PPSMI ASSESMENT 2007 ppr maths nbk MATHEMATICS 1449/2

FORM 4

1

No Marking Scheme Marks 1 (a)

(b)

P1 P2

32 (a) ∠QXV

22 63 +

tan θ = 22 63

6+

or 456

θ = 41⋅81° or 41° 48’

P1 K1 K2 N1

(b) ∠SPR

tan θ = 87

θ = 41⋅19° or 41° 11’

P1 K2 N1

93

1077722

×××

877722

31

××××

877722

311077

722

××××+×××

1950⋅67 ( accept 1951 )

K1 K1 K1 N1

4

P Q

R

P Q

R

PPSMI ASSESMENT 2007 ppr maths nbk MATHEMATICS 1449/2

FORM 4

2

No Marking Scheme Marks4 2y 2 − 5y − 3 = 0

( 2y + 1 ) ( y − 3 ) = 0

y = 3,21

−

K1 K1 N1 N1

45 12n 2 − 8n + 1 = 0

( 6n − 1 ) ( 2n − 1 ) = 0

21,

61

=n

K1 K1 N1 N1

46 3v − 9w = 15 or any other correct method.

−8w = 12

23

−=w

21

=v

K1 K1 N1 N1

47 4d − e = 24 or any other correct method.

7d = 35 d = 5 e = −4

K1 K1 N1 N1

48

(a) 217222

360300

×××

2121217222

360300

++×××

152

K1 K1 N1

(b)

221

221

722

360180@2121

722

360300

××××××

221

221

722

3601802121

722

360300

×××−×××

75981@43981 ⋅

K1 K1 N1

6

PPSMI ASSESMENT 2007 ppr maths nbk MATHEMATICS 1449/2

FORM 4

3

No Marking Scheme Marks 9 (a) All even numbers are divisible by 6 or 3 is a factor of 6.

P1

(b) If ∠M and ∠N are vertically opposite angles then ∠M = ∠N. If ∠M = ∠N then ∠M and ∠N are vertically opposite angles.

P1 P1

(c) Ali will not receive a certificate. P2 510

(a) 41

13−−−

=PQm

= 52

−

K1 N1

(b) c+−−= )5(

521 or c = −1 or any other correct method

152

−−= xy

K1 N1

411

(a) 543

+−= xy

x = −5

K1 N1

(b) c+−−= )5(

430 or

415

−=c or any other correct method

4

1543

−−= xy

4

15intercept −=−y

K1 N1 N1

5

PPSMI ASSESMENT 2007 ppr maths nbk MATHEMATICS 1449/2

FORM 4

4

No Marking Scheme Marks 12 (a)(i)

(ii)

P1 P2

3 (b)(i) h = 6

(ii) 0306

−− or 2

6 = 2 (7) + c or c = −8 any other correct method y = 2x − 8 (iii) ( 4 , 0 )

P1 K1 K1 N1 P1

5 (c) ∠VQR

86θtan =

θ = 36⋅87° @ 36° 52’

P1 K2 N1

4 12

P Q

R

P Q R

PPSMI ASSESMENT 2007 ppr maths nbk MATHEMATICS 1449/2

FORM 4

5

No Marking Scheme Marks 13 (a)(i) (a) False

(b) True (ii) If k2 > 49 then k > 7. If k > 7 then k2 > 49 . (iii) 6 × m ≠ 18.

P1 P1 P1 P1 P2

6

(b)(i) 27

7222

360180@7

7222

360180

××××××

727

7222

3601807

7222

360180

+×××+×××

40

(ii) 27

27

722

360180@77

722

360150

××××××

27

27

722

36018077

722

360150

×××−×××

44⋅92

K1 K1 N1 K1 K1 N1

6 1214 (a) 2x 2 + 7x − 15 = 0

( 2x − 3 ) ( x + 5 ) = 0

23

=x , −5

K1 K1 N1 N1

4 (b) x + 4y = 68 or 3x − y = 9 or any other correct method

13x = 104 or 264

13=x

x = 8 y = 15

K1 K1 N1 N1

4

(c) 108831

×××

444 ××

444108831

××−×××

149⋅3

K1 K1 K1 N1

4 12

PPSMI ASSESMENT 2007 ppr maths nbk MATHEMATICS 1449/2

FORM 4

6

No Marking Scheme Marks 15 (a)

Frequency Cumulative Frequency Time (minutes) Column I Column II I 5 – 9 3 3 II 10 – 14 7 10 III 15 – 19 12 22 IV 20 – 24 11 33 V 25 − 29 5 38 VI 30 − 34 2 40

4 class interval correct ( row III to VI ) 6 values correct ( column I ) 6 values correct ( column II ) Note: 4 or 5 correct give P1 (b) Using uniformly scaled axis for x-axis with 4⋅5 ≤ x ≤ 34⋅5 and for y-axis with 0 ≤ y ≤ 40 Using the upper boundaries for the horizontal axis 6 points plotted correctly Note: 5 points plotted correctly give P1 The point ( 4⋅5 , 0 ) plotted or ogive passes through ( 4⋅5 , 0) A smooth and continuous curve passing through 6 correct points (c)(i) 19 ± 0⋅5 (ii) The 30th pupil took “20⋅5 minutes” ( refer to candidate’s median) to go to school. OR Less than 30 pupils took less than “20⋅5 minutes” ( refer to candidate’s median) to go to school. OR More than 30 pupils took more than “20⋅5 minutes” (refer to candidate’s median) to go to school.

P1 P1 P2 P1 P1 P2 P1 G1 P1 P1

12

PPSMI ASSESMENT 2007 ppr maths nbk MATHEMATICS 1449/2

FORM 4

7

No Marking Scheme Marks 16 (a)

Midpoint Frequency Height (cm) Column I Column III 150 − 154 152 6 II 155− 159 157 4 III 160 – 164 162 6 IV 165 – 169 167 8 V 170 − 174 172 9 VI 175 − 179 177 7

4 class interval correct ( row III to VI ) 6 values correct ( column I ) 6 values correct ( column II ) Note: 4 or 5 correct give P1

(b) ( ) ( ) ( ) ( ) ( ) ( )40

177717291678162615741526 ×+×+×+×+×+×

165.875 ( 165.9 ) (c) Using uniformly scaled axis for horizontal axis with 149⋅5 ≤ x ≤ 179⋅5 and for vertical axis with 0 ≤ y ≤ 9 Using the correct lower and upper boundaries OR midpoints for the horizontal axis 6 vertical bars drawn correctly Note: 5 bars drawn correctly give P1 (d) Any correct information. Example: There are 4 pupils whose height are in the range 155 − 159 cm.

P1 P1 P2 K2 N1 P1 P1 P2 P1

12

PPSMI ASSESMENT 2007 ppr maths nbk MATHEMATICS 1449/2

FORM 4

8

∗

9⋅5 4⋅5 14⋅5 19⋅5 24⋅5 29⋅5 34⋅50

5

10

15

∗

∗

∗

∗∗

20

25

30

35

40

Graph is not drawn to scale.

Graph for Question 15.

PPSMI ASSESMENT 2007 ppr maths nbk MATHEMATICS 1449/2

FORM 4

9

149⋅5 154⋅5 159⋅5 164⋅5 169⋅5 174⋅5 0

1

2

3

4

5

6

7

8

Graph is not drawn to scale.

Graph for Question 16.

9

179⋅5