MM2 Marking Sbh

8/14/2019 MM2 Marking Sbh

1/14

1

MARKING SCHEME PAPER 2 EXCEL 2

Question Solution and Mark Scheme Marks

1 (a)

(b)

P1

P2 3

2

( )

23 5 2 0

3 1 ( 2) 0 or equivalent.

2

1or 0.3333

3

n n

n n

n

n

=

+ =

=

=

Note:

1. Accept without = 02. Do not accept solutions solved not using factorization.

K1

K1

N1

N1

4


2/14

2

3 13 6 or 7 or equivalent

2x y x y+ = =

55 20 or 5 or equivalent

6y x= =

or

1414 2 or or equivalent

2

55 20 or 5 or equivalent

6

xx y y

y x

= + =

= =

(K1)

(K1)

or

3 2 141

1 1 61(3) ( 2)(1)

6

4

x

y

x

y

=

=

=

(K2)

Note:

3 211.

1 11(3) ( 2)(1)

62. as final answer, award N1

4

x

y

=

K1

K1

N1

N1

4

4 Identify orTRS SRT

0'13.53853

6

8tan

or

equivalentor

o=

=

P1

K1

N1

3


3/14

3

5(a)

2 1

6 ( 3) 3

t=

t = 5

(b)

2 0

3 ( 4)RSm

=

y = 2 x 7

(c) y-intercept is 7 or c = - 7.

K1

N1

K1

N1

N1

5

6 (a)

135 22 45 222 14 or 2 21

360 7 360 7

135 22 45 222 14 + 2 21 7 21 14

360 7 360 7

or equivalent

1 18391 or 91.5 or

2 2

+ + +

(b)

2

2

45 22 121 or 14 14

360 7 2

45 22 121 14 14

360 7 2

1 30175 or 75.25 or4 4

Note:

1. Accept for K mark.2. Correct answer from incomplete working, award KK2.

K1

K1

N1

K1

K1

N1

6


4/14

4

7 (a) 3 is an odd number or 14 ( 2) 7 = .

(b) sin 135o is positive.

(c) A + B = 90oA and B are complementary angles

P2

K1

P1

P1 5

8 (a) n = 3

1 (4) ( - 3)(2) = m(3) 2

m = 4(b)

4 3 61

2 1 21(4) ( 3)(2)

3

1

3

1

p

q

p

q

p

q

=

=

=

=

Note:

1.

*p 6

q 2

inverse

matrix

=

or

4 31seen, award K1.

2 11(4) ( 3)(2)

2. Do not accept

* *1 3 1 0

or .2 4 0 1

inverse inverse

matrix matrix

= =

3.3

as final answer, award N11

p

q

=

4. Do not accept any solutions solve not using matrices.

P1

K1

N1

K2

N1

N1

7


5/14

5

9 (a) (4,8), (4,9)

2 1or

24 12

(b) (4, G), (4, J), (4, K)

(B, 8), (B, 9), (F, 8), (F, 9)Note: Any two groupings correct, award K1.

7

24

K1

N1

K2

N1

5

10 (a) 12s

(b)

2 2

10 3

4

7or 1.75

4ms ms

(c)

1 1(3 10)4 (16 4)10 (10 22)( 16) 306

2 2

26

t

t s

+ + + + =

=

P1

K1

N1

K2

N1

6

112

3

2 3

223

7

1 4 223

2 3 7

22 1 4 22 63 3 282

7 2 3 7 7

12

t

t

cm

=

Note:

1. Accept for K mark.2. Correct answer from incomplete working, award KK2.

K1

K1

K1

N1

4


6/14

6


12(a) (i) (7,5)

Note :

Award P1 if coordinate (7,5) marked on diagram orcoordinate (4,7) indicated in answer space.

[P2]

(ii) (1,5)

Note :Award P1 if coordinate (1,5) marked on diagram or

coordinate (5,5) indicated in answer space.

[P2] 4

(b) (i)

(ii)

U : Reflection in the line GH ory = 9-x

Note :

1. Award P1, if the word reflection seen.

V : Enlargement at centre (9,4) with scale factor of 2.

Note :

1. Award P2, if Enlargement at centre (9,4) orEnlargement scale factor of 2 seen.

2. Award P1, if the word Enlargement seen.

[P2]

[P3] 5

(c) Area of image = scale factor2 x Area of object

336 = 22 x Area of objectArea of object = 336 4

= 84 unit2.

[K2]

[N1] 3

Jumlah 12


7/14

7


13(a) 2

5.5

[K1]

[K1] 2

(b) Graph

1. Axes drawn in correct direction with uniformscales in

-2.5x 3 and -8y 30.5

2. All points correctly plotted or curve passesthrough these points for -2.5x 3

3.

Smooth and continuous curve without anystraight line and passes through all correct

points

Note :

1. 6 or 7 points correctly plotted, award K1

[P1]

[K2]

[N1] 4

(c) (i) 9 y 10 [P1]

(ii) -2.2x -2.1 [P1] 2

(d)y = 4x2 5x 7

- 0 = 4x2 + 2x 2

y = 7x 5

Straight line y = 7x 5 correctly drawn

0.4x 0.6

-1.1x -0.9

Note :1. Allow P mark or N mark if values ofy andxshown on graph.

2. Values of y and x obtained by computations,award P0 or N0.

[K1]

[K1]

[N1]

[N1] 4

Jumlah 12


8/14

8

2Graph for Question 13

Graph for Question 13

1 2 3-1-2-3 0

5

10

15

20

25

30

-5

-10

X

Y

y = 4x2

-5x-7

y = -7x-5


9/14

9


14(a) Mass

(kg)

Frequency Mid Point

1-5 5 3 I

6-10 4 8 II

11-15 5 13 III

16-20 6 18 IV

21-25 9 23 V

26-30 7 28 VI

31-35 3 33 VII

36-40 1 38 VIII

Class interval : II - VIIIFrequency : II VIII

Midpoint : II - VIII

Note :

Allow 1 mistake in Frequency for P1

[P1]

[P2]

[P1]

4

(b) (3x5)+(8x4)+(13x5)+(18x6)+(23x9)+(28x7)+(33x3)+(38x1)40

760

40

= 19

Note :1. Allow 2 mistakes for K1

Award KK2, if incomplete working shown.

[K2]

[N1]

3

(c) Graph

1. Axes drawn in correct direction with uniform scalesfor

0.5x 40.5 and 0y 9

Accept midpoint/class interval for the horizontalaxis.

2. All bar correctly drawnNote :

6 or 7 bar correctly drawn, award K1

[P2]

[K2]

4

(d) The modal class is 21-25 [P1] 1

Jumlah 12


10/14

10



5.5 105 15.5 20.5 25.5 30.5 35.5 40.5

1

2

3

4

5

6

7

Mass (kg)

Frequency

0.5

8

9


11/14

11


15(a)

J /F I H/Q/G P/ N

6cm

E/A D C/M/ B L/ K

2cm 2cm 3 cm

Correct shape with rectanglesEDIJ,DCHIand CLPH.

All solid lines.

ED=DC, EL>JE>CL>ED

Measurement correct to 0.2 cm (one way) and all anglesat the vertices of rectangles = 90o 1o.

[K1]

[K1] dep

K1

[N1] dep

K1K13


12/14

12


15(b)(i)E C

D

6cm

5cm

R7cm

M

2cm

L

4 cm

A 4cm B 3 cm K

Correct shape with pentagonABCDEandBKLRM.All solid lines.

AE>CM>AB>CD>BK >RL

BK=LK

Measurement correct to 0.2 cm (one way) and angle A,

angle B and angle K= 90o 1o.

[K1]

[K1] depK1

[N2] dep

K1K1 4


13/14

13


15(b)(ii)

C H

1cmD I

2cm

R S

2 cm

L P

2cm

K N6cm

Correct shape with rectangleKLPN,RLPSand CRSH

All solid lines.

Note :

Ignore dotted lineDI

D and I joined with dotted line to form rectangle CDIH

CK>KN, IS>PN>PS >IH

Measurement correct to 0.2 cm (one way) and all angle at

the vertices of rectangles = 90o

1o.

[K1]

[K1]

dep K1

[K1]

dep

K1K1

[N2]

dep

K1K1

K1

5

Jumlah 12


14/14

14


16(a) 175oE

Note :

a. 175o

or E, award P1

[P2]

2

(b) (180o-54o-54o)x60

=72 x 60=4320 n.m.

[K2

]

[N1

]

3

(c) (5+25) x 60 x Cos 54o

= 1058 n.m

Note:

Award K1, ifa. (5+25) orb. Cos 54o used correctly.

[K2

]

[N1

]

3

(d) 550 = Distance

6

Distance = 550 x 6= 3300 n.m

330060

=55o

55o-54o

=1

o

N

[K2

]

[K1

]

[K1

]

4

Ju

mla

h

12

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MM2 Marking Sbh