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### 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

**Warning**: Division by zero in

**/home/physandm/public_html/php/class.exercise.php**on line

**800**

Ex. 0:

A sequence has the following terms: a_{9}= -119, a

_{10}= -131, a

_{11}= -143, a

_{12}= -155, ...

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}= -11, d = -12, a

_{50}= -599]

Ex. 1:

A sequence has the following terms: u_{4}= -3.02, u

_{5}= -1.81, u

_{6}= -1.09, u

_{7}= -0.65, u

_{8}= -0.39, u

_{9}= -0.24, ...

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 = 0.60, u

_{15}= -0.01]

Ex. 2:

A sequence has the following terms: a_{6}= -59, a

_{7}= -69, a

_{8}= -79, a

_{9}= -89, ...

What type of sequence is it? Find the first term and the common difference/ratio, and hence the 58

^{th}term (a

_{58}).

[Arithmetic, a

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

_{58}= -569]

Ex. 3:

A sequence has the following terms: u_{3}= 1.21, u

_{4}= -0.32, u

_{5}= 0.09, u

_{6}= -0.02, u

_{7}= 0.01, u

_{8}= -0.00, ...

What type of sequence is it? Find the first term and the common difference/ratio, and hence the 13

^{th}term (a

_{13}).

[Geometric, u

_{1}= 17.00, r = -0.27, u

_{13}= 0.00]

Ex. 4:

A geometric sequence has the following terms: u_{5}= -0.160, u

_{6}= -0.053, u

_{7}= -0.018, u

_{8}= -0.006, u

_{9}= -0.002, u

_{10}= -0.001, ...

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

_{inf}) of the series.

[u

_{1}= -13.00, r = 0.33, S

_{inf}= -19.50]

Ex. 5:

A geometric sequence has the following terms: u_{5}= 0.004, 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}= 1.00, r = -0.25, S

_{inf}= 0.80]

Ex. 6:

A geometric sequence has the following terms: u_{5}= 0.500, u

_{6}= -0.250, u

_{7}= 0.125, u

_{8}= -0.063, u

_{9}= 0.031, u

_{10}= -0.016, ...

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

_{inf}) of the series.

[u

_{1}= 8.00, r = -0.50, S

_{inf}= 5.33]

Ex. 7:

A sequence has the following terms: u_{5}= 1.75, u

_{6}= 0.99, u

_{7}= 0.56, u

_{8}= 0.32, u

_{9}= 0.18, u

_{10}= 0.10, ...

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 = 0.57, u

_{15}= 0.01]

Ex. 8:

A geometric sequence has the following terms: u_{3}= 17.000, u

_{4}= 17.000, u

_{5}= 17.000, u

_{6}= 17.000, u

_{7}= 17.000, u

_{8}= 17.000, ...

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

_{inf}) of the series.

[u

_{1}= 17.00, r = 1.00, S

_{inf}= 0.00]

Ex. 9:

A sequence has the following terms: u_{4}= 0.07, 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 14

^{th}term (a

_{14}).

[Geometric, u

_{1}= -9.00, r = -0.20, u

_{14}= 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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