2.2.2. a, b only

8.2.2.2.1. simple factorisations

8.2.2.3. a, c only

8.2.2.3.1. difference of two squares

### 8.3. factorising

### 8.4. solving by factorisation

### 8.5. solving

8.5.1. solving by trial and error

8.5.2. the formula

8.5.2.1. Understanding the formula

8.5.2.2. what you can find out using the formula

8.5.2.2.1. how many roots?

8.5.2.2.2. symmetry line

8.5.2.2.3. max and min

8.5.3. completing the square

8.5.3.1. to solve

8.5.3.2. to rearrange

## 9. trial and improvement

### 9.1. Start by choosing a value in the middle of the given range

### 9.2. Substitute this value into the expression and compare it to the given answer

### 9.3. Label each trial 'too high', or 'too low'

### 9.4. Keep changing the value of x until you have two value - one just above and one just below the answer given

### 9.5. Find the average of these two

9.5.1. the answer is the closest to this average

### 9.6. Only try values of x to the number of decimal places suggested

## 10. Checking

### 10.1. does your answer work?

### 10.2. Why you should always check

10.2.1. learn mental maths

10.2.2. good habit

## 11. Graphs

### 11.1. y=mx+c

11.1.1. all variations of m and c

11.1.2. parallel lines

11.1.2.1. perpendicular lines

### 11.2. real-life graphs

11.2.1. filling a container

11.2.2. speed

11.2.2.1. s/d

11.2.2.2. v/t

### 11.3. gradient

11.3.1. rel

11.3.1.1. tangent

11.3.1.2. ratio

### 11.4. transformations