__Algebra__

**1) Factorise completely
120x**^{2} - 10x - 5

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__
Geometry__

**2) A hemispherical wine
glass of radius 6 cm is filled with wine to the brim. The wine is then poured
into a cylindrical bottle of radius 6 cm and height 20 cm. How high up the
bottle will the wine go?**

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__
Indices__

**3) Evaluate 8**^{0.5}
* 16^{-0.5}

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Irrational numbers__

**4) Write
0.123123123123123...... as a fraction**

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__
Circle theorems__

**5) Prove that the
alternate segment theorem is always true**

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Simultaneous equations__

**6) Solve by substitution:**

**2x**^{2} + 3y = 7

**5x + y - 2 = 3**

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Equations of circles__

**7) Write down the formula
for a circle of radius 9cm centred on the origin**

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Proportionality__

**8) The gravitational field
strength of a planet is inversely proportional to the square of distance from
the centre. At a distance of 100Km the field strength is 5 units. What will be
the field strength at a distance of 215Km ?**

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Rearranging equations__

**9) Make r the subject of
the following equation**

F-r = mv^{2}r + mr + m

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Sampling__

**10) State one advantage
and one disadvantage of systematic sampling**

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Probability__

**11) In the card game
POKER, the best hand you can possibly get is called a "royal flush"**

Calculate the probability
that I will get an Ace of Hearts, followed by a King of Hearts, followed by a
Queen of Hearts, followed by a Jack of Hearts, followed by a Ten of Hearts... IN
THAT ORDER!

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Proof__

**12) Prove that the sum of
any three consecutive integers is always a multiple of three**

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Accuracy and Error__

**13) I measured a table and
wrote down that it is 1.62 m long. What are the upper and lower bounds of this
measurement?**

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Trigonometric functions__

**14) Write down the cosine
rule for finding side lengths**

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Transformations__

**15) y = f(x) is
transformed into y = f(0.5*x). State the type of transformation and describe
what happens to the appearance of the line**

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EXTRA!__

**16) Show how to construct
an angle of exactly 60**^{o} using just a ruler, compass and pencil!