F4 Final Sbp 2007 Maths P2

ppr maths nbk

SEKTOR SEKOLAH BERASRAMA PENUH BAHAGIAN SEKOLAH

KEMENTERIAN PELAJARAN MALAYSIA

PEPERIKSAAN DIAGNOSTIK TINGKATAN EMPAT 2007

Pemeriksa

Bahagian Soalan Markah Penuh

Markah Diperoleh

1 4

MATEMATIK

Kertas 2

Dua jam tiga puluh minit

2 4

3 5

4 4

5 3

6 4

7 6

8 6

9 4

10 7

A

11 5

12 12

13 12

14 12

15 12

B

16 12

JANGAN BUKA KERTAS SOALAN INI

SEHINGGA DIBERITAHU

1. Kertas soalan ini mengandungi dua bahagian : Bahagian A dan Bahagian B. Jawab semua soalan daripada Bahagian A dan empat soalan dalam Bahagian B.

2. Jawapan hendaklah ditulis dengan jelas dalam

ruang yang disediakan dalam kertas soalan. Tunjukkan langkah-langkah penting. Ini boleh membantu anda untuk mendapatkan markah.

3. Rajah yang mengiringi soalan tidak dilukis

mengikut skala kecuali dinyatakan. 4. Satu senarai rumus disediakan di halaman 2 & 3. 5. Anda dibenarkan menggunakan kalkulator

saintifik yang tidak boleh diprogram. Jumlah

Kertas soalan ini mengandungi 24 halaman bercetak.

SULIT 1449/2 Matematik Kertas 2 Oktober 2007

212 jam

1449/2

1449/2 © 2007 Hak Cipta Sektor SBP [Lihat sebelah SULIT

NAMA :

TINGKATAN :

SULIT 1449/2

1449/2 SULIT

2

Untuk Kegunaan Pemeriksa

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

RELATIONS 1 am x an = a m+ n 2 am ÷ an = a m – n 3 ( am )n = a mn

4 A-1 = bcad −

1⎟⎟⎠

⎞⎜⎜⎝

⎛−

−acbd

5 P ( A ) = )()(

SnAn

6 P ( A′ ) = 1 − P(A)

7 Distance = 2 21 2 1 2( ) ( )x x y y− + −

8 Midpoint, ( x, y ) = ⎟⎠⎞

⎜⎝⎛ ++

2,

22121 yyxx

9 Average speed = 10 Mean = 11 Mean = 12 Pythagoras Theorem c2 = a2 + b2

13 m = 12

12

xxyy

−−

14 -intercept-intercept

ymx

=

distance travelled time taken

sum of data number of data

sum of (class mark × frequency) sum of frequencies

SULIT 1449/2

1449/2 [Lihat sebelah SULIT

3


SHAPES 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 = 31 πr2h

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 arc length angle subtended at centrecircumference of circle 360

=o

13 area of sector angle subtended at centrearea of circle 360

=o

14 Scale factor , k = PAPA'

15 Area of image = k 2 × area of object

SULIT 1449/2

1449/2 SULIT

4


Section A [52 marks]

Answer all questions in this section.

1 Solve the quadratic equation 3

343

−−

=x

xx

[4 marks]

Answer :

2 Calculate the value of p and of q that satisfy the following simultaneous linear equations:

394632−=+

=−qpqp

[4 marks]

Answer :

SULIT 1449/2


5


3 (a) State whether the following statement is true or false. 63and326 2 ==÷ (b) Write down two implications based on the sentence below. 4m > 20 if and only if m > 5

(c) Given the number sequence 5, 18, 39, 68, … which follows the pattern

5 = 1 + 4(12)

18 = 2 + 4(22)

39 = 3 + 4(32)

68 = 4 + 4(42) …………….. ……………..

Form a general conclusion by using the induction method for the numerical sequence above.

[5 marks]

Answer : (a)

(b) Implication 1 : _________________________________________________

Implication 2 : _________________________________________________ (c)

SULIT 1449/2

1449/2 SULIT

6


4 Diagram 1 shows a combined solid consists of a cuboid JKLMPQRS and half cylinder

JMNTSP.

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

[4 marks]

Answers:

J K

L M

P Q

R S T

N 8 cm

7 cm

16 cm

DIAGRAM 1

SULIT 1449/2


7


5 The Venn diagram in the answer space shows sets P, Q and R such that the universal set,

ξ = P ∪ Q ∪ R.

On the diagrams in the answer space, shade

(a) P′ ∩ R′

(b) Q ∩ R ∪ P

[3 marks] Answer :

(a) (b)

P

Q R

P

Q R

SULIT 1449/2

1449/2 SULIT

8


6 Diagram 2 shows a cuboid with horizontal rectangular base, ABCD. Calculate the angle between the plane ABE and the base ABCD.

[4 marks] Answer :

A B

C D

E

F G

H

DIAGRAM 2

10 cm

8 cm

6 cm

SULIT 1449/2


9


7 In Diagram 3, O is the origin. KL, PQ and RS are straight lines. PQ is parallel to RS. The equation of the straight line KL is 62 +−= xy .

Find the

(a) coordinate of P,

(b) gradient of the straight line PQ,

(c) equation of the straight line RS.

[6 marks]

Answer:

(a)

(b)

(c)

x O

K R

S

L

DIAGRAM 3

y

P

Q(−3, −3) •

•

SULIT 1449/2

1449/2 SULIT

10


8 (a) Identify the antecedent and consequent in the following implication.

‘ If a triangle has two equal sides, then it is an isosceles triangle.’

(b) State the converse of the following implication.

If 5>x , then x2 > 25

(c) Complete the premise in the following argument. Premise 1 : If x is an angle in a semicircle, then x = 90° Premise 2 : _________________________________________________ Conclusion : x = 90°

(d) Complete the following argument Premise 1 : _________________________________________________

Premise 2 : M ∩ N ≠ M

Conclusion : M ⊄ N

[6 marks]

Answer:

(a) Antecedent : …………………………………………………………………

Consequent : …………………………………………………………………. (b) ………………………………………………………………………………… (c) Premise 2 : …………………………………………………………………… (d) Premise 1 : …………………………………………………………………….

SULIT 1449/2


11


9 Ten cards are placed in an empty box.

(a) If a card is selected at random from the box, state the probability that the card marked

C is selected.

(b) A number of cards marked C are added into the box. If a card is selected at random

from the box, the probability of selecting a card marked C is 73 .

Find the number of cards that has been added into the box.

[4 marks]

Answer : (a) (b)

E X C E L L E N C E

SULIT 1449/2

1449/2 SULIT

12


10 In Diagram 4, ABOD is a square and PQR is a semicircle with centre O.

OR = 7 cm. Using π = 722 , calculate

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

[7 marks] Answer : (a)

(b)

A B

D O

P

Q

R

DIAGRAM 4

14 cm

SULIT 1449/2


13


11 Diagram 5 shows a right pyramid with rectangular base PQRS .

The apex V is 5 cm vertically above the point T.

Calculate the angle between the line VP and the base PQRS.

[5 marks] Answer:

R

8 cm

V

P Q

S

6 cmT

DIAGRAM 5

SULIT 1449/2

1449/2 SULIT

14


Section B

[48 marks]

Answer any four questions in this section.

12 Table 1 in the answer space shows the distribution of the ages of 200 participants in a big

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

[4 marks]

(b) 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]

(c) Based on your ogive in (b),

(i) find the inter quartile,

(ii) explain briefly the meaning of the third quartile.

[3 marks]

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) Refer graph on page 15.

(c) (i) (ii)

TABLE 1

SULIT 1449/2


15


Graph for Question 12

SULIT 1449/2

1449/2 SULIT

16


13 (a) Diagram 6 shows sectors OTQR, OABC and OCP with the same centre O. TAOP and OCR are straight lines.

OR = 2OC , OC = 221 cm and ∠COP = 60°.

Using π = 722 , calculate

(i) the perimeter, in cm, of the whole diagram,

[3 marks] (ii) the area, in cm2, of the shaded region.

[4 marks]

(b) Diagram 7 shows some number cards.

A card is picked at random. State the probability of choosing a card containing

(i) digit 5,

(ii) a multiple of 5,

(iii) a number such that when divided by 5, the remainder is 1.

[5 marks]

T A

B C

Q R

P O

DIAGRAM 6

45 46 47 48 49 50 51 52

53 54 55 56 57 58 59 60

DIAGRAM 7

SULIT 1449/2


17


Answer:

13 (a) (i)

(ii)

(b) (i)

(ii) (iii)

SULIT 1449/2

1449/2 SULIT

18


14 The data in Diagram 8 show the marks of 40 students for the Mathematics monthly test.

46 53 44 60 42 38 31 55

35 37 54 32 46 56 40 60

52 40 34 45 52 35 50 36

47 38 40 48 45 42 53 44

50 44 58 51 36 48 56 32

(a) Using the data in Diagram 8 and a class interval of 5 marks, complete Table 2

in the answer space.

[4 marks]

(b) Based on Table 2 in (a),

(i) state the modal class,

(ii) calculate the mean mark of the Mathematics monthly test and give your answer

correct to 2 decimal places.

[4 marks]

(c) For this part of the question, use the graph paper provided on page 19.

By using a scale of 2 cm to 5 marks on the horizontal axis and 2 cm to 1 student on the

vertical axis, draw a histogram for the data.

[4 marks]

DIAGRAM 8

SULIT 1449/2


19


Answer:

14 (a)

Class interval Midpoint Frequency

31 – 35

36 - 40

(b) (i)

(ii)

(c) Refer to the graph on page 20.

TABLE 2

SULIT 1449/2

1449/2 SULIT

20


Graph for Question 14

SULIT 1449/2


21


15 (a) Diagram 9 is a Venn diagram showing the number of students in a class who play at least

one of the three games. Given the universal set, ξ = F ∪ R ∪ H.

Given that set F = { students who play football }

set R = { students who play rugby } and

set H = { students who play hockey}.

(i) Find the number of students who play hockey.

(ii) If the number of students who play football is 30, find

(a) the number of students who play rugby,

(b) the number of students who play one game only.

[6 marks]

Answer:

(a) (i)

(ii) (a)

(b)

R

F

H

x

7 2x

5

18 – 2x 10 + x 10

DIAGRAM 9

SULIT 1449/2

1449/2 SULIT

22


15 (b) In Diagram 10 , TQRS, NR and OQ are straight lines drawn on a Cartesan plane. O is the

origin and OQ is parallel to NR. The gradient of NR = 2.

Find

(i) the value of p,

(ii) the coordinate of R,

(iii) the equation of the straight line ST.

[6 marks]

Answer:

(b) (i)

(ii)

(iii)

y

x

R

•

N(-6, 0)

Q(p, 3)

T 0

•

• •

DIAGRAM 10

S

SULIT 1449/2


23


16 (a) Solve the equation 15

32 2

=−

ww .

[4 marks] (b) Calculate the values of x and y that satisfy the following simultaneous linear equations: 2x + y = 3 4x - 3y = 11

[4 marks] (c) (i) Form a true compound statement by combining the two statements given below. (a) 52 = 10

(b) 41 = 0.25

(ii) Form a general conclusion by induction based on the numerical sequence below.

2, 9, 16, 23 … 2 = 2 + 7 (0) 9 = 2 + 7 (1) 16 = 2 + 7 (2) 23 = 2 + 7 (3) ………………. (iii) Complete the following sentence using a suitable quantifier to make it a true statement. ‘………………. prime numbers are odd numbers.’

[4 marks]

SULIT 1449/2

1449/2 SULIT

24


Answer:

16 (a)

(b)

(c) (i)

(ii)

(iii)

F4 Final Sbp 2007 Maths P2

Economy & Finance

Transcript of F4 Final Sbp 2007 Maths P2