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If you can do these questions without looking at the answers then you are well on the way

to passing the exam.

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Two yachts leave from harbour H.

Yacht A sails on a bearing of 072°for 30 kilometres and stops.

Yacht B sails on a bearing of 140°for 50 kilometres and stops.

How far apart are the two yachts whenthey have both stopped?

Do not use a scale drawing.

140°

68° h

2 2= 30 +50 -2×30×50cos68° = 47.7kmh

SAS Cosine Rule

Bearing 072°

Bearing

140°

N

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72°

2 2 2=a +b -2×abcos(h)°h

A mug is in the shape of a cylinder withdiameter 10 cms and height 14 cms.

a) Calculate the volume of the mug.

b) 600 mls of coffee are poured in. Calculate the depth of the coffee in the cup.

2Volume r h 25 14Volume mls1100

2600 5 h

Let height be h cms

2

600

5h

cms7.64h

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The number of diagonals, d, in a polygon with n sides is given by the formula:

A polygon has 20 diagonals. How many sides does it have?

n(n-3)d=

2

What are we trying to find ? n

n(n-3)20 =

240 =n(n-3) 240 =n -3n

2n -3n- 40 =0 n-8 n+5 =0 n=8 or n=-5

Polygon has 8 sides

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In the diagram

Angle STV = 34°

Angle VSW = 25°

Angle SVT = Angle SWV = 90°

ST = 13.1 centimetres

Calculate the length of SW

SVsin34°=

13.1SV =13.1×sin34° cm=7.33

SWcos25°=

SVSW =7.33×cos25° cm=6.64

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The area of triangle ABCis 38 square centimeters.

AB is 9 centimetres andBC is 14 centimetres.

Calculate the size of the acute angle ABC

SAS Use Area = ½ a b sin Cneed to transpose

letters !!!138= ×9×14×sinB

238=63sinB

38sinB=

63

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2y=x +2x-8

y=0 2-4 -1

when x = -1 2y=(-1) +2(-1)-8 y=-9

(-1, -9)

min t.p. = (-1, -9)

when x = 0 2y=0 +2(0)-8 y=-8 y-intercept = (0, -8)

Find points where curve cuts the axesand co-ordinates of minimum turning point.

x-2 x+4 =0x -2=0 x =2

x+4 =0 x =-4

2x +2x-8=0

Axis of symmetry is between the roots x = -1

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y=k(x - a)(x -b)

The diagram shows part of the graph of aquadratic function, with equation of the form

The graph cuts the y-axis at (0, -6) andthe x-axis at (-1, 0) and (3, 0)a) Write down the values of a and b.

b) Calculate the value of k.

c) Find the coordinates of the minimum turning point of the function a = -1 and b = 3

Choose a point on the curve (0, -6)

y=k x+1 x-3

-6=k 0+1 0-3 -6=-3k k =2

1

y=2 x+1 x-3 y=2 1+1 1-3 y=-8 1, -8

1, 8

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Two perfume bottles are mathematically similar in shape.The smaller one is 6 centimetres highand holds 30 millilitres of perfume.

The larger one is 9 centimetres high.What volume of perfume will the larger one hold.

Find the linear scale factor9 36 2

Since we are finding volume – scale factor is cubed

3 3 3 30×2730× × × = =101.25

2 2 2 8Volume = 101.25 mls

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A sheep shelter is part of a cylinder as

shown figure 1. It is 6 metres wide and 2

metres high. The cross-section of the shelter

is a segment of a circle with centre O, as

shown in Figure 2.

OB is the radius of the circle.

Calculate the length of OB. Pythagoras

rO

BM 3

r - 2

rr

22 2r =3 +r -2 2 2 2r =3 +r - 4r +4 4r =13 metresr =3.25

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a) A driver travels from A to B, a distance of x miles at a constant speed of 75 kilometres per hour. Find the time taken for the

journey in terms of x.

b) The time for the journey from B to A is hours. Calculate the

driver’s average speed for the whole journey. 50

x

D

S T

DT =

ST =

75x

hours

DS =

T

Distance = 2 x Total time = +50 75x x 3 2

= +150 150

x x 5=

150x

=30x

Speed = Distance TimeSpeed =

2 ÷30x

x 30=2x

x mph=60

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Fiona checks out the price of a litre of milk in several shops.The prices in pence are:49 44 41 52 47 43

a) Find the mean price of a litre of milk.

b) Find the standard deviation of the prices.

c) Fiona also checks out the price of a kilogram of sugar in the same shops and finds that the standard deviation of the prices is 2.6.

Make one valid comparison between the two sets of prices.

xx (x - x) 2x- x

49

44

41

52

47

43

276Mean =

276=46

6

3

-2

-5

6

1

-3

9

4

25

36

1

9

84

84=4.1

5Price of milk varies more than price of sugar 2x - x

s =n-1

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A microwave oven is sold for £150.

This price includes VAT at 17.5%

Calculate the price of the microwave oven without VAT.

Price without VAT 1.175 = £ 150

Price without VAT =150

1.175= £ 127.66

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Solve the equation2

2x -3x - 7 =0Give your answers correct to 1 decimal place.

Use the quadratic formula2-b± b - 4ac

x =2a

a = 2, b = -3, c = -72-(-3)± (-3) - 4(2)(-7)

x =2(2)

3± 65x =

4

3+ 65 3- 65x = or x =

4 4x =2.8 or x =-1.3

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