1 candidate’s name ... maths replacement paper.pdf · 309/ii/13 candidate’s name:...

309/II/13 Candidate’s Name: ……………………………………………………………………………..

Candidate’s Examination Number: …………………………………………………………. Centre Number: …………………………………………………………………………………

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LESOTHO AND SWAZILAND EXAMINATIONS SYNDICATE JUNIOR CERTIFICATE EXAMINATION, OCTOBER 2013 MATHEMATICS - PAPER II (REPLACEMENT PAPER) TIME: 2½ Hours MARKS: 100 Additional materials: NONE INSTRUCTIONS: 1. Write your Name, Examination Number and Centre Number on the dotted line at

the top of each page. 2. Answer ALL questions in Section A and B. 3. All necessary working must be shown on the question paper. 4. Pencil should be used for drawing ONLY. 5. A calculator should NOT be used.

MARKS

SECTION A

SECTION B

12

13

14

15

16

17

TOTAL

This question paper contains 14 printed pages.



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Section A (40 Marks)

1. Mpho packed tins in the shop using the pattern shown in the diagram. Pattern 1 2 3 4 (a) Draw the number of tins that would be in pattern 4. (1) (b) How many tins would be in pattern 10? .................................................... (2) [3] 2. The logo of a company is in the shape shown.

(a) How many lines of symmetry does the shape have? ................................................... (1)

(b) What is the order of rotational symmetry of the shape?

.................................................... (1) [2]



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3. Nkau (N) bought a drink, tea, salt and bread while Topo (T) bought sugar, bread

and meat from the shop.

(a) Represent this information in the venn diagram shown. N T (2)

(b) List the items represented by NI∩T

.................................................... (1) [3]

4. Mrs Polo sells her radio M360. If she included 20% profit, calculate the cost price of the radio.

................................................... [3]

ε



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5. The length of a house measured to the nearest metre is 8 metres.

(a) Write the minimum and maximum possible lengths of the house.

minimum possible length………… m maximum possible length………….m (2)

(b) The width of the house is represented by the inequality

2.5 ≤ W < 3.5 What is the width of the house if it was measured correct to the nearest metre?

................................... (1) [3] 6. The diagram shows a road with two lanes, a pavement and a pedestrian crossing.

ABC = 120˚ and BD = 8m A B 120o

lane 1 lane 2 E D C pedestrian crossing (a) State angle .

= ………………………... (1)

(b) Calculate the distance BC and leave your answer in terms of .

BC = .................................. m (2) [3]

pavement

^



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7. The diagram shows a supported wheel and a rope turning around it. This is

used to collect water out of the toilet pit. AB is the diameter of 21cm. turning wheel

Use as

rope

300 cm Calculate the total length of the rope. ................................................ [3] 8. The diagram shows a lab-top lid at the position (A) when it is closed and at

its new position (B) when opened. lab-top lid opened turning point lab-top lid closed A B

Describe fully the transformation that maps the position of the lab-top lid when it is closed to its position when opened.

.......................................... [3]

A B

80 cm



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9. The diagram shows a box of fruit juice and its dimensions. NOT TO SCALE 30 cm fruit juice

8 cm 10 cm

(a) Calculate the total surface area of the box. (3)

(b) Calculate the amount of juice that can fill up the box. (2)

(c) If three people share this juice equally, what is the amount of juice would

each of them drink? .............................................. (2)

[7] 10. A cell-phone company charges M2.00 when one makes a call and then 30

cents for every minute. The equation represents this information where A is total charge in Maloti

and t is time in minutes. A = 0.3t + 2

(a) How much would be a total charge for a call which last 2 minutes?

............................................... (2)

(b) If Tefo wants to use all his M5.00 airtime, how long will his call last?

............................................... (3) [5]



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11. The pie-chart represents the number of different types of animals Mr. Mpo

has. NOT TO SCALE

cows sheep 120o 80o goats 70o

pigs

(a) What is the modal type of animal Mr. Mpo has?

............................................... (1)

(b) If the total number of animals is 150, calculate the number of sheep.

............................................... (2)

(c) What is the probability that an animal chosen at random is a goat?

............................................... (2) [5]



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SECTION B (60 Marks)

12. Mabea clinic recorded the number of boys who were circumcised in winter 2013 for different ages.

The table shows the results.

Age 12 13 14 15 16

Number of boys 3 8 12 2 5

(a) What is the modal age of boys who were circumcised.

............................................... (1)

(b) What is the median age?

............................................... (2)

(c) What is the probability that a boy chosen at random is 14 years? (simplify your answer)

............................................... (2)

(d) Calculate the total number of boys who were circumcised.

............................................... (2)



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(e) Draw a bar-chat to represent this information.

12 13 14 15 16 Age

(3) [10]

2

4

6

8

10

12 N

um

be

r o

f b

oy

s



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13. The diagram shows a house and a ladder leaning against the house. AB = 5m, BC = 3m, CE = 2m and EĈD = 30o. NOT TO SCALE 2m C 30O D 5m 3m A B G You may use this information Sin 30o = 0.5 Sin-1 = 36.9o Cos 30o = 0.866 Cos-1 = 53.1o

Tan 30o = 0.577 tan-1 = 31.0o

(a) Calculate the length (i) AB

...............................................m (2)

(ii) ED ...............................................m (2)

(b) Calculate the angle .............................................. (2)

(c) Write a trigometric ratio for angle ACB

............................................... (1)

(d) If the length of the house BG is 8 m, calculate the area of CHFE. (the roofing of the house).

...............................................m2 (3) [10]

H

E F



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14. The table shows the cost of goods bought and the profit made for every cost.

Cost (Maloti) 200 300 400 500 600 700 800

Profit (Maloti) 50 150 200 250 300 250 200

0 200 400 600 800 1000 1200

(a) Plot the results on the grid and join points to make a smooth curve. (3)

(b) Use the graph to determine the profit when the cost of goods was M460.

............................................... (1)

(c) Calculate the selling price when the cost was M400.

............................................... (2)

(d) What shape of the graph shows that the business was making good profit and later less profit? For good profit the graph is ........................................................................ (1) For less profit the graph is .......................................................................... (1)

(e) Calculate the percentage profit when the profit was M50.

............................................... (2) [10]

Cost (Maloti)

150

100

200

250

300

350

50

Pro

fit

(Mal

oti

)



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15. The table shows the scales used by an insurance company when a client is

insuring a new car.

Purchase price of a new car (VAT included)

Percentage of purchase price to be paid per year for insuring a car

M100 000 12%

M100 001 – M250 000 7%

M250 001 – M400 000 5%

M400 001 and above 4%

It is assumed that the car will travel 20 000km or less per year.

(a) Calculate the amount of money that would be paid per year for a car that is M100 000.

............................................... (2)

(b) How much would be the amount paid per month for a car which is M300 000? ............................................... (3)

(c) Mrs Mpolo bought a car ranging from M250 001 to M400 000 and pays M1500 per month. Calculate the amount she paid to buy the car. ............................................... (3)

(d) Calculate the total amount of money that Mrs Mpolo would have paid after 5 years.

............................................... (2) [10]



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16. The diagram shows the original position of the excavator at O and its new

position at OI. N S OI

O 0 1 2 3 4 5 6 7 8 9 10 11 12

(a) Describe fully the transformation that maps the excavator from O onto OI.

............................................... (3)

(b) When at a new position OI, the excavator was moved 2m East and 1m North. Draws the excabator after being moved and label it OII. (2)

(c) The excavator was used to make a pit at corners (8, 4), (8, 6), (10, 4) and (10, 6). Draw this pit using these points and label it P. (3)

(d) Calcuate the top surface area of the pit.

...............................................m2 (2) [10]

E W

1

2

3

4

5

6

7

8

9

10

Dis

tan

ce (

d2)

Distance (d1)



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17. The diagram shows a field and its corners A, B, C and D. The scale 1cm represent 5km. N D C A B

(a) What is the bearing of B from A?

............................................... (2)

(b) What is the actual distance of BC?

.............................................. (2)

(c) There is a tree in the field such that it is (i) equidistant from AB and AD,

(ii) equidistant from A and B.

Construct and mark the position of the tree with * and label it T. (5)

(d) Measure the angle ABC

............................................... (1) [10]

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1 candidate’s name ... maths replacement paper.pdf · 309/ii/13 candidate’s name:...

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