ujianmathf3.kem mate.docx

7/30/2019 ujianmathf3.kem mate.docx

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KEM SEHARI CERIA MATEMATIK

NAMA : ......................................................................

TAJUKMARKAH

PENUH

MARKAH

DIPEROLEHI

GEOMETRICAL CONSTRUCTION 16

LOCI IN TWO DIMENSIONS 15

TRANSFORMATIONS 6

GRAPH OF FUNCTIONS 4

STATISTICS 7

JUMLAH 48

UJIAN PENGESANAN MATEMATIK KERTAS 2 PMR 2012

11 OGOS 2012


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MODUL PECUTAN AKHIR PMR, SMK. GUNUNG RAPAT

MATHEMATICS PAPER 2

2

1.Set squares and protractors are not allowed for part (a) of this question.Diagram 4 shows triangle PQR.

DIAGRAM 4

(a) Using only a ruler and a pair of compasses, construct triangle PQR using themeasurement given, beginning from the straight line PQ provided in the answer

space.

(b) Based on the diagram constructed in (a), measure PRQ by using a protractor.

[5 marks]

Answer :

(a)

(b)

Diagram 4

6 cm

120o

R

QP

QP


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MATHEMATICS PAPER 2

4

3.Set square and protractors are not allowed for this question.Diagram 2 in the answer space shows a straight line AB.

(a) Using only a ruler and a pair of compasses,

(i) construct a triangle ABC beginning from a straight line AB such that BC = 6 cmand AC = 5 cm,

(ii) hence, construct the perpendicular line to the straight line AB passes through thepoint C.

(b) Based on the diagram constructed in (a), measure the perpendicular distancebetween point C and the straight line AB.

[6 marks]

Answer :

A B

Diagram 2


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MATHEMATICS PAPER 2

5

4.Diagram 6 in the answer space shows a square PQRS drawn on a grid of equal squares withsize of 1 unit.

W, X and Y are three moving points in the diagram.

(a) W is the point which moves such that its equidistant from the straight lines PQ and PS.By using the letters in the diagram, state the locus of W.

(b) On the diagram, draw

(i) the locus for the point X that is constantly 5 units from the point P,

(ii) the locus for the point Y that is constantly 4 units from the straight line QR.

(c) Hence, mark with the symbol the intersections of the locus of X and the locus of Y.

[5 marks]

Answer:

P

S R

Q

Diagram 6


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MATHEMATICS PAPER 2

6

5.Diagram in the answer space shows an isosceles triangle PQR drawn on the grid of equalsquares with sides of 1 unit. X and Y are two moving points inside the triange PQR.

a) On diagram, drawi. The locus of point X which moves such that its distance is constantly 6 units from

the point Q.

ii. The locus of point Y which moves such that its distance is constantly 3 units fromthe line PQ.

b) Hence, mark with the symbol the intersection of the locus X and the locus Y.[5 marks]

Answer :

R

QP


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MATHEMATICS PAPER 2

7

6.Diagram in the answer space shows a square KLMN with sides of 6 units drawn on a grid of equal squares withside 1 unit. X, Y and Z are three moving points inside the square.

a) X is the point which moves such that it is always equidistant from point K and point M.

By using the letters in diagram, state the locus of X.

b) On diagram, draw

i) The locus of the point Y which moves such that it is always equidistant from the straight lines KL

and KN,

ii) The locus of point Z which moves such that its distance is constantly 2 units from point P,

c) Hence, mark with the symbol the intersections of the locus of Y and the locus of Z.

[5marks]

Answer :

(a)

(b)(i),(ii)

(c)

P

N M

LK


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MATHEMATICS PAPER 2

8

7. In Diagram, P is the image ofP under transformation M.[2 marks]

y

O 2 4 6

8

10

12

x

4

6

8

10

12

P

P '

2

Describe in full transformation M.

Answer :


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MATHEMATICS PAPER 2

9

8.Diagram in the answer space shows two quadrilaterals, ABCD and ABCD. ABCD is the image of ABCD undera reflection.

On the diagram in the answer space, draw the axis of reflection.

Answer :

[2 marks]

A

B

C D

A'

B'C'

D'

9.Diagram in the answer space shows object P and straight line MN drawn on a grid of equalsquares.

On Diagram 8 in the answer space, draw the image of P under a reflection in the straight

line MN. [2 marks]

Answer:

N

M

P


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MATHEMATICS PAPER 2

10

10. Table below shows the values of two variables, x and y, of a function.

x 2 1 0 1 2 3 4

y 32 18 8 2 0 2 8

The x-axis and y-axis are provided on the graph paper.

(a) By using the scale of 2 cm to 4 units, complete and label the y-axis.

(b) Based on Table 2, plot the points on the graph paper.

(c) Hence, draw the graph of the function. [4 marks]


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MATHEMATICS PAPER 2

11

11. Table 1 shows three activities participated by a group of 50 students.

Activities Number of students

Chess 24

Hockey MChoir 18

(a) Find the value of M

(b) Hence, represent all the data by drawing a bar chart in the answer space.

[4 marks]

Answer :

(a)

(b)

Table 1

Number ofstudents

ActivitiesChess Hockey Choir

28

24

20

16

12

8

4

0


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MATHEMATICS PAPER 2

12

[3 marks]

Answer :

a)b)

Hockey

Football

Tennis

Netball

Games Number of students

Hockey35

FootballP

Tennis40

Netball65

12. Table shows four games played by 200 students.

a) Find the value of pb) Hence, complete the bar chart in diagram in the answer

space by using the data in the table.

Number of students

70

60

50

40

30

20

10

0 Games

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