Aswer SSI Mathematics Module

7/29/2019 Aswer SSI Mathematics Module

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1

SSI MATHEMATICS MODULE SPM 2009

ANSWERS:

SIMULTANEOUS EQUATIONS

No Answer Mark

1. n = 5 m 2

2 m +3

1( 5m 2 ) = 3

m = 1

n = 3

1

11

1

4

2.x =

2

34 y

3 (2

34 y) - 5 y = 13

y = - 2x = 1

1

1

11

4

3.

3

d- 2 = e

2 d + 3 (3

d- 2 ) = 9

d = 5

e = -3

1

1

1

1

1

4

4. 3 v - 13 = w

v +2

133 v= 1

v = 3

w = 4

1

11

1

4

5.p =

6

38 q+

2 (6

38 q+) -

3

2q= 2

q = -2

p =31

1

1

1

1

4


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2

MATHEMATICAL REASONING

Q1 Answer :

(a) (i) SOME of the perfect squares are odd numbers. (1M)

(ii) ALL hexagons have six sides. (1M)

(b) Premise 2 : NNM (1M)

(c) If y< -1, then y 0 (1M)(c) Implication 1 : If three points A , B , and C are on a straight line

thenlines AB and BC have common point and they are

parallel(1m)

Implication 2 : If lines AB and BC have common point and they are parallelthen

the three points A , B , and C are on a straight line(1m)

Q5 Answer:

(a) i) < (1M)ii) < (1M)

(b) 3 + ( -2 ) = 5 or 16 is a perfect square (1M)(c) (i) Si Hitam is a cow (1M)

(ii) LMNOPGRS has eight sides of equal length (1M)


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3

VOLUME AND SURFACE AREA

ANSWER

1

= (3.142 X 10 X 10 X 10) + (32 X 3.142 X 10 X 10 X 10) [2]

= 3142 + 2094.67 [1]

= 5236.67 cm3

[1]

2.

= (7

22X 7 X 7 X 20 ) - (

3

1X

7

22X 7 X 7 X 10) [2]

= 3080 - 513.33 [1]

= 2566.67 cm3 [1]

3.

= (4 X 6 X 3) + (6 X 6) + (4 X2

1X 6 X 5) [3]

= 72 + 36 + 60 [1]

= 168 cm2

[1]

4.

= ( 7

22

X 7 X 7 X 20) [1]

= 3080 [1]

Hence, 20 X 15 X d = 3080 [1]

d =1520

3080

X[1]

d = 10.27 cm [1]

5.

= (2 X7

22X 7 X 20) + (

7

22X 7 X 7) + (2 X

7

227 X 7 ) [3]

= 880 + 154 + 308 [1]

= 1342 cm2

[1]


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4

STRAIGHT LINE

Q10.1a) m RS =

20

04

+

5 = 2( 3) + C

y = 2x + 11

b) 0 = 2x + 11

x-intercept =2

11

K1

K1

N1

K1

N1

5 marks

Q10.2 a) y = 7

b) m ST =2

1

5 =2

1( 12) + C

y =2

1x + 1

c) x-intercept = 2

P1

K1

K1

N1

P1

5 marks

Q10.3a) m OR =

04

012

6 = 3 ( 3) + C

y = 3 x 15

b)03

06

40

12y

=

+

y-intercept = 20

K1

K1

N1

K1

N1

5 marks


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5

Q10.4a) x-intercept =

2

15

b) m RS = 2

7 = 2 ( 8) + C

y = 2 x 9

c) y-intercept = 9

P1

K1

K1

N1

P1

5 marks

Q10.5 a) k = 8

b) m ST =2

1

8 = 2 ( 5) + C

y = 2 x 2

c) 2x3

08=

= 2

x-intercept = 7

P1

K1

K1

N1

K1

N1

5 marks


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MATRICES

Q11.1a) n =

)2)(3()1(8

1

=2

1

b)

=

3

16

v

u

12

38

=

3

16

82

31

2

1

v

u

u =

2

7

v = 4

K1

N1

K1

K1

N1

N1

6 marks

Q11.2a) k =

)1)(3()2(4

1

=

11

1

h = 3

b)

=

21

4

y

x

21

34

=

21

4

41

32

11

1

y

x

x = 5

y = 8

N1

P1

K1

K1

N1

N1

6 marks


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7

Q11.3 a) p = 3( 5) (2)(4)

= 7

b)

=

19

16

y

x

54

23

=

19

16

34

25

7

1

y

x

x = 6

v = 1

K1

N1

K1

K1

N1

N1

6 marks

Q11.4a)

)5)(4()3(6

1

OR

64

53

=2

1

64

53

b)

=

4

7

y

x

34

56

=

4

7

64

53

2

1

y

x

x =2

1

y = 2

K1

N1

K1

K1

N1

N1

6 marks


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Q11.5 a) n = 3( 8) (9)(2)

= 6

m = 3

b)

=

12

6

39

28

6

1

w

u

u = 12

w = 15

K1

N1

P1

K1

N1

N1

6 marks

Answer

SETS

( 1 ) a)

K

b)

( 2) a) R

P Q

G

M

G M


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9

b )

Answer:

(3)J L J L

a) K b) K

4) a) (.P Q R) b) .P Q R

5) a) ( A B) C b) A ( B C)

LINES AND PLANES IN 3-DIMENSIONS

1) SBD = tan -1 10

1414

= 35.27

2) a) ON = 5 cm

b) cos KON = 5

10

= 60

3) a) 13 cmb) PRSc) PRS = 6723

4) a) PRS

b) RPQc) RLMd) PRS = 3341

5) a) BH = 20.98 cmb) HBD = 2529

QUADRATIC EQUATIONS


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10

1) x = 5 or x=-1

2) x =1 or x= -8

3) s =2 or s=3

4) x =1 or x = 7

3

5) x = -5 or x = 2

Statistics

Answer:

1. a)

Height (cm) Frequency Midpoint

121-125 3 123

126-130 1 128

131-135 4 133

136-140 1 138

141-145 2 143

146-150 11 148

151-155 9 153

156-160 2 158

b) i) 146-150

ii) 4774/33 = 144.67

c)

0

12

3

4

5

6

7

8

9

10

11

12

118 123 128 133 138 143 148 153 158 163

Height

Frequency

2. a) i) 53 marks


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ii)

Mark Frequency Midpoint Upper boundary

20-29 0 24.5 29.5

30-39 4 34.5 39.5

40-49 6 44.5 49.5

50-59 10 54.5 59.560-69 8 64.5 69.5

70-79 7 74.5 79.5

80-89 5 84.5 89.5

90-99 0 94.5 99.5

b) 2410/ 40 = 60.25

c)

0

1

2

3

4

5

6

7

8

9

10

11

24.5 34.5 44.5 54.5 64.5 74.5 84.5 94.5

Midpoint

Frequency

3. a) i) 29ii)

Time (s) Frequency Midpoint Upper boundary

20-24 6 22 24.5

25-29 6 27 29.5

30-34 9 32 34.5

35-39 3 37 39.5

40-44 4 42 44.5

45-49 2 47 49.5

b) i) 30-34

ii) 31.83 s


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c)

0

1

2

3

4

5

6

7

8

9

10

22 27 32 37 42 47

Midpoint

Frequency

4. a)

Number of pages Frequency Midpoint

10-12 2 11

13-15 1 14

16-18 3 17

19-21 5 20

22-24 8 23

25-27 6 26

28-30 5 2931-33 2 32

b) 736/32 = 23

c)

0

1

2

3

4

5

6

7

8

9

11 14 17 20 23 26 29 32

Midpoint

Frequency

d) The modal class is 22-24

5. a)


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13

Mass(kg) Upper boundary Frequency Cumulative

frequency

200-229 229.5 2 2

230-259 259.5 3 5

260-289 289.5 4 9

290-319 319.5 7 16

320-349 349.5 10 26350-379 379.5 10 36

381-409 409.5 3 39

410-439 439.5 1 40

b)

0

5

10

15

20

25

30

35

40

45

199.5 229.5 259.5 289.5 319.5 349.5 379.5 409.5 439.5

Mass

CummulativeFrequency

c) i) 358.5 g

ii) 3/4 of the total number of the packages weighed less than 358.5 g

TRANSFORMATION

1. (a) (i) line CD(ii) line EF

(iii) line AB

(b) (i) Scale factor =TQ

RQ

=16

14

=3

7

= 2

3

1

(ii) Area of image = k2 x Area of object

16 =

3

12

2x Area of SQT


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14

Area of SQT = 16

3

12

2

= 16

3

7 2

= 16

7

3 2

=

49

144

= 2.9388cm2

2. (a) (i) (-3, 4)

(ii) (a) (-2, 3)(b) (0, 4)

(b) R reflection in the line DGS- an enlargement about the centre D with scale factor 3

3. (a)

(b) Transformation R1R

2is equivalent to a single rotation of 180o

clockwise / anticlockwise about the origin (0,0)

4. (a) (i) The coordinates of the centre of rotation = (1, 1)

(ii) 90o


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15

(iii) (6, 2)

(b) Y is a translation of

3

4

X is an enlargement with a scale factor of 2 at the centre (1, 1)

5) (a)

(b) A(12, -3), B(6, -3), C(8, -5), D(10, -5)

ANSWERS (PLAN AND ELEVATION)

1(a)

M/N

Q/P

RJ

E/F

5 cm

2 cm

H/G

5 cm


16/26

16

2

X/T

G/P/S

H/QJ/R

F/N/W

V/U

E/M

L

5 cm

2 cm

7 cm

5 cm

2 cm

(b)(i)

X/L/V

S/W

P/NG/F

H/J

T/UK

E M

Q/R

7 cm3 cm

2 cm

2 cm

5 cm 2 cm


17/26

17

K/L

D/E

J/MH/N

G/F

3 cm

6 cm

2 cm

J

H/G

P/U Q/T

R/S

N/F

M/W

L/EK/D4 cm

2 cm

5 cm

3 cm

3 cm

R

QP

T/S

K/J/HL/M/N

D/G

2 cm

2 cm

4 cm

3 cm

(a)

(b)(i)

(b)(ii)

U/E/W/F

3.


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18

J/K

H/LG/M

F/NE/P8 cm

4 cm

4 cm

7 cm

6 cm

4 cm 4 cm

3 cm

3 cm

X/W

G/F

M/NK/P

U/V

S/EH/T

L

E/FP/N

L/M H/G

S/TV/W

UK

X

3 cm

3 cm

3 cm

2 cm

2 cm

(a)

(b)(i)

(b)(ii)

4.


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19

Q/B

R/C

T/P/A

U/S/D

6 cm

6 cm

3 cm

(a)

T

DA

QRSP

U

BC

6 cm

4 cm

RP

UT

Q/S

CAB/D

4 cm

2 cm

3 cm 3 cm

(b) (c)

5.


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20

P/AS/E/D

R/F/H

G/C

Q/M

B

3 cm

3 cm

4 cm

4 cm

3 cm

4 cm 3 cm

Q/P R/S

G/F/E

HM

B/AC/D

P/S Q/R

EF G

A/D B/C

M/H

3 cm

4 cm

6 cm

(b) (c)

(a)


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Marking Scheme Mod Paper 2, Q13

Q13.1 a)

x 3 1.5

y 8 16

b) Graph

Both x-axis and y-axis are correctly oriented , uniform scales

are used in the range 4 4x and 24 y 24

7 points and *2 points are plotted correctly

The curve is smooth, continuous , without any straight lineand passes through all the points.

-25

-20

-15

-10

-5

0

5

10

15

20

25

-4 -3 -2 -1 0 1 2 3 4

c) (i) 8 < y 9

(ii) 1.8 x 1.9d) y = 2x + 5

The straight line y = 2x + 5 is drawn correctlyon the graph

2.5 < x < 2.3

K1, K1

K1

K2

N2

P1P1

K1

K1

N1

12marks


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22

Q13.2 a) (i) k = 10

(ii) m = 0

b) Graph

Both x-axis and y-axis are correctly oriented , uniform scalesare used in the range 2 5x and 8 y 24


The curve is smooth, continuous , without any straight line

and passes through all the points.

-10

-5

0

5

10

15

20

25

-3 -2 -1 0 1 2 3 4 5 6

c) (i) 4 y 5

(ii) 2.1


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23

Q13.3 a)

x 1 4

y 20 5

b) Graph

Both x-axis and y-axis are correctly oriented , uniform scalesare used in the range 2 x 5 and 22 y 24




-25

-20

-15

-10

-5

0

5

10

15

20

25

-3 -2 -1 0 1 2 3 4 5 6

c) (i) 1.5 y 2.5

(ii) 4.2


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24

Q13.4 a)

x 2 2

y 8 12

b) Graph



The curve is smooth, continuous , without any straight lineand passes through all the points.

-10

-5

0

5

10

15

20

25

30

-4 -3 -2 -1 0 1 2 3 4

c) (i) 10.5 y 11.5

(ii) 2.5


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Q13.5 a)

x 2 3

y 19 31

b) Graph





-60

-50

-40

-30

-20

-10

0

10

20

30

40

50

60

-4 -3 -2 -1 0 1 2 3 4

c) y = 4x

The straight line y = 4x is drawn correctly

on the graph

1.8 x< 2.0d) The straight line y = 10x + 40 is drawn correctly

on the graphThe straight line y = 20 is drawn correctly

on the graphRegion R is shaded correctly

K1, K1

K1

K2

N1

K1

K1

N1

K1

K1N1

12

marks

R


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Aswer SSI Mathematics Module