Paper Reference(s) 7361/02 London Examinations GCE

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7361/02London Examinations GCEMathematics Syllabus BOrdinary LevelPaper 2Thursday 13 January 2011 – MorningTime: 2 hours 30 minutes

Materials required for examination Items included with question papersNil Nil

Candidates are expected to have an electronic calculator when answering this paper.

Paper Reference

7 3 6 1 0 2

This publication may be reproduced only in accordance with Edexcel Limited copyright policy.©2011 Edexcel Limited.

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N36657AW850/U7361/57570 6/4/6/6/6

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Instructions to CandidatesIn the boxes above, write your centre number, candidate number, your surname, initials and signature. Check that you have the correct question paper.Answer ALL the questions. Write your answers in the spaces provided in this question paper.If you need more space to complete your answer to any question, use additional answer sheets.

Information for CandidatesThe marks for individual questions and the parts of questions are shown in round brackets: e.g. (2).Full marks may be obtained for answers to ALL questions.There are 11 questions in this question paper. The total mark for this paper is 100. There are 24 pages in this question paper. Any blank pages are indicated.

Advice to CandidatesWrite your answers neatly and legibly.

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1.

Figure 1

In Figure 1, O is the centre of the circle BCD. The tangent to the circle at D is ADE and ABOC is a straight line.

Given that CAD = 60°, calculate the size, in degrees, of CDE.(3)

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___________________________________________________________________________ Q1

(Total 3 marks)

A60°

B

C

O

D E

Diagram NOTaccurately drawn


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2. In a class of 35 boys, 20 play football (F ), 16 play cricket (C ) and 7 do not play eitherfootball or cricket.

The number of boys who play both football and cricket is x.

(a) Complete the Venn diagram, using x where necessary, to show this information.(3)

Figure 2

(b) Find the value of x.(2)

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___________________________________________________________________________ Q2

(Total 5 marks)

E

CF


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3.

Figure 3

Figure 3 shows a toy made from a solid right circular cylinder of radius 2.5 cm and height 9 cm.A right circular cone of radius 2.5 cm is attached to one end of the cylinder.The height of the cone is 6 cm.

Calculate the total surface area, in cm2 to 3 significant figures, of the toy.(4)

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Curved surface area of a right circular cone = π rl⎡

⎣

⎢⎢⎢

Curved surface area of a right circular cylinder = 2π rh

⎡

⎣

⎢⎢⎢

Area of circle = πr 2

9 cm

6 cm

2.5 cm



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Question 3 continued

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4. A map is drawn to a scale of 1 : 20 000

On the map, a road has a length of 1.5 cm.

(a) Calculate the actual length, in m, of the road.(2)

The actual length of a sea wall is 1.2 km.

(b) Calculate the length, in cm, of the wall on the map.(2)

The actual area of a field is 60 000 m2.

(c) Calculate the area, in cm2, of the field on the map.(3)

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5. A =

3 2x y

⎛⎝⎜

⎞⎠⎟

, B = 1 4y x

⎛⎝⎜

⎞⎠⎟

, C = 20

13

⎛⎝⎜

⎞⎠⎟

, D = 54

156

⎛⎝⎜

⎞⎠⎟

.

Given that A + BC = D , calculate the value of x and the value of y.(8)

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6.

Figure 4

Figure 4 shows a fair, circular spinner with 4 sectors numbered 1, 2, 3 and 4. The angle of sector 1 is 120°, the angle of sector 2 is 60° and the angle of each of sectors 3 and 4 is 90°.The spinner is to be spun. The number of the sector in which the spinner’s pointer stops is called the score.

Calculate the probability that the score is

(a) 1(1)

(b) 1 or 3(2)

The spinner is now to be spun twice.

(c) Calculate the probability of a score of 2 with the first spin and then a score of 4 with the second spin.

(2)

When the spinner is spun twice, the total score is the sum of the two scores, so in part (c), the total score is 2 + 4 = 6

(d) Calculate the probability of a total score of 5 from two spins.(4)

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1

120°

60°

2

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7.

Figure 5

Figure 5 shows a parallelogram OACB. The vector OA = a and the vector OB = b P is the point on OA such that OP : PA = 1 : 4

(a) Find in terms of a and b or a or b,

(i) PA , (ii) AB.(2)

Q is the point on AB such that AQ : QB = 4 : 5

(b) Find in terms of a and b or a or b and simplify where possible,

(i) AQ , (ii) PQ , (iii) QC .(5)

(c) Hence show that PQC is a straight line.(4)

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A C

BO

P

b

Q Diagram NOTaccurately drawn


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8. The points A(1, 1), B(2, 3) and C(3, 2) are the vertices of ∆ABC.

(a) On the grid using a scale of 1 cm for 1 unit on each axis, draw and label ∆ABC.(1)

S = 20

11

⎛⎝⎜

⎞⎠⎟

∆ABC is transformed to ∆A1B1C1, where A1 , B1 and C1 are respectively the images of A, B and C under the transformation with matrix S.

(b) (i) Find the coordinates of A1 , B1 and C1 .

(ii) Draw and label ∆A1B1C1 .(3)

T = 01

21−

⎛⎝⎜

⎞⎠⎟

∆A1B1C1 is transformed to ∆A2B2C2, where A2 , B2 and C2 are respectively the images of A1 , B1 and C1, under the transformation with matrix T.

(c) Draw and label ∆A2B2C2 .(3)

An enlargement, centre O, followed by a rotation about O transforms ∆ABC to ∆A2B2C2 .

(d) Find

(i) the scale factor of the enlargement,

(ii) the angle of the rotation.(3)

(e) Find the matrix for the transformation that maps ∆ABC to ∆A2B2C2 .(2)

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___________________________________________________________________________ Q8

(Total 12 marks)

3

4

y

x

1

1 2 3 4 5 6 7 8 9

2

0

–6

–5

–4

–3

–2

–1

–7


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9. A stone is thrown from the top of a cliff. The height, h metres, of the stone above the seat seconds after it was thrown is given by h = 30 + 7t – t 2, t 0.

(a) Find how long it takes the stone to reach the sea.(2)

(b) Complete the table for h = 30 + 7t – t 2, giving your answers to 1 decimal place where necessary.

t 0 1.5 2.5 3 4 4.5 5.5 6

h 30 41.3 42 36

(3)

(c) On the grid, plot the points from your completed table and join them to form a smooth curve.

(3)

(d) Find from your graph the time, in seconds to one decimal place, when the stone is at its greatest height above the sea.

(1)

(e) Use your graph to find the speed, in m/sec to the nearest m, of the stone when it is first 40 m above the sea.

(2)

(f) Using your graph, write down the interval of time during which the stone is more than 40 m above the sea.

(2)

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Q9

(Total 13 marks)

h

t

40

45

50

10 2 3 4 5 6

35

30


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10.

Figure 6

Figure 6 shows a symmetrical trapezium with AD = 18x cm, BC = 10x cm and BA = CD = L cm.

The perpendicular distance between AD and BC is 3x cm.

Find an expression, in terms of x, for

(a) L,(2)

(b) the area of ABCD in cm2.(2)

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B C

DA 18x cm

10x cm

3x cm L cm Diagram NOTaccurately drawn


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Figure 7

Figure 7 shows a solid resting on a horizontal plane APSD. Faces ABCD and PQRS are identical symmetrical trapezia and are vertical. Faces ABQP, DCRS, BQRC and APSD are rectangles in which AP = BQ = CR = DS = y cm.

The total surface area of the solid is 1008 cm2.

(c) Show that y = 1008 8438

2− xx

.(3)

(d) The volume of the solid is V cm3. Show that V = 2119

x (1008 – 84x 2).(2)

(e) Find the value of x for which V is a maximum.(5)

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[ Area of a trapezium 12

(a + b)h ]

B

P

Q R

S

DA

C

18x cm

10x cm

10x cm

3x cm L cmL cm

L cm

y cm



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11.

Figure 8

In Figure 8, triangles ABE, BEC and ECD are right-angled triangles so that AED is a straight line.

ABE = BEC = ECD = 90° and CDE = 35°AB = 3 cm and ED = 2 cm.

Calculate the length, in cm to 3 significant figures, of

(a) CE,(2)

(b) BE,(2)

(c) BC.(2)

(d) Calculate the size, in degrees to the nearest degree, of BCE .(2)

The lines BC and AED are extended to meet at P.

(e) Calculate the size, in degrees to the nearest degree, of BPA .(2)

(f) Calculate the length, in cm to 3 significant figures, of AP.(4)

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B

C

DE 2 cm

35°

3 cm

A



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TOTAL FOR PAPER: 100 MARKS

END

Q11

(Total 14 marks)


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Paper Reference(s) 7361/02 London Examinations GCE