Additional Maths GCSE Past Paper 2 2012

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General Certificate of Secondary Education
Additional Mathematics
Paper 2
Mechanics and Statistics
2 hours.
Write your Centre Number and Candidate Number on the Answer Booklet and the Supplementary
Answer Booklet provided.
Answer all twelve questions.
At the conclusion of the examination attach the Supplementary Answer Booklet to your Answer
Booklet using the treasury tag supplied.
The total mark for this paper is 100.
Figures in brackets printed down the right-hand side of pages indicate the approximate marks
awarded to each question or part question.
You may use your calculator.
A copy of the formulae list is provided.
Take g 5 10 m/s2 when required.

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Page 2

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Answer all twelve questions.
1 A particle rests in equilibrium at a point O on a smooth horizontal plane.
The particle is acted upon by four horizontal forces of magnitude 6N, 10N, RN and SN. The
direction of each of these forces relative to the horizontal axes Ox and Oy is shown in Fig. 1.
10 N 6N
O x
Fig. 1
(i)Show that R 5 11 [2]
(ii)Find the value of S.…read more

Page 3

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A stone of mass 0.45kg is released from rest on the surface of the water in a pond.
The water exerts a constant resistance of 3N.
(i)Show that the acceleration of the stone is m/s2.[3]
The stone takes 1.5 seconds to reach the bottom of the pond.
(ii) the speed with which the stone hits the bottom of the pond, [2]
(iii)the depth of the pond.…read more

Page 4

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Jordan recorded the number of points scored in each match by Jumpers basketball team
throughout the season.
The mean number of points scored for all 30 games was 36 and the standard deviation
was 8.2
The mean number of points scored for the 14 home games was 40 and the standard deviation
was 7.8
(i) the mean number of points scored for the 16 away games, [3]
(ii) the standard deviation for these 16 away games.…read more

Page 5

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There are 24 books on a bookshelf, 16 of which are poetry books and the rest are drama
Eighteen of the books on the shelf are paperback and 12 of these are poetry books.
The rest of the books on the shelf are hardback.
(i) Complete Table 3 in your Supplementary Answer Booklet to show the number of poetry
books and the number of drama books on this shelf. [1]
Two students each take a book at random from this shelf.…read more

Page 6

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A box of mass 8kg, initially at rest, is pulled in a straight line along a rough horizontal plane
by a light inextensible rope which is held parallel to the plane. The box moves with constant
After travelling 18m along the plane the box is moving with velocity 3m/s.
(i) Show that the acceleration of the box is 0.25m/s2. [1]
The tension in the rope is 26N, as shown in Fig. 4.
26 N
Fig.…read more

Page 7

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Benedict has a part-time job where he works the first weekend in each month. He recorded
how much he earned in tips each night, correct to the nearest pound. His results are
summarised in Table 4 below.
Table 4
Friday Saturday Sunday
August 17 42 25
September 18 46 29
October 20 49 32
November 22 52 33
These data have been plotted on the graph given in Fig. 6 in your Supplementary Answer
(i) Calculate appropriate moving averages to smooth the data.…read more

Page 8

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Two packages A and B of masses 5kg and mkg respectively, where m 5, are connected by
a light inextensible string which passes over a smooth pulley fixed to the ceiling of a store, as
shown in Fig. 7.
Fig. 7
The packages are held so that both parts of the string are hanging vertically with the string
taut. The system is released from rest and the magnitude of the acceleration of each package
during the subsequent motion is 2.5 m/s2.…read more

Page 9

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B rises after A strikes the platform, [2]
(vii)the time which elapses between A striking the platform and the string becoming taut
again. [2]
11 A car and a motorcycle are travelling in the same direction along a dual carriageway. At the
same instant they pass a sign warning them of a checkpoint ahead.
The car passes the warning sign at a speed of 20m/s, continues at this speed for 1 minute and
then decelerates uniformly to rest at the checkpoint.…read more

Page 10

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The total number of hours of sunshine and the total amount of rainfall, in mm, were recorded
in different areas of the United Kingdom last year. The results are given in Table 5.
Table 5
1364 1478 1644 1450 1364 1412 1538 1670
1260 1005 806 1244 1314 1056 780 599
(i) Find the rank orders for the numbers of hours of sunshine and the amounts of rainfall.[2]
(ii) Calculate Spearman's coefficient of rank correlation.…read more


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