# 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:

-4 x

^{2}+ 3 x + -1 = 0=>

No real roots

(x -

-3 + i √7

-8

) (x -

-3 - i √7

-8

)

Ex. 1:

-2 x

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

No real roots

(x -

2 + i √68

-4

) (x -

2 - i √68

-4

)

Ex. 2:

8 x

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

(x -

7 + √241

16

) (x -

7 - √241

16

)

Ex. 3:

8 x

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

(x -

0

16

) (x -

-1

8

)

Ex. 4:

-7 x

^{2}+ 7 x + 9 = 0=>

(x -

-7 + √301

-14

) (x -

-7 - √301

-14

)

Ex. 5:

5 x

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

No real roots

(x -

-8 + i √56

10

) (x -

-8 - i √56

10

)

Ex. 6:

-4 x

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

(x -

5 + √105

-8

) (x -

5 - √105

-8

)

Ex. 7:

1 x

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

No real roots

(x -

-3 + i √7

2

) (x -

-3 - i √7

2

)

Ex. 8:

7 x

^{2}+ 1 x + 7 = 0=>

No real roots

(x -

-1 + i √195

14

) (x -

-1 - i √195

14

)

Ex. 9:

9 x

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

No real roots

(x -

-7 + i √23

18

) (x -

-7 - i √23

18

)

### 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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