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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

### 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

Ex. 0:

A sequence has the following terms: u_{4}= 0.04, u

_{5}= 0.01, u

_{6}= 0.00, u

_{7}= 0.00, u

_{8}= 0.00, u

_{9}= 0.00, ...

What type of sequence is it? Find the first term and the common difference/ratio, and hence the 15

^{th}term (a

_{15}).

[Geometric, u

_{1}= 17.00, r = 0.13, u

_{15}= 0.00]

Ex. 1:

A geometric sequence has the following terms: u_{5}= 0.010, u

_{6}= -0.002, u

_{7}= 0.000, u

_{8}= -0.000, u

_{9}= 0.000, u

_{10}= -0.000, ...

Find the first term and the common ratio, and hence the sum to infinity (S

_{inf}) of the series.

[u

_{1}= 6.00, r = -0.20, S

_{inf}= 5.00]

Ex. 2:

A geometric sequence has the following terms: u_{4}= -0.019, u

_{5}= -0.002, u

_{6}= -0.000, u

_{7}= -0.000, u

_{8}= -0.000, u

_{9}= -0.000, ...

Find the first term and the common ratio, and hence the sum to infinity (S

_{inf}) of the series.

[u

_{1}= -14.00, r = 0.11, S

_{inf}= -15.75]

Ex. 3:

A sequence has the following terms: a_{6}= -38, a

_{7}= -45, a

_{8}= -52, a

_{9}= -59, ...

What type of sequence is it? Find the first term and the common difference/ratio, and hence the 17

^{th}term (a

_{17}).

[Arithmetic, a

_{1}= 4, d = -7, a

_{17}= -108]

Ex. 4:

A sequence has the following terms: a_{8}= -114, a

_{9}= -126, a

_{10}= -138, a

_{11}= -150, ...

What type of sequence is it? Find the first term and the common difference/ratio, and hence the 34

^{th}term (a

_{34}).

[Arithmetic, a

_{1}= -18, d = -12, a

_{34}= -414]

Ex. 5:

A geometric sequence has the following terms: u_{4}= 0.020, u

_{5}= 0.003, u

_{6}= 0.000, u

_{7}= 0.000, u

_{8}= 0.000, u

_{9}= 0.000, ...

Find the first term and the common ratio, and hence the sum to infinity (S

_{inf}) of the series.

[u

_{1}= 7.00, r = 0.14, S

_{inf}= 8.17]

Ex. 6:

A sequence has the following terms: a_{6}= 62, a

_{7}= 70, a

_{8}= 78, a

_{9}= 86, ...

What type of sequence is it? Find the first term and the common difference/ratio, and hence the 50

^{th}term (a

_{50}).

[Arithmetic, a

_{1}= 14, d = 8, a

_{50}= 406]

Ex. 7:

A sequence has the following terms: a_{6}= 25, a

_{7}= 27, a

_{8}= 29, a

_{9}= 31, ...

What type of sequence is it? Find the first term and the common difference/ratio, and hence the 33

^{th}term (a

_{33}).

[Arithmetic, a

_{1}= 13, d = 2, a

_{33}= 77]

Ex. 8:

A sequence has the following terms: u_{4}= 4.44, u

_{5}= 2.96, u

_{6}= 1.98, u

_{7}= 1.32, u

_{8}= 0.88, u

_{9}= 0.59, ...

What type of sequence is it? Find the first term and the common difference/ratio, and hence the 14

^{th}term (a

_{14}).

[Geometric, u

_{1}= 15.00, r = 0.67, u

_{14}= 0.08]

Ex. 9:

A sequence has the following terms: u_{3}= 0.52, u

_{4}= 0.10, u

_{5}= 0.02, u

_{6}= 0.00, u

_{7}= 0.00, u

_{8}= 0.00, ...

What type of sequence is it? Find the first term and the common difference/ratio, and hence the 15

^{th}term (a

_{15}).

[Geometric, u

_{1}= 13.00, r = 0.20, u

_{15}= 0.00]

### 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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