# 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