Maths Ppsmi 2006 F4 P2

Form Four

1449/2 Mathematics

Paper 2 October

2006

hours12 JABATAN PELAJARAN NEGERI

NEGERI SEMBILAN DARUL KHUSUS

Name : ………………………………… Form : …………………………………

2

PPSMI ASSESSMENT 2

MATHEMATICS Paper 2 Two hours and thirty minutes DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO

1 This question paper consists of two sections, Section A and Section B. Answer all questions in Section A and four questions in Section B.

2 Write your answers clearly in the spaces provided

in the question paper. 3 Write in blue / black pen. You may use a pencil for

diagrams or graphs. 4 The marks allocated are given in brackets at the

end of each question or part question. 5 Diagrams in the question paper are not drawn to

scale unless stated. 6 Show all your working. Omission of essential

working will result in loss of marks. 7 You are allowed to use non-programmable

calculators. 9 This question paper must be handed in at the end of the examination.

This question paper

Panel Pakar Runding GC MMMT

https://panelmathsad

006

For examiner’s use only

Section Question Total Marks

Marks Obtained

1 3 2 4 3 4 4 6 5 4 6 5 7 5 8 4 9 5 10 6

A

11 6 12 12 13 12 14 12 15 12

B

16 12 Total

has 26 printed pages [Turn Over

dmathswordpress.com/

2

The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used.

RELATIONS 1 am × an = am+n

2 am ÷ an = am−n

3 (am) n = amn

4 ⎟⎟⎠

⎞⎜⎜⎝

⎛−

−−

=−acbd

bcad1A 1

5 )S(n)A(n)A(P =

6 P(A’) = 1 − P(A)

7 Distance = 221

221 )yy()xx( −+−

8 Midpoint

(x, y ) = ⎟⎠⎞

⎜⎝⎛ ++

2yy,

2xx 2121

9 Average speed = takentimetravelledcetandis

10 Mean = dataofnumber

dataofsum

11 Mean = sfrequencieofsum

)frequencymarkclass(ofsum ×

12 Phythagoras Theorem c2 = a2 + b2

13 m = 12

12xxyy

−−

14 m = erceptintxerceptinty

−−

−

PPSMI/Maths/F4/P2


https://panelmathsaddmathswordpress.com/

3

SHAPE AND SPACE

1 Area of trapezium = 21× sum of parallel sides × height

2 Circumference of circle = πd = 2πr 3 Area of circle = πr2

4 Curved surface area of cylinder = 2πrh 5 Surface area of sphere = 4πr2 6 Volume of right prism = cross sectional area × length 7 Volume of cylinder = πr2h

8 Volume of cone = 31πr2h

9 Volume of sphere = 34πr3

10 Volume of right pyramid = 31 × base area × height

11 Sum of interior angles of a polygon = ( n − 2) × 180°

12 o360centreatsubtendedangle

circleofncecircumferelengtharc

=

13 o360centreatsubtendedangle

circleofareatorsecofarea

=

14 Scale factor, k = PA

'PA

15 Area of image = k2 × area of object

PPSMI/Maths/F4/P2



4

1449/2 For

Examiner’s Use

Section A

[52 marks]

Answer all questions in this section. 1. The Venn diagrams in the answer space shows sets P, Q and R. On the diagram provided in the answer spaces, shade

(a) the set P’ ∩ Q’

(b) the set (Q ∩ R)’ ∩ P

[3 marks] Answer: (a) (b)

1449/2

R

ξ Q P

P Q R

ξ

PPSMI/Maths/F4/P2



5

1449/2 2. Diagram 1 shows a solid formed when a cylinder is taken out from the pyramid.

The base of the pyramid is a square.

DIAGRAM 1

The height of the cylinder is 9 cm and the diameter is 7 cm. The height of the pyramid is 21 cm.

By using 722

=π , calculate the volume, in cm3, of the solid.

[4 marks]

Answer:

For Examiner’s

Use

1449/2 [ Turn Over

15 cm

PPSMI/Maths/F4/P2



6

1449/2

For Examiner’s

Use

3. Calculate the values of m and n that satisfy the following simultaneous linear equations:

2m + n = 3 4m − 3n = 11

[4 marks]

Answer:

1449/2

PPSMI/Maths/F4/P2



7

1449/2 4. Diagram 2 shows two sectors OPJQ and OSR with the same centre O.

DIAGRAM 2

OR = 21cm and OQ = 14cm.

Using 722

=π , calculate

(a) the perimeter, in cm, of the whole diagram, (b) the area, in cm2 , of the shaded region.

[6 marks] Answer:

For Examiner’s

Use

1449/2 [ Turn Over

J

S

RQ

P

O

60°

PPSMI/Maths/F4/P2



8

1449/2

For Examiner’s

Use

5. Solve the equation x(2x – 5) + 3 = 0 [4 marks]

Answer:

1449/2

PPSMI/Maths/F4/P2



9

1449/2 6. (a) Is the sentence below a statement or non-statement? “ 3 + 5 = 1 + 9 ”.

(b) Write down two implications based on the following sentence. “ 4k < 20 if and only if k < 5”

(c) Complete the premise in the following argument :

Premise I : If n + 1 is an even number then n is an odd number.

Premise II : n is not an odd number. Conclusion :

[4 marks] Answer: (a) (b) Implication 1:

Implication 2:

(c) Conclusion:

For Examiner’s

Use

1449/2 [ Turn Over

PPSMI/Maths/F4/P2



10

1449/2

For Examiner’s

Use

7. In Diagram 3, the graph shows the straight lines JK, JL and RS. DIAGRAM 3 J is on the y-axis and R is on the x-axis. JL is parallel to the x-axis and JK is parallel to RS. The equation of JK is 2y = 6x + 8. (a) State the equation of the straight line JL.

(b) Find the equation of the straight line RS. (c) State the x-intercept of the straight line RS.

[6 marks] Answer: (a) (b) (c)

1449/2

J

y

O

L

S(13,20)

Rx

K

PPSMI/Maths/F4/P2



11

1449/2 8. Diagram 4 shows a cube with DCGH as the horizontal base. DIAGRAM 4

[4 marks] Calculate the angle between the line AG and the plane DCGH. Answer:

For Examiner’s

Use

1449/2 [ Turn Over

H G

F E

D

A

6 cm

4 cm

3 cm

B

C

PPSMI/Maths/F4/P2



12

1449/2

For Examiner’s

Use

9. (a) While on vacation in Cherating, Samuri decides to buy 6 postcards for Jamil, 3 postcards for Mala and 2 postcards for Teck Sin. All the postcards are kept in a bag. If a postcard is taken at random from the bag, find the probability that the postcard is for Jamil. (b) In a class, 12 pupils are from Perak. If a pupil is chosen at random from the class, the probability of choosing a

pupil from Perak is 31 .

Find the number of pupils in the class. [5 marks]

Answer: (a) (b)

1449/2

PPSMI/Maths/F4/P2



13

1449/2 10. In Diagram 5 , O is the origin. DIAGRAM 5 OP is parallel to RQ. Find (a) the gradient of RQ, (b) the equation of the straight line RQ, (c) the x-intercept of RQ.

[6 marks] Answer: (a) (b) (c)

For Examiners’s

Use

1449/2 [ Turn Over

y

O R

Q(3,10) P(9,15)

x

PPSMI/Maths/F4/P2



14

1449/2 For

Examiner’s Use

11. (a) Complete the following mathematical statements in the using the symbols < or > to form (i) a true statement

2 × 3 2 + 3 (ii) a false statement

(2 +3)2 22 + 32

(b) Complete the premise in the following argument: Premise 1 : All pentagons have five sides. Premise 2 : ________________________ Conclusion : PQRST has five sides. (c)

Based on the inregarding the n

Answer: (a) (i)

2 × 3 (ii)

(2 +3)2 (b) Premise 2 :

(c)

1449/2

PPSMI/Maths/F4/P2


https://panelm

0 = 3(0)2

3 = 3(1)2

12 = 3(2)2

27 = 3(3)2

formation above, make a general conclusion by induction umber sequence 0 , 3 , 12 , 27 , . . .

[6 marks]

2 + 3

22 + 32

athsaddmathswordpress.com/

15

1449/2 Section B [48 marks]

Answer four questions in this section.

12. (a) In Diagram 6, OABC is a parallelogram. O is the origin. DIAGRAM 6 Find

(i) the gradient of OA (ii) the equation of the straight line BC (iii) the y-intercept of the line AB.

[5 marks] (b) Diagram 7 shows a pyramid JKLMN. DIAGRAM 7 The base JKLM is a square. MN = 13 cm. (i) Calculate the angle between the line NL and the base JKLM. (ii) Calculate the angle between the plane NLM and the base JKLM.

[7 marks]

For Examiner’s

Use

1449/2 [ Turn Over

A(1,4)

C(5,2)

O

B y

x

J

K

L

M

N

5 cm

PPSMI/Maths/F4/P2



16

1449/2

For Examiner’s

Use

Answer: 12. (a) (i) (ii) (iii) (b) (i) (ii)

1449/2

PPSMI/Maths/F4/P2



17

1449/2 13. (a) Diagram 8 shows some number cards. DIAGRAM 8 All the cards are put inside a box. A card is drawn at random from the box. (i) List its sample space. (ii) List the elements of the event of getting even number (iii) Find the probability of getting an odd number (iv) A boy adds 2 even numbered cards to the box. A card is then drawn at random from the box. Find the probability of getting an even number.

[6 marks]

(b) In Diagram 9, JK and PQ are arcs of two different circles with centre O. DIAGRAM 9 ORTQ is a square. OJ = 28 cm and P is a centre of OJ.

Using π = 722 , calculate

(i) the perimeter, in cm, of the whole diagram. (ii) the area, in cm2, of the shaded region.

[6 marks]

For Examiner’s

Use

1449/2 [ Turn Over

K

Q T

R

J

P

O

150°

12119 8 6 5 3 2

PPSMI/Maths/F4/P2



18

1449/2

For Examiner’s

Use

Answer: 13. (a) (i) (ii) (iii) (iv) (b) (i) (ii)

1449/2

PPSMI/Maths/F4/P2



19

1449/2 14. (a) Solve the equation .1143 2 nn =−

[4 marks]

(b) Solve the equation 82120 2 +=+ xx .

[4 marks] (c) Diagram 10 shows a solid formed by joining a half cone and a half cylinder. DIAGRAM 10 The diameters of the cylinder and the base of the cone are both 14 cm. The height of the cone is 5 cm.

Using π = 722 , calculate the volume, in cm3 , of the solid.

[4 marks]

For Examiner’s

Use

1449/2 [ Turn Over

10 cm

PPSMI/Maths/F4/P2



20

1449/2 For

Examiner’s Use

14. (a) (b) (c)

1449/2

PPSMI/Maths/F4/P2



21

1449/2 15. Diagram 11 shows the ages, in years, of 30 participants in a game on a family day.

3 11 13 14 18 12 23 24 7 13 22 13 19 27 6 16 24 29 13 25 8 11 20 17 14 17 18 16 9 16

DIAGRAM 11 a) Based on the data in the diagram above, complete the following table in the answer space.

Age Frequency Midpoint Upper boundary

1 - 5 6 - 10 11 - 15 16 - 20 21 - 25 26 - 30

[4 marks]

b) Based on the table in (a), calculate the estimated mean age of the participants.

[3 marks]

c) By using a scale of 2 cm to 5 years on x-axis and 2 cm to 1 participant on the y-axis, draw a histogram for the data.

[4 marks]

d) From the histogram, find the percentage of participants who are more than 15 years old.

[1 mark]

For Examiner’s

Use

1449/2 [ Turn Over

PPSMI/Maths/F4/P2



22

1449/2

For Examiner’s

Use

Answer: 15. (a)

Age (Years)

Frequency Midpoint Upper Boundary

1 − 5 6 − 10 11 − 15 16 − 20 21 − 25 26 − 30

(b) (c) Refer to page 23 (d)

1449/2

PPSMI/Maths/F4/P2



PPSMI/Maths/F4/P2

23



24

1449/2

For Examiner’s

Use 16. Table 1 shows the distribution of the ages of 200 participants in a big walk event.

TABLE 1

(a) Using the data in Table 1, complete the table provided in the answer space.

[4 marks]

(b) Calculate the estimated mean age of the participants.

[3 marks]

(c) By using a scale of 2 cm to 5 years on the x-axis and 2 cm to 20 participants on

the y-axis , draw an ogive for the data. [5 marks]

Age ( years) Frequency

15 - 19

20 - 24

25 - 29

30 - 34

35 - 34

40 - 44

45 - 49

10

20

50

60

36

18

6

1449/2

PPSMI/Maths/F4/P2



25

1449/2 Answer: (a)

Age (years) Frequency Cumulative Frequency

Upper Boundary

15 − 19 10

20 − 24

20

25 − 29

50

30 − 34

60

35 − 39

36

40 − 44

18

45 − 49

6

(b) (c) Refer to page 26

For Examiner’s

Use

1449/2 [ Turn Over

PPSMI/Maths/F4/P2



PPSMI/Maths/F4/P2

26



Maths Ppsmi 2006 F4 P2

Business

Transcript of Maths Ppsmi 2006 F4 P2