3. PPSMI ASSESMENT 2007 ppr maths nbk
MATHEMATICS 1449/2
FORM 4
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. P1
If ∠M = ∠N then ∠M and ∠N are vertically opposite angles. P1
(c) Ali will not receive a certificate. P2
5
10 3 −1 K1
(a) m PQ =
−1− 4
2 N1
= −
5
2 K1
(b) 1 = − (−5) + c or c = −1 or any other correct method
5
2
y = − x −1 N1
5
4
11 3 K1
(a) y = − x+5
4
x = −5 N1
3 15 K1
(b) 0 = − (−5) + c or c=− or any other correct method
4 4
3 15
y =− x− N1
4 4
15
y − intercept = − N1
4
5
3
4. PPSMI ASSESMENT 2007 ppr maths nbk
MATHEMATICS 1449/2
FORM 4
No Marking Scheme Marks
12 (a)(i)
Q
P R
P1
(ii) Q
P R
P2
3
(b)(i) h = 6 P1
6−0 K1
(ii) or 2
3−0
6 = 2 (7) + c or c = −8 any other correct method K1
y = 2x − 8
N1
(iii) ( 4 , 0 )
P1
5
(c) ∠VQR P1
6
tan θ = K2
8
N1
θ = 36⋅87° @ 36° 52’
4
12
4
6. PPSMI ASSESMENT 2007 ppr maths nbk
MATHEMATICS 1449/2
FORM 4
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
P1
4 class interval correct ( row III to VI )
P1
6 values correct ( column I )
P2
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
P1
and for y-axis with 0 ≤ y ≤ 40
Using the upper boundaries for the horizontal axis P1
6 points plotted correctly P2
Note: 5 points plotted correctly give P1
The point ( 4⋅5 , 0 ) plotted or ogive passes through ( 4⋅5 , 0) P1
A smooth and continuous curve passing through 6 correct points G1
(c)(i) 19 ± 0⋅5 P1
(ii) The 30th pupil took “20⋅5 minutes” ( refer to candidate’s median) to go P1
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.
12
6
7. PPSMI ASSESMENT 2007 ppr maths nbk
MATHEMATICS 1449/2
FORM 4
No Marking Scheme Marks
16 (a)
Midpoint Frequency
Height (cm)
Column I Column II
I 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
P1
4 class interval correct ( row III to VI ) P1
6 values correct ( column I )
P2
6 values correct ( column II )
Note: 4 or 5 correct give P1
(b)
(6 × 152) + (4 × 157 ) + (6 × 162) + (8 × 167 ) + (9 × 172) + (7 × 177 ) K2
40
165.875 ( 165.9 ) N1
(c) Using uniformly scaled axis for horizontal axis with 149⋅5 ≤ x ≤ 179⋅5 P1
and for vertical axis with 0 ≤ y ≤ 9
Using the correct lower and upper boundaries OR midpoints P1
for the horizontal axis
6 vertical bars drawn correctly P2
Note: 5 bars drawn correctly give P1
(d) Any correct information. P1
Example:
There are 4 pupils whose height are in the range 155 − 159 cm.
12
7
8. PPSMI ASSESMENT 2007 ppr maths nbk
MATHEMATICS 1449/2
FORM 4
Graph for Question 15.
Graph is not drawn to scale.
40 ∗
∗
35
∗
30
25
∗
20
15
10 ∗
5
∗
0
4⋅5 9⋅5 14⋅5 19⋅5 24⋅5 29⋅5 34⋅5
8
9. PPSMI ASSESMENT 2007 ppr maths nbk
MATHEMATICS 1449/2
FORM 4
Graph for Question 16.
Graph is not drawn to scale.
9
8
7
6
5
4
3
2
1
0
149⋅5 154⋅5 159⋅5 164⋅5 169⋅5 174⋅5 179⋅5
9
