MATHEMATICS – SEC LEVEL
MS06
MARKING SCHEME – PAPER IIB
MAY 2006 SESSION
Question
Number
Answer
Mark
1(i)
2006 − 1922 = 84 years
B1
(ii)
1922 + 100 = 2022
B1
Notes
Total: 2 marks
2(a)
B2
40, 46
(b)
(c)
12 + 22 + 32 + …
Hence term is: 852 (or 7225)
M1
A1
For correct rotation
For precise position
M1
For establishing pattern [e.g. the following
2 consecutive terms] [e.g +3, +5, +7, at
least 3 consecutive]
Accept both as correct.
A1
Total: 6 marks
3
C 2.1m
4
0.6
0.125
B1
60%
1
8
11
4
or 2 34
275%
B2
B2
[do not accept 0.13]
B2
Total: 6 marks
Page 1 of 6
MATHEMATICS – SEC LEVEL
5(i)
MS06
1
2
Median lies at
(60 + 1)
Hence between 30 & 31st
Median is 2
(ii)
Mean =
1
60
(0 + 11 + 34 + 60 + 24 + 10 + 6)
= 2.4166 = 2.42 (2 d.p)
M1
A1
Award M1 only if ‘17’ given as answer
Full marks for answer only
M1
Multiply and add [accept 1 incorrect
product]
Divide the ‘multiplied and added terms’
by 60
2 d.p.
M1
A1
Total: 5 marks
6
AĈB = 60 180 − 90 − 60 = 30º = RĈS (angles on a
straight line)
x = 180 − 90 − 30 (angles in a ∆)
x = 60º
B1
M1
M1
A1
Reason must be given
Reason must be given
Total: 4 marks
7
M1
M1
2(x + 3x ) = 14
x + 3x = 7
4x = 7
x = 74 = 1.75 cm
Ratio ‘Length : breadth’ used correctly
Forming equation for perimeter
A1
Total: 3 marks
8(a)
2 4 ×32
4
= 164×9 = 36
36 = 62
(b)
(c)
(15 )2 = 251
(15 )−2 = 25
2
Hence (15 ) ,
3
4
−
5
6
5,
× 103
= 34 − 14 =
2
4
=
1
2
(15 )−2
M1
M1
A1
Correct interpretation of 24 and 32
Simplify to 36
Accept both 62 and p = 6
M1
For evaluating both
A1
Or equivalent
M1
A1
A1
(15 )2 and (15 )−2
÷ as inverted ×
For obtaining 14
Total: 8 marks
Page 2 of 6
MATHEMATICS – SEC LEVEL
9
MS06
a = 67
b = 67 × 2 = 134
B1
B1
If values of a and b not indicated clearly
award only one B mark.
Total: 2 marks
10
108% … 162cm
1% … 162
108
Hence 100% …
M1
162
× 100
108
= 150cm
M1
A1
Equating 162cm with 108% or
proportional statement
For correct proportion [including
substitution]
Or 1.5m [accept 1.5 only if working with
1.62]
Total: 3 marks
11(a)
(b)
45 × 30 = 1350 pupils
1350 ÷ 25
= 54 classes
M1
M1
A1
Multiplying 45 by 30
Dividing by 25
Full marks for answer only
5 + 6 + 4 = 15 parts
1 part = 120 ÷ 15 = 8
Hence 8 × 5
= 40
M1
M1
M1
A1
Adding the three given ratios
Dividing 120 by ‘sum of ratios’
Multiplying (120 ÷ sum of ratios) by 5
Total: 7 marks
12
1253 × 2.6 = 3257.8 cents
= Lm32.578 + Lm2
17
= Lm35.578 + 100
× 34.578
= Lm34.578 + Lm5.878
= Lm40.456
= Lm40.46
M1
For multiplying 1253 by 2.6
A1
M1
Lm34.578 [or Lm34.58 or 3458c]
Add 17% of bill total [even if
Lm2 has not been added] to itself [or
117% of bill]
A1
Total: 4 marks
Page 3 of 6
MATHEMATICS – SEC LEVEL
13(i)
T = 2π
MS06
38.7
9.8
M1
A1
For substitution of values in formula
M1
M1
Squaring both sides
A1
Or equivalent
= 12.48 = 12.5
(ii)
T 2 = 4π 2
()
l
g
4π 2l = gT 2
l=
gT 2
For dividing by 4π 2 or multiplying by g
4π 2
Total: 5 marks
14
2x − 4y + 14
= 2(a2 + 2a − 1) − 4(a + 3) + 14
M1
= 2a2 + 4a − 2 − 4a − 12 + 14
= 2a2
M1
M1
A1
For both substitutions [award with no
brackets only if second M1 is awarded]
For expanding both brackets
For adding/subtracting like terms
Total: 4 marks
15
Area small trapezium = 5(12 + 4) ÷ 2
= 40cm2
M1
For using formula for area of trapezium
and substitution
A1
Area large trapezium = 17(4 + 16) ÷ 2
= 170cm2
M1
For using formula for area of trapezium
and substitution
Area semi-circle = π(82) ÷ 2 = 32π
= 100.53cm2
M1
For using formula for area of semi-circle
and substitution
Total area = 40 + 170 + 100.53
= 310.53 = 310.5cm2 (1 d.p.)
M1
A1
Adding the areas to give the total area
Total: 6 marks
Page 4 of 6
MATHEMATICS – SEC LEVEL
16(i)
P(Girls) =
MS06
19
11+19
=
19
30
B1
B1
Numerator 19
Denominator 30
(ii)
30 − (7 + 5) = 18
P(Brown) = 18
= 53
30
M1
A1
Subtracting (7 + 5) from 30
Or equivalent [e.g. 0.6 and 60%]
(iii)
18 Brown eyes: 9 Boys & Girls
5 Blue eyed Girls [or 2 green eyed Boys]
19 − (9 + 5) = 5 Green eyed Girls
5
P(Green eyed Girl) = 30
= 16
A1
A1
M1
A1
For number of Brown eyed Girls
For number of Blue eyed Girls
For obtaining 19 − (9 + 5)
Or equivalent
Total: 8 marks
17(i)
(ii)
BÂC = 75 − 45
= 30º
sin 30 =
AC =
10
AC
10
sin 30
AC = 20km
[or cosine ratio]
M1
A1
M1
M1
A1ft
Full marks for answer only
For correct ratio and substitution
For making AC subject
[ft for incorrect (ii) - for acute angles
only]
Total: 5 marks
18(i)
(ii)
 − 9
 
 −1
B1
A1
For correct values of x and y
For correct column vector notation
[including correct values]
M1
For 180º rotation
A1
Accuracy of image
Total: 4 marks
Page 5 of 6
MATHEMATICS – SEC LEVEL
19(i)
MS06
60º = 30 + 30 [5min ≡ 30º]
5min + 5min = 10min
M1
For equivalence between minutes and
degrees [accept if shown on diagram]
A1
(ii)
1h 25min: 360º + 150º
= 510º
B1
M1
A1
150º
For adding 360º to previous answer
Total: 5 marks
20(i)
Length = 42 ÷ 7 = 6cm
Width = 12 ÷ 4 = 3cm
B1
B1
Do not award B marks unless clear
reference is made to which is which [okay
if marked on diagram]
(ii)
Area of 1 rectangle = 6 × 3 = 18cm2
Total area = 18 × 16 = 288cm2
M1
M1
A1
For obtaining area of 1 rectangle = 6 × 3
For multiplying area of 1 rectangle by 16
Award full marks for answer only [No ft
here]
(iii)
2 × (42 + 12)
= 2 × 54
= 108cm
M1
M1
A1
Sum of horizontal lengths = 42
Sum of vertical parts = 12
Award full marks for answer only
[If answer is 114, award M2, A0]
Total: 8 marks
21
2x − 3y + 6 = 0
3y = 2x + 6
y = 23 x + 2
Gradient =
y = mx + 5
y = 23 x + 5
2
3
M1
For making y subject
A1
M1
A1
For using y = mx + c and substituting
c=5
Or equivalent
Total: 4 marks
Page 6 of 6