Queen’s College 2010-2011
Yearly Exam, Maths paper I
Page total
QUEEN’S COLLEGE
Yearly Examination, 2010-2011
Class
Class Number
MATHEMATICS PAPER 1
Question-Answer Book
Secondary 1
Date: 16 – 6– 2011
Time: 8:30 am – 9:45 am
Marking Scheme
Teacher’s Use Only
1.
Write your class, class number in the spaces
provided on this cover.
2.
This paper consists of TWO sections, A and B.
Section A carries 80 marks and Section B carries
40 marks.
3.
Attempts ALL questions in this paper. Write your
answers in the spaces provided in this
Question-Answer Book.
4.
Unless otherwise specified, all working steps must
be clearly shown.
5.
The diagrams in this paper are not necessarily
drawn to scale.
 page 1–
Question No.
Max. marks
1
10
2
5
3
7
4
6
5
10
6
8
7
10
8
11
9
13
10
20
11
20
Total
120
Marks
Queen’s College 2010-2011
Yearly Exam, Maths paper I
Page total
SECTION A
Short questions. (80 marks)
Answer ALL questions in this section and write your answers in the spaces provided.
1.(i) State, for each of the following pairs of figures, the corresponding transformation. (c) is an
example which is done for you.
Reflection:(1),
Rotation:(2),
(a) 2
e.g.(c)
Translation:(3),
Reduction:(4) or Enlargement:(5).
(b) 3
1
(e) 1 or 2
(d) 1 or 2
(f) 4
(5 marks)1 mark for each question
(ii)
Given the following symbols.
Classify them according to their numbers of fold.
(5 marks)
symbols
No rotational symmetry
[, }, 3, 6
1A: any 2 correct,
2-fold rotational symmetry
8
1A
4-fold rotational symmetry
+
1A
6-fold rotational symmetry
*
1A
 page 2–
2A: all correct
Queen’s College 2010-2011
Yearly Exam, Maths paper I
2.
Page total
N identical metal cubes of sides 2cm are melted and recast into a cuboid which measures
4m × 6m × 8m. Find the value of N.
(5 marks)
N  2 3  400  600  800
1M : set up eqt., 1M : change unit, 1A
N  400  600  800  2 3
 400  600  100
 24000000
3.
2A
The figure shows a triangle ABC, where BC is horizontal and AB is vertical.
(a) Write down the coordinates of B.
A(2, 7)
(b) Find the area of triangle ABC.
B
C(10, 1)
(7 marks)
(a) B = (2, 1)
1A, 1A
(b) AB  7  1
1M
6
1A
BC  10  2
8
Area of ABC  6  8  2
 24 sq.units
1A
1M : using the length of AB and BC
1A
 page 3–
Queen’s College 2010-2011
Yearly Exam, Maths paper I
4.
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A point P(3, 1) is translated 4 units upward to point Q, and Q is then reflected in the y-axis
to point R. If R is rotated anticlockwise about the origin through 270 to point S, find the
coordinates of Q, R and S.
(6 marks)
Q = (3, 1+4)
1M
= (3, 5)
1A
R = (3+2×3, 5)
= (3, 5)
1M
1A
Or R = ((3), 5)
S= (5, (3))
= (5, 3)
1M
1A
5.
In the figure, AB // CD.
(a) Express DEB in terms of a and c.
(b) Express. CEA in terms of b and c.
(c) Express. CEA in terms of a.
(d) Hence find a relation of a, b and c.
E
C
D
c
A
b
a
B
(10 marks)
(a) DEB  c  a  180
int. s , AB//CD
DEB  180  a  c
(b) CEA  c  b
1A
alt. s , AB//CD
1A, 1R
CEA  b  c
(c) CEA  a
1A, 1R
1A
alt. s , AB//CD
1A, 1R
(d) By (b) and (c), a  b  c
1M, 1A
b  ac
Or c  b-a
 page 4–
Queen’s College 2010-2011
Yearly Exam, Maths paper I
6.
(a)
(b)
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The figure shows the grassland on the right. The area of grassland is A m 2 .
Express A in terms of a.
(3a-2)m
Suppose a is an even number, the grassland is divided into
several pieces of square grassland with side 2m. If a tree is
2a m
planted in each square grassland, how many trees are
2a m
planted.
(c)
The cost of one tree is $p and planting a tree is sponsored
$q by the sponsor. Express the amount required of planting trees in terms of a, p and q.
(d)
Given that a = 10, p = 200 and q = 120. find the amount required of planting trees.
(8 marks)
(a ) A  (3a  2)( 2a  4)  (2a)( 2a)
1M
 6a 2  12a  4a  8  4a 2
1A
 2a 2  8a  8
1A
(b) no. of trees  (2a 2  8a  8)  4

1M
2a 2  8a  8
4
a 2  4a  4

2
1A
(c) the cost  $( p  q) 
a 2  4a  4
2
(d ) the cost  ( p  q ) 
a 2  4a  4
2
1A
10 2  4  10  4
2
100  40  4
 80 
2
 80  68
 $5440
 (200  120) 
 page 5–
1M
1A
(2a+4)m
Queen’s College 2010-2011
Yearly Exam, Maths paper I
Page total
7. A man left 40% of his legacy to his wife, 20% of the remainder to his children and the rest to 10
charitable organisations.
(a) What percentage of his legacy was given to the charitable organisations?
(b) If each of the charitable organisations received $y, how much was the whole legacy worth?
(Express your answer in terms of y.)
(c) How much did the children get ? (Express your answer in terms of y.)
(10 marks)
(a) the percentage of the legancy given to the children and the charitable organisati ons
 100%  40%
 60%
1A
the required percentage  60%  (1  0.2)
1M
 60%  0.8
 48%
(b) the whole legacy  y 
1A
48%
10
 y  4.8%
1000
 y
48
125
5
$
y / $20 y
6
6
1M : using(a), 1A
1A
125
y  (1  40%  48%) 1M : using(b), 1M : percentage , 1A
6
125

y  12%
6
125
12

y
6
100
5
 $ y / $2.5 y
1A
2
(c) the amount the childen get 
Or the amount the childen get 
125
y  (1  40%)  20%
6
 page 6–
Queen’s College 2010-2011
Yearly Exam, Maths paper I
Page total
A
8.
(a)
(b)
Refer to the figure,
Find a triangle which is congruent to ABC . Give the reason.
Find (i)
ABC ,
(ii) DEB ,
(iii) AD.
D
(All working steps with references must be clearly shown)
(11 marks)
5cm
F
E
B
(a) ABC  EBD
30
5cm
C
1A :, 1A : ΔEBD , 1R
ASA
(b) (i) ABC  30  90  180
 sum of 
1A, 1R
ABC  180  120
 60
(ii) DEB  CAB  30
1A
corr.  s ,   s
Or In DBE , DBC  DEB  90  180
(iii) AB  EB
5cm
corr. sides ,   s
1A, 1R
 sum of 
1R
1A, 1R
AD  5  10
AD  5cm
1A
 page 7–
Queen’s College 2010-2011
Yearly Exam, Maths paper I
9.
(a)
(b)
(c)
(d)
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The pie chart shows the students’ favourite sports
and the distribution in Sam’s school. Given that
favour soccer has 112 students and favour volleyball
has 80 students.
Find the number of students in school.
Find the percentage of students favour basketball.
Find the values of x and y.
Find the number of students favour to table tennis.
Basketball
Soccer
42
123
Volley Ball x
y
Table Tennis
(13 marks)
42
360
360
 112 
42
 960
(a ) no of students  112 
1M, 1A
1A
123
 100%
360
42

 100%
120
1
205
 34 % or
%
6
6
(b) the percentage of students favour basketball 
80
 360
960
1
  360
12
 30
(c) x 
1M, 1A
1A
1M : using the result of (a)
1A
y  360  123  42  x
 360  123  42  30
 165
1M : using the value of x
1A
165
360
11
 960 
24
 440
(d ) no of students favour tab le tennis  960 
 page 8–
1M : using the value of y, 1A
1A
Queen’s College 2010-2011
Yearly Exam, Maths paper I
SECTION B
Page total
Long Questions. (40 marks)
Answer ALL questions in this section and write your answers in the spaces provided.
Each question carries 20 marks.
10.
Fig.(a) shows a wooden prism. Its cross-section is a trapeizum in which the upper base is
5cm, the lower base is twice the upper base and the length of the prism is twice the lower
base of the trapezium.
(a)
If the volume of the wooden prism is 600 cm 3 , find the height of the trapezium.
(a) Let hcm be the height of the cross - section.
(5  5  2)  h
 ((5  2)  2)  600
2
(5  10)  h
 (20)  600
2
h  600  2  20  15
4
 the height of the trapezium is 4 cm.
(b)
(6 marks)
1M, 1A : lower base, 1A : the length, 1A : eqt
2A
If the sum of the remaining two sides of the trapezium is 9.4 cm, find the total surface areas
of prism.
(6 marks)
(b) the perimeter of the trapezium  9.4  5  10
 24.4
1A
the total surface areas  24.4  (10  2) 
(5  5  2)  4
2
2
1M : bases' area,
1M : lateral faces' area, 1A
 24.4  20  15  4
 488  60
 548cm 2
2A
 the total surface areas is 548cm .
2
 page 9–
Queen’s College 2010-2011
Yearly Exam, Maths paper I
(c)
Page total
A rectangular block is removed from the prism shown in Fig.(a) (see Fig.(b)).
The side of the square base is 1.5 cm long.
Find (i)
(ii)
the volume of the remaining solid,
the percentage decrease in volume.
(c)(i) the volume of the rectangula r block  1.5 2  20
(4 marks)
(4 marks)
1M, 1A
 45
the volume of the remainimg solid  600-45
 555 cm
3
1M
1A
 the volume of the remaining solid is 555cm 3 .
600  555
45
 100% Or
 100% 1M, 1A
600
600
45

 100%
600
 7.5%
2A
(c)(ii) the percentage decrease in volume 
 the percentage in volume is 7.5%
 page 10–
Queen’s College 2010-2011
Yearly Exam, Maths paper I
Page total
11. Refer to the figure.
A
D
6
5
3
B
4
E
C
(a) Name a pair of similar triangle and give reason. (3 marks)
(a ) CAB ~ CED
AAA
1A :~, 1A, 1R
In (b) and (c), all working steps with references must be clearly shown
(b) Find the lengths of
(i)
AC,
(ii)
AD,
(iii)
BE.
(11 marks)
AC AB

EC ED
AC 6

4
3
6
AC  4 
3
8
(b) (i)
corr. sides, ~  s
1M, 1A, 1R
1A
(b) (ii) AD  AC  DC
1M
85
3
BC
AB

DC ED
BE  4 6

5
3
6
BE  5   4
3
6
(b) (iii)
1A
corr. sides , ~  s
1M, 1A, 1R
1M : any correct method
1A
 page 11–
Queen’s College 2010-2011
Yearly Exam, Maths paper I
Page total
AC AB BC


EC ED DC
AC 6 BE  4
 
4
3
5
AC 6
(i)

4
3
6
AC  4 
3
8
corr. sides, ~  s
Or (b)
1M, 1A, 1R
1A
1M
1A
(ii) AD  AC  DC
1M
85
3
1A
BE  4 6

5
3
6
BE  5   4
3
6
(iii )
1A
1M : any correct method
1A
(c) If ABC  53 , find EDC .
(c) EDC  ABC
(3 marks)
corr. s , ~  s
1M, 1R
EDC  53
(d) Find
1A
Area of ABC
.
Area of DEC
(3 marks)
AB  AC
Area of ABC
2
(d)

Area of DEC DE  EC
2
AB  AC

DE  EC
68

3 4
4
Area of ABC  AB 
or


Area of DEC  ED 
1M, 1A
1A
2
1M, 1A
 22
4
1A
END OF PAPER
 page 12–