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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 geometric sequence has the following terms: u_{3}= -0.327, u

_{4}= 0.047, u

_{5}= -0.007, u

_{6}= 0.001, u

_{7}= -0.000, u

_{8}= 0.000, ...

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

_{inf}) of the series.

[u

_{1}= -16.00, r = -0.14, S

_{inf}= -14.00]

Ex. 1:

A sequence has the following terms: u_{4}= -0.64, u

_{5}= 0.23, u

_{6}= -0.09, u

_{7}= 0.03, u

_{8}= -0.01, u

_{9}= 0.00, ...

What type of sequence is it? Find the first term and the common difference/ratio, and hence the 16

^{th}term (a

_{16}).

[Geometric, u

_{1}= 13.00, r = -0.37, u

_{16}= -0.00]

Ex. 2:

A sequence has the following terms: u_{4}= -12.65, u

_{5}= 12.22, u

_{6}= -11.82, u

_{7}= 11.42, u

_{8}= -11.04, u

_{9}= 10.67, ...

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}= 14.00, r = -0.97, u

_{15}= 8.71]

Ex. 3:

A geometric sequence has the following terms: u_{5}= 0.070, u

_{6}= -0.018, u

_{7}= 0.004, u

_{8}= -0.001, 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}= 18.00, r = -0.25, S

_{inf}= 14.40]

Ex. 4:

A sequence has the following terms: u_{5}= -0.10, u

_{6}= -0.03, u

_{7}= -0.01, u

_{8}= -0.00, u

_{9}= -0.00, u

_{10}= -0.00, ...

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

^{th}term (a

_{17}).

[Geometric, u

_{1}= -19.00, r = 0.27, u

_{17}= -0.00]

Ex. 5:

A geometric sequence has the following terms: u_{3}= -2.250, u

_{4}= -1.125, u

_{5}= -0.563, u

_{6}= -0.281, u

_{7}= -0.141, u

_{8}= -0.070, ...

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

_{inf}) of the series.

[u

_{1}= -9.00, r = 0.50, S

_{inf}= -18.00]

Ex. 6:

A sequence has the following terms: a_{5}= 80, a

_{6}= 95, a

_{7}= 110, a

_{8}= 125, ...

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}= 5, d = 15, a

_{34}= 500]

Ex. 7:

A sequence has the following terms: a_{6}= -17, a

_{7}= -21, a

_{8}= -25, a

_{9}= -29, ...

What type of sequence is it? Find the first term and the common difference/ratio, and hence the 41

^{th}term (a

_{41}).

[Arithmetic, a

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

_{41}= -153]

Ex. 8:

A sequence has the following terms: u_{4}= -7.16, u

_{5}= -6.21, u

_{6}= -5.38, u

_{7}= -4.66, u

_{8}= -4.04, u

_{9}= -3.50, ...

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}= -11.00, r = 0.87, u

_{14}= -1.71]

Ex. 9:

A sequence has the following terms: a_{7}= -10, a

_{8}= -10, a

_{9}= -10, a

_{10}= -10, ...

What type of sequence is it? Find the first term and the common difference/ratio, and hence the 46

^{th}term (a

_{46}).

[Arithmetic, a

_{1}= -10, d = 0, a

_{46}= -10]

### 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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