kem bagan lalang -mathematics

8/7/2019 KEM BAGAN LALANG -MATHEMATICS

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SMK ST. JOHNKUALA LUMPUR

KEM PEMANTAPAN ILMU

BAGAN LALANG,SEPANG

MATHEMATICS


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TARGET SOALAN DAN MARKAH :

KERTAS 1 :

BIL TOPIK MARKAH CATATAN1 ALGEBRAIC EXPRESSIONS 2

SUKATAN

PMR

2 LINEAR EQUATIONS 1

3 POLYGONS 1

4 TRANSFORMATIONS 2

5 STATISTICS 2

6 STANDARD FORM 4SUKATAN

TING.47 SETS 1

8 PROBABILITY 2

9 NUMBER BASES 2SUKATAN

TING.510 GRAPH OF FUNCTIONS 1

11 MATRICES 2

JUMLAH 20 MARKAH

KERTAS 2 :

BIL TOPIK MARKAH CATATAN

1 LINEAR EQUATIONS SIMULTANEOUS 4

SUKATAN

PMR

2 LINEAR INEQUALITIES SHADE THE

REGION **

3 **

3 CIRCLES PERIMETER & AREA 64 SOLID GEOMETRY 4

5 SETS SHADE THE REGION ** 3 **

SUKATAN

TING.4

6 MATHEMATICAL REASONING 6

7 STATISTICS 12

8 PROBABILITY 2

9 LINES AND PLANES IN 3D 1

10 GRAPH OF FUNCTIONS 8SUKATAN

TING.511 MATRICES 4

12 PLAN AND ELEVATIONS 12

JUMLAH 62 MARKAH

** Kemahiran melorek rantau yang ditentukan (shade the region) adalah berselang-seli

antara topic set atau topic Linear Inequality

JUMLAH MARKAH DIPEROLEHI = ( 20 + 62 ) X 100 %

140

= 59 %


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QUESTION 1 : QUADRATIC EQUATIONS [ 4 marks ]

1. 17

24=

m

m

2.

3.

QUESTION 2 : SIMULTANEOUS EQUATIONS [ 4 marks ]

1.

2.

3.

h

hh

23

=

hhh

=

32

)32(

12

1365

=+

=

nm

nm

113

12

=

=+

yx

yx

623

83

22

=+

=

wv

wv


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QUESTION 3 : SETS [ 3 marks ]

1. The Venn diagram in the answer space shows sets L, M and N. Given thatuniversal set, = L M N. On the diagram provided in the answer space,

shade the region that satisfied

(a) ( L N)

M

L N

(b) ( L M) N.

M

L N

2. The Venn diagram in the answer space shows set A, set B and set Csuch that the

universal set A B C= .On the diagram provided in the answer space, shade

(a) set ( ) 'A B ,

(b) set ( A B ) ( B C ).

Answers:(a) A B

C


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(b)

3. The Venn diagram in the answer space shows sets P, Q and R such that the

universal set.P Q R = On the diagram in the answer spaces, shade the set of

(a) RP ,

(b) ( )'P R Q .

Answer/ Jawapan :

(a)

(b)

CBA

P

R

Q

P

R

Q


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QUESTION 4 : LINEAR INEQUALITIES [ 3 marks ]

1. On the graph, in the answer space, shade the region which satisfies the inequalitiesgiven

x 3, y 43

4+x dan x + y < 4.

43

4+= xy

2. On the graph provided, shade the region which satisfy the three inequalities

x + y 5 , y x 5 and y< 5 .

y

0

4

4 x

x = 3

y

0

-5

5x

x + y = 5

y = x 5


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3. On the graph provided , shade the region which satisfies the three inequalities

5,y x x and 5y > .

QUESTION 5 : LINES AND PLANES IN 3D [ 3 or 4 marks ]

1. Diagram 2 shows a pyramid VEFGH.

DIAGRAM 2

EFGHis a horizontal square base. Vertex Vis vertically above point H. VG = 10

cm. Calculate the angle between line FVand the base EFGH.

y

0 5x

y = x

5

- 5

- 5

E F

V

H G

10 cm6 cm


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2. Diagram 2 shows a right prism with the base PQRS is a horizontal rectangle.

Diagram 2

Isosceles triangle PST and QRU is the uniform cross-section of the prism. M and

NPoints M and N are the midpoints of PS and QR respectively

Given PT = 5 cm and QR = 6 cm.

Calculate the angle between the plane PUS and the base PQRS..

3. Diagram 2 shows a right prism. The base CDEF is a horizontal rectangle .

B

A

C

P Q

UT

R

10 cm

S

NM

F

E D


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DIAGRAM 2

Triangle AED is the uniform cross section prism.AE = 7 cm, ED = 12 cm and AB = 8 cm

Calculate the angle between the plane BED and the base CDEF.

QUESTION 6 : MATHEMATICAL REASONING [ 5 marks ]

1. (a) Is the sentence below a statement or non-statement ?

1 1 2

3 4 7+ =

Answer : .

(b) Write down two implications based on the following sentence:Sin = 1 if only if = 90 0

Implication 1 :..

Implication 2 :.

(c) Complete the premise in the following argument:

Premise 1 : ...

Premise 2 : m not divisible by 2.

Conclusion : m is not an even number.


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2 (a) (i) Complete the following statement using the quantifier all or some,

to make it a false statement.

.................... factors of are factors of 24.

(ii) Combine the two following statements to form a true statement.

Statement 1: 7 is an odd number

Statement 2: 72 = 14

Answer : ..

(b) Write down the converse of the following statement and state whether it is

true or false:

Answer : .

(c) Make a general conclusion by induction for the sequence of numbers -3, -1,

1, 3, 5, . Which follows the following pattern :

-3 = 2(0) - 3

-1 = 2(1) - 3

1 = 2(2) - 3

3 = 2(3) - 3

5 = 2(4) - 3

Answer : .

3 (a) State whether each of the following statement is true or false.

(i) 4 2 = 8 and 4 8 = 2 Ans : .

(ii)3

1

4

1> or 4 > 5 Ans : .

Ifx is prime number then x has 2 factors


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(b) Write premise 2 to complete the following argument:

Premise 1 : All pentagons have five sides.

Premise 2 : ............................................................................

Conclusion: PQRSThas five sides.

(c) Make a general conclusion by induction for a list of numbers1

42

, 8,1

172

,

36, . which follows the following pattern :

1

42

=1

2(1) 2 + 4

8 =1

2(2) 2 + 4

117

2=

1

2(3) 2 + 4

36 =1

2(4) 2 + 4

..

Answer :

QUESTION 7 : MATRICES [ 6 marks ]

1. (a) The inverse matriks of

41

52is

p

1

21

5r

Find the value ofp and ofr

Answer :


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(b) Using matrices, calculate the value ofx and ofy that satisfy the following

simultaneous liner equation :

2x + 5y = 12

x + 4y = 3

2 (a) It given that matrix P=

23

1n, find the value ofn if matrix Pdoes not

have inverse matrix.

Ifn = 5,find theinverse matrix ofP.


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(b) Hence, by using matrices, calculate the value of x and ofy that satisfy the

equations.

=

17

2315

yx

3 Mis a matrix 2 2 such that M 4 3 1 07 5 0 1

=

(a) Find the matrix M.

(b) Write the following simultaneous linear equations as a matrix equation .


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4x + 3y = 23

7x 5y = 11

Hence, by using matrices, calculate the value of x and ofy that satisfy theequations.

QUESTION 8 : GRADIENT AND AREA UNDER A GRAPH

[ 6 MARKS ]

1 Diagram 4 shows the distance-time graph of a bus on a to-and-fro trip for a period

of tminutes.

DIAGRAM 4(b) State the length of time, in minutes, during which the bus is stationary.

Distance (km)

Time (minute)

035 t50

7

20

10


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(b) Calculate the average speed, in km/minute, of the bus in the first 50 minutes

(b) Calculate the value of tin the average speed of the bus on its return trip is

0.8 km/minute.

2. Diagram 4 shows the speed-time graph for the movement of a particle for a period

of 18 seconds .

Diagram 4

(a) State the uniform speed, in ms 1 , of the particle.

0

Speed (ms1)

10 18Time (s)

13

v


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(b) Calculate the distance in m, travelled by the particle with uniform speed.

(c) Given that average speed in the first 15 seconds is 13.8 ms 1 , find the value

ofv.

3. Diagram 5 shows the distance-time graph of the journey of a lorry starts fromtown A to the factory, then to town B after a 15 minutes rest. Graph OP

represents the journey from town A to factor . The graph QR represents the

journey from the factory to town B.

58

O

28

Distance/Jarak

(km)

P Q

R

35 t Time/Masa

(min)50


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(a) Find the distance, in km, from town A to town B.

(b) Calculate the speed of the lorry, in kmh-1, the journey from town to the

factory.

(c) Given that the speed of the lorry from the facotry to town B is 45 kmh1 ,calculate the value oft.

QUESTION 9 : PROBABILITY [ 5 MARKS ]

1. Given that set P= { 9, 12, 15, 17, 25, 26 } and set Q = { 5, 7, 8, 15, 17 }

If a number is choosen at random from each set, calculate the probability that

(a) prime number from set Q.

(b) Both numbers chosed are even number

(c) The number from set Q is greater than the number from set P

2.


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