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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_{4}= -0.128, u

_{5}= -0.026, u

_{6}= -0.005, u

_{7}= -0.001, 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}= -16.00, r = 0.20, S

_{inf}= -20.00]

Ex. 1:

A sequence has the following terms: a_{9}= 109, a

_{10}= 122, a

_{11}= 135, a

_{12}= 148, ...

What type of sequence is it? Find the first term and the common difference/ratio, and hence the 39

^{th}term (a

_{39}).

[Arithmetic, a

_{1}= -8, d = 13, a

_{39}= 486]

Ex. 2:

A geometric sequence has the following terms: u_{5}= -0.007, u

_{6}= -0.001, 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}= -9.00, r = 0.17, S

_{inf}= -10.80]

Ex. 3:

A sequence has the following terms: u_{5}= -0.00, u

_{6}= -0.00, u

_{7}= -0.00, 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 15

^{th}term (a

_{15}).

[Geometric, u

_{1}= -7.00, r = 0.10, u

_{15}= -0.00]

Ex. 4:

A sequence has the following terms: a_{3}= 38, a

_{4}= 55, a

_{5}= 72, a

_{6}= 89, ...

What type of sequence is it? Find the first term and the common difference/ratio, and hence the 18

^{th}term (a

_{18}).

[Arithmetic, a

_{1}= -13, d = 17, a

_{18}= 276]

Ex. 5:

A sequence has the following terms: a_{7}= -30, a

_{8}= -34, a

_{9}= -38, a

_{10}= -42, ...

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}= -2, d = -4, a

_{46}= -182]

Ex. 6:

A sequence has the following terms: a_{10}= -11, a

_{11}= -14, a

_{12}= -17, a

_{13}= -20, ...

What type of sequence is it? Find the first term and the common difference/ratio, and hence the 40

^{th}term (a

_{40}).

[Arithmetic, a

_{1}= 19, d = -3, a

_{40}= -98]

Ex. 7:

A geometric sequence has the following terms: u_{5}= 0.002, u

_{6}= 0.000, 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}= 12.00, r = 0.11, S

_{inf}= 13.50]

Ex. 8:

A sequence has the following terms: a_{4}= 7, a

_{5}= 6, a

_{6}= 5, a

_{7}= 4, ...

What type of sequence is it? Find the first term and the common difference/ratio, and hence the 26

^{th}term (a

_{26}).

[Arithmetic, a

_{1}= 11, d = -1, a

_{26}= -14]

Ex. 9:

A geometric sequence has the following terms: u_{3}= 0.111, u

_{4}= -0.012, u

_{5}= 0.001, u

_{6}= -0.000, 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}= 9.00, r = -0.11, S

_{inf}= 8.10]

### 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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