Mathematics Oct 2012

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NATIONAL ASSESSMENT - FORM III

NAME

SCHOOL

CLASS/SECTION

MATHEMATICS October 2012Specimen Paper 1 hour 45 minutes

Students answer on the Question Paper.

READ THESE INSTRUCTIONS FIRST

Write your name, the name of your school and your class/section in the spaces provided above.

Write in dark blue or black pen.

You may use a soft pencil for diagrams or rough working.

Do not use correction fluid.

There are 21 questions in this paper.

Answerall questions.

If working is needed for any question it must be shown in the space below that question.

Omission of essential working may result in loss of marks.

Diagrams are not drawn to scale.

ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER

The number of marks is given in brackets [ ] at the end of each question or part question.

The total number of marks for this paper is 100.


2/172

1. Evaluate

(a) 81,Answer.. [1]

(b) 12 6 2 + 4,

Answer.. [1]

(c) 145.89 17.395.

Answer.. [1]

2.

(a) Write down the two next term in the sequence

3, 4 , 7, 11, 18, .

Answer , .. [1]

(b) Convert 2.625 kilograms into grams.

Answer.. [1]

(c) Convert 4.69 kilometres into metres.

Answer.. [1]

(d) Write down 175.836 correct to two decimal places.

Answer.. [1]

(e) Write down 75.384 correct to three significance figures.

Answer.. [1]


3/173

3.

(a) Express the ratio 42

3 1 1

3in its simplest form.

Answer.. : .... [1]

(b) Express1

8as a percentage.

Answer.. [1]

(c) Simplify

(i) 32

5

,

Answer.. [1]

(ii) 49 85.

Answer.. [1]

4.(a) Find the value of 1

3

4

6

21giving your answer as a fraction in its lowest term.

Answer.. [1]

(b) Given that vector = 815

, find

(i) ,

Answer.. [1]


4/174

(ii) ,

Answer.. [1]

(iii) given that = 52.

Answer.. [1]

5. A = 2 31 6 andB =

5 0

4 2 .

Find

(a) 2A + B,

Answer.. [2]

(b) AB

Answer.. [2]


5/175

6.

(a) Given that = 5 and = 3, find the value of 2

Answer.. [1]

(b) Factorise

(i) 62 9

Answer.. [1]

(ii) 362 81

Answer... [1]

7.(a) = {x:x is an integer between 1 and 15 inclusive}

A = {x:x is multiple of 5} andB = {x:x is a prime number}

(i) List the elements of

Answer... [1]

(ii) Find().

Answer.. [1]


6/176

(b) In a bag of 12 fruits, there are 3 oranges, 5 apples and the rest are mangoes. A

fruit is drawn at random from the bag. Expressing your answer as a fraction in

its simplest form, find the probability that the fruit chosen at random, is

(i) a mango.

Answer.. [1]

(ii) not an orange.

Answer.. [1]

8. Solve the simultaneous equations

4 3 = 103 + 5 = 7

Answer x = ..

y = .. [3]


7/177

9. A fair five-sided spinner numbered with the numbers 1, 2, 3, 4 and 5, is spun 20

times. The table shows the number of times that each possible score occurred.

For the above distribution, find the

(a) mode,

Answer.. [1]

(b) mean,

Answer.. [2]

(c) median.

Answer.. [2]

10.

(a) Solve the equation5

2+1 =10

31

Answer.. [2]

(b) Solve the inequality 3 4 < 2 + 15

Answer.. [2]

Score 1 2 3 4 5

Frequency 3 4 7 2 41

4 32


8/178

A

B

C

3x

20

x

60

A

B

21cm

O

11.

(a) The diagram shows a sector OAB of a circle with centre O and radius 21cm.

[Use = ]

Calculate

(i) The length of the arc AB.

Answer.. [2]

(ii) Area of the sector OAB

Answer.. [2]

(b) Each of the exterior angles of a regular polygon is 30

. Calculate the numberof sides in the polygon.

Answer.. [1]

(c) ABC is a triangle. Find the value ofx.

Answer.. [2]


9/179

12.

(a) Find the equation of the line passing through the points (1,3) and (4, 7).

Answer.. [2]

(b) Find the equation of the line parallel to the line = 3 + 2 and whichpasses through the (1, 2).

Answer.. [2]

(c) Makex the subject of formula in the equation

=

3+72

Answer.. [2]


10/1710

LadderWall2 m

50.2

13. A ladder rests against the top of a vertical wall making an angle of 53.1 with the

wall of 2.4m.

[. = . , . = . , . = . ]Using as much as of the given information as necessary,

(a) calculate the length of the ladder

Answer.. [3]

(b) calculate the horizontal distance from the foot of the wall to the foot of the

ladder.

Answer.. [2]

14.

(a) The profit of a business is shared among the three owners in the ratio 3:4:5.

The lowest share is Rs 6000. Calculate the total profit made by the business.

Answer.. [1]


11/1711

(b) 300 fruits are to be filled in boxes. Each box can be filled with a maximum of

24 fruits. What is the least number of boxes needed?

Answer.. [1]

(c) A shop sells some goods at Rs 56000 to make a loss of30%. Calculate the

price at which the goods were bought.

Answer.. [2]

(d) A man invested $ 3000 at 6% simple interest per year. Calculate how much

interest had been earned after 7 months.

Answer.. [1]

(e) A bank exchanged Mauritian Rupees (Rs) and UK pounds () at a rate of

1 = Rs 48. Calculate

(i) in Rupees, the amount received for 200.

Answer.. [1]

(ii) in pounds, the amount received forRs 1200.

Answer.. [1]


12/1712

A

B C

E

F

12

109

D

15. The diagram shows a solid prism ABCDEF with BC = ED = 12cm, A B = F E =

9cm, AF = BE = CD = 10cm andABC = D EF = 90.

(a) Calculate the length AC.

Answer.cm [1]

(b) Find the area of triangle ABC.

Answer.cm2 [1]

(c) Find the total surface area of the prism.

Answer.cm2 [3]

(d) Find the volume of the prism.

Answer.cm3 [2]


13/1713

16. A cylindrical tank, closed at both ends, has radius 7 cm and height 2 m.

(a) Find the volume of water, in cm3, given it is completely filled with water.

Answer.cm3 [3]

(b) Find the total surface area of the tank.

Answer.. [3]

2 m

7 cm


14/1714

2

+ 5 C

A B

D

17. ABCD is a rectangle with length AB = ( + 5)cm and width BC = ( 2)cm.The area of the rectangle is 8 cm2.

(a) Using the information above, form an equation inx and show that it reducesto 2 + 3 18 = 0.

[3]

(b) Solve the equation 2 + 3 18 = 0.

Answer =.. or =.. [3](c) Hence find length AB

Answer.. [1]


15/1715

North

North

C

A

B120

18. On a map, three villages are represented by A, B and C. ABC is a right-angled

triangle with ABC = 9 0and BAC = 4 0.

(a) Find ACB.

Answer.. [1]

(b) Find the bearing of B from A.

Answer.. [1]

(c) Find the bearing of C from B.

Answer.. [1]

(d) Find the bearing of A from C.

Answer.. [1]


16/1716

19.(a) Express 24 and 90 as the product of its prime factors

Answer = .. [1]

Answer = .. [1](b) Using the above results find

(i) the highest common factor of 24 and 90.

Answer.. [1]

(ii) the least common multiple of 24 and 90.

Answer.. [1]

(iii) The smallest integer, such that 24 is a square number.

Answer =.. [1](iv) The smallest integer, such that 90 is a square number.

Answer =.. [1]


17/17

120

45

Mauritius

Madagascar

Reunion

Rodrigues

20.(a) In an airports control tower, three different lights flash at intervals of 5, 8 and

10 minutes respectively. They flashed altogether at 08 00. At what time will

they next flash together?

Answer.. [2]

(b) Given that 2 + 2 = 425 and = 100, find the value of ( )2.

Answer.. [2]

21. A tourist visits countries Mauritius, Rodrigues,Madagascar and Reunion Island. The pie chartillustrates the number of days he visits each country.

Given that he spent 24 days in Mauritius, calculate

(a) the number of days he visited Rodrigues.

Answer.. [1]

(b) the total number of days he visited the four countries.

Answer.. [1]End of question paper

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Mathematics Oct 2012