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Write down your both your working and the answers. When you have finished, check the answers but also look at the working to see if you are going about problems in the most effective way!

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Algebra

1) Factorise completely 120x2 - 10x - 5

 

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?

 

Indices

3) Evaluate 80.5 * 16-0.5

 

Irrational numbers

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

 

Circle theorems

5) Prove that the alternate segment theorem is always true

 

Simultaneous equations

6) Solve by substitution:

2x2 + 3y = 7

5x + y - 2 = 3

 

Equations of circles

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

 

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 ?

 

Rearranging equations

9) Make r the subject of the following equation

F-r = mv2r + mr + m

 

Sampling

10) State one advantage and one disadvantage of systematic sampling

 

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!

 

Proof

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

 

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?

 

Trigonometric functions

14) Write down the cosine rule for finding side lengths

 

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

 

EXTRA!

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

 

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