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## Physics and Maths Tuition and coaching for all - from GCSE through A-Level to Degree

## Now also coaching in GCSE/A-level Computer Science

### Proper, Improper and Mixed Fractions

### Fractional Arithmetic

### Changing the Subject of an Expression

### Multiplying Expressions

### Factorising Quadratic Expressions

Ex. 0:

-6 x

^{2}+ -6 x + -7 = 0=>

No real roots

(x -

6 + i √132

-12

) (x -

6 - i √132

-12

)

Ex. 1:

-3 x

^{2}+ 3 x + 0 = 0=>

(x -

0

-6

) (x -

-1

-1

)

Ex. 2:

1 x

^{2}+ 6 x + -8 = 0=>

(x -

-6 + √68

2

) (x -

-6 - √68

2

)

Ex. 3:

-3 x

^{2}+ 7 x + -6 = 0=>

No real roots

(x -

-7 + i √23

-6

) (x -

-7 - i √23

-6

)

Ex. 4:

-6 x

^{2}+ 9 x + 6 = 0=>

(x -

1

-2

) (x -

-2

-1

)

Ex. 5:

5 x

^{2}+ 3 x + -4 = 0=>

(x -

-3 + √89

10

) (x -

-3 - √89

10

)

Ex. 6:

2 x

^{2}+ 8 x + -2 = 0=>

(x -

-8 + √80

4

) (x -

-8 - √80

4

)

Ex. 7:

-6 x

^{2}+ 9 x + 0 = 0=>

(x -

0

-12

) (x -

-3

-2

)

Ex. 8:

-4 x

^{2}+ -2 x + -9 = 0=>

No real roots

(x -

2 + i √140

-8

) (x -

2 - i √140

-8

)

Ex. 9:

-4 x

^{2}+ 1 x + 4 = 0=>

(x -

-1 + √65

-8

) (x -

-1 - √65

-8

)

### Solving Linear Equations

### Rationalising the Denominator

### Solving Simultaneous (Linear) Equations

### Solving Simultaneous Quadratic Equations

### 2 and 3 Part Ratios

### Completing the Square

### Sequences and Series

### Polynomial Long Division

### Factor and Remainder Theorem

### Roots of a cubic

### Differentials

### Finding Turning Points

### Pythagorus

### Sine and Cosine Rules

### Vectors

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