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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PPSMI ASSESMENT 2006 MATHEMATICS 1449/2
FORM 4 No Marking Scheme Marks
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
Panel Pakar Runding GC MMMT
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PPSMI ASSESMENT 2006 MATHEMATICS 1449/2
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
Panel Pakar Runding GC MMMT
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PPSMI ASSESMENT 2006 MATHEMATICS 1449/2
FORM 4 No Marking Scheme Marks
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
Panel Pakar Runding GC MMMT
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PPSMI ASSESMENT 2006 MATHEMATICS 1449/2
FORM 4 No Marking Scheme Marks
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
Panel Pakar Runding GC MMMT
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PPSMI ASSESMENT 2006 MATHEMATICS 1449/2
FORM 4 No Marking Scheme Marks
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
Panel Pakar Runding GC MMMT
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PPSMI ASSESMENT 2006 MATHEMATICS 1449/2
FORM 4 No Marking Scheme Marks 14.
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
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PPSMI ASSESMENT 2006 MATHEMATICS 1449/2
FORM 4 No Marking Scheme Marks
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
Panel Pakar Runding GC MMMT
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PPSMI ASSESMENT 2006 MATHEMATICS 1449/2
FORM 4 No Marking Scheme Marks 16.
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
Panel Pakar Runding GC MMMT
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