maths answer ppsmi2006 f4 p2

PPSMI ASSESMENT 2006 MATHEMATICS 1449/2

FORM 4 No Marking Scheme Marks

P1 P2

1.

a) ∈ b. ∈

3

K1 K1 K1 N1

2.

1 x 15 x 15 x 21 3 22 x 7 x 7 x 9 7 2 2 1 x 15 x 15 x 21 + 22 x 7 x 7 x 9 3 7 2 2 1228.5

4 K1 K1 N1 N1

3.

4m + 2n = 6 @ 6m + 3n = 9 5n = -5 @ 10m = 20 n = -1 , m = 2

4

P Q

P Q R

1

Panel Pakar Runding GC MMMT

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K1 K1 N1 K1 K1 N1

4.

a) 270o x 2 x 22 x 21 @ 90o x 2 x 22 x 14 360o 7 360 o 7 270o x 2 x 22 x 21 + 90o x 2 x 22 x 14 + 7 + 7 360o 7 360 o 7 135 b) 270o x 22 x 21 x 21 @ 60o x 22 x 14 x 14 360o 7 360 o 7 270o x 22 x 21 x 21 60o x 22 x 14 x 14 360o 7 360 o 7 936.8 6

K1 K1 N1 N1

5.

2x2 5x + 3 = 0 ( x - 1 ) ( 2x - 3 )= 0 x = 1 , 3 2

4

P1 P2 P2

6.

a) Statement

b) If 4k < 20, then k < 5

If k < 5, then 4k < 20

c) n + 1 is not an even number 5

2




FORM 4 No Marking Scheme Marks 7.

a) y = 4 b) Identify mRS = 3

31320

=−−

xy or equivalent

y = 3x − 19 or equivalent c) 0 = 3x − 19

3

19=x or

316

P1 P1 K1 N1 K1 N1 P1 K2 N1

8.

< AGD Tan θo = 6 5 θo = 50.19 o @ 50° 11’

4

P2 K2 N1

9.

a) 6 11 b) 1 = 12 3 x x = 36 5

3





P1 K1 K1 N1 K1 N1

10. a) mRQ = 5 3 b) 10 = 5 ( 3) + c 3 c = 5 y = 5 x + 5 3 c) 0 = 5 x + 5 3 x = -3 6

P1 P1 P2 P2

11.

a) i. >

ii. <

b) PQRST is a pentagon c) 3n2 where n = 0, 1, 2, 3, …

6

4





P1 K1 N1 K1 N1 P1 K1 K1 N1 P1 K1 N1

12.

a) i. m OA = 4

ii. c = -18 y = 4x – 18

iii. mAB = 2 5 c = 18 5

b) i. Identify ∠ NLJ 97161212 22 ⋅+= orJL

tan θo = 5 16.97

θo = 16.42o or 16o 25’

ii. Identify ∠NMJ tan θo = 5

13 θo = 22⋅62o or 22o 37’

12

5





P1 P1 P2 P2 K1 K1 N1 K1 K1 N1

13.

a) i. { 2, 3, 5, 6, 8, 9, 11, 12 } ii. { 2, 6, 8, 12 }

iii. 21@

84

iv.53@

106

b) i. 60o x 2 x 22 x 28 360o 7 60o x 2 x 22 x 28 + 28 + 14 + 14 + 14 +14 360o 7 113 1 3 ii. 60o x 22 x 28 x 28 @ 150o x 22 x 14 x 14 360o 7 360o 7 60o x 22 x 28 x 28 + 14 x 14 - 150o x 22 x 14 x 14 360o 7 360o 7 350

12

6





a) 3n2 – 11n – 4 = 0

( n – 4 ) ( 3n + 1 ) = 0 n = 4, - 1 3

b) x2 – 2x + 24 = 0 ( x – 6 ) ( x + 4 )= 0 x = 6, - 4 c) 1 x 22 x 7 x 7 x 10 2 7 1 x 1 x 22 x 7 x 7 x 5 2 3 7 1 x 22 x 7 x 7 x 10 + 1 x 1 x 22 x 7 x 7 x 5 2 7 2 3 7 898 1 3

K1 K1 N1, N1 K1 K1 N1, N1 K1 K1 K1 N1

15.

a).

Age Frequency Mid point Upper boundary

1-5 6-10 11-15 16-20 21-25 26-30

( I ) 1 4 9 9 5 2

( II ) 3 8 13 18 23 28

( III ) 5.5 10.5 15.5 20.5 25.5 30.5

All values in column ( I ) correct All values in column ( II ) correct All values in column ( III ) correct

b) Mean= 1(3) + 4(8) + 9(13) + 9(18) + 5(23) + 2(28) or 485 30 30

= 16.17

P2 P1 P1 K2 N1

7





K1 K2 N1 P1

c) Histogram

Using the uniform scales for 0.5 ≤ x ≤ 30.5 and 0 ≤ y ≤ 9 6 bars* drawn correctly. Note: 5 or 4 bars* drawn correctly. K1 The 6 bars with correct frequencies are drawn. d) 16 x 100 = 53.33%

30 * referring to candidates frequencies

12

8





a) Age (years)

Frequency Cumulative frequency

Upper boundary

10 – 14

0

( I ) 0

( II ) 14.5

Row I

15 - 19 10 10 19.5 20 – 24 20 30 24.5 25 – 29 50 80 29.5 30 – 34 60 140 34.5 35 - 39 36 176 39.5 40 - 44 18 194 44.5 45 - 49 6 200 49.5

All values in Row I correct. All values in Column ( I ) correct excluding Row I correct. All values in Column ( II ) correct excluding Row I correct. b) Mean = 10(19.5) + 20(24.5) + 50(29.5) + 60(34.5) +36(39.5) + 18(44.5) +6(49.5) 200 Or 6750 200 33.75 c) x-axis is drawn with the right direction and uniform scaled from 14.5 ≤ x ≤ 49.5 y-axis is drawn with the right direction and uniform scaled from 0 ≤ y ≤ 200 All eight points* plotted correctly. Note : Seven or six points* plotted correctly. P1 All the right eight points plotted correctly and ogive is drawn smoothly passing

through all the points. * referring to candidates frequencies

P1 P2 P1 K2 N1 P1 P1 P2 N1

9



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