# Welcome to Physics and Maths.co.uk

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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:

5 x

^{2}+ -5 x + 6 = 0=>

No real roots

(x -

5 + i √95

10

) (x -

5 - i √95

10

)

Ex. 1:

6 x

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

No real roots

(x -

-2 + i √92

12

) (x -

-2 - i √92

12

)

Ex. 2:

9 x

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

(x -

0 + √72

18

) (x -

0 - √72

18

)

Ex. 3:

-2 x

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

No real roots

(x -

0

-4

) (x -

0

-4

)

Ex. 4:

-4 x

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

(x -

4 + √48

-8

) (x -

4 - √48

-8

)

Ex. 5:

-8 x

^{2}+ 5 x + -1 = 0=>

No real roots

(x -

-5 + i √7

-16

) (x -

-5 - i √7

-16

)

Ex. 6:

-7 x

^{2}+ -8 x + -3 = 0=>

No real roots

(x -

8 + i √20

-14

) (x -

8 - i √20

-14

)

Ex. 7:

3 x

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

No real roots

(x -

8 + i √32

6

) (x -

8 - i √32

6

)

Ex. 8:

1 x

^{2}+ -5 x + -8 = 0=>

(x -

5 + √57

2

) (x -

5 - √57

2

)

Ex. 9:

7 x

^{2}+ 5 x + 4 = 0=>

No real roots

(x -

-5 + i √87

14

) (x -

-5 - i √87

14

)

### 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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