Queen’s College 2009-2010
Yearly Exam, Maths paper I
QUEEN’S COLLEGE
Yearly Examination, 2009-2010
Class
MATHEMATICS PAPER 1
Question-Answer Book
Secondary 1
Class Number
Date: 15 – 6 – 2010
Time: 8:30 am – 9:45 am
Question
No.
Teacher’s Use Only
Max.
marks
1.
7
2.
5
3.
6
4.
9
5.
9
6.
9
Attempt ALL questions in this paper. Write your
answers in the spaces provided in this
Question-Answer Book.
7.
10
8.
13
4.
Unless otherwise specified, all working must be
clearly shown.
9.
12
10.
20
5.
The diagrams in this paper are not necessarily drawn
to scale.
11.
20
Total
120
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 78 marks and Section B carries 42
marks.
3.
6.
Use of calculator is not allowed for this paper.
Page 1
Queen’s College 2009-2010
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. The following back-to-back stem-and-leaf diagram shows the weights of students in S1A
and S1B. Study it carefully and answer the following questions, write your answers in the
spaces provide below.
The weights of students in S1A and S1B
S1A Leaf (1 kg) Stem (10 kg) S1B Leaf (1 kg)
9
8
9
8
7
9
8
6
7
9
6
4
6
6
7
3
4
5
3
6
6
2
2
3
2
4
5
2
2
3
2
3
5
2
0
2
1
2
4
0
1
3
2
1
0
3
4
5
6
7
8
1
1
3
2
2
2
2
5
2
3
4
2
5
4
3
6
4
7
6
5
8
6
8
8
7
9
6
9
8
9
9
9
9
9
(a) Find the total number of students in S1A and the total number of students in S1B
(2 marks)
(b) Find the number of students in S1A with weights equal 62 kg.
(1 mark)
(c) Find the weight of the heaviest student(s) in S1A.
(1 mark)
(d) Find the weight of the thinnest student(s) in S1B
(1 mark)
(e) From the diagram above, students of which class are generally thinner?
(1 mark)
(f)
If students heavier than 80 kg are recommended to join a weight controlling (1 mark)
camp, how many students in S1B will be recommended to join the camp?
(7 marks)
(a) the total number of students in S1A is 3
9
39
the total number of students in S1B is 4
0
40
(b) the number of students in S1A with weights equal 62 kg is 3
3
(c) the weight of the heaviest student(s) in S1A is 8 6
kg
86 kg
(d) the weight of the thinnest student(s) in S1B is 3
kg
30 kg
(e) students of class
1a
0
are generally thinner
(f) No. of students in S1B recommended to join the camp is 5
-2–
5
Queen’s College 2009-2010
Yearly Exam, Maths paper I
+
2. Three students, Peter, John and Henry have $16.8, $24.3 and $32.5 respectively.
Page total
(a) By rounding down the amount owned by each student to the nearest dollar,
(3 marks)
estimate the total amount they have.
(b) If the three students want to buy a football of price $70, will they have enough
(2 marks)
money to buy the football? Use the result of (a) to explain your answer.
(5 marks)
(a) the total amount they have = 16.8 + 24.3 + 32.5
1A
16 + 24 + 32
1A
= $ 72
1A u-1 for missing unit
(b) Yes.
1A
because the round down total is always less than the exact total, so
1A
their exact total must be greater than $72, which is more than enough
to pay for a football which costs $70 only.
3. Study the polar coordinate plane below, and answer the following questions.
120o
60o
P
╳
Q╳
o
180
O 2
╳
240o
R
6
4
X
Q
╳
300o
(a) Find the polar coordinates of P and the polar coordinates of Q.
(2 marks)
(b) Find the size of ∠POQ.
(2 marks)
(c) Find the area of Δ POQ.
(2 marks)
(6 marks)
(a)
(b)
the coordinates of the point P are (4, 60o)
1A
the coordinates of the point Q are (6, 330o)
1A
the size of ∠POQ = 30o × 3 or 60o + 30o
= 90o
(c)
the area of Δ POQ. =
1M
1A
1M
=9
-3–
1A
For using data from (a)
Queen’s College 2009-2010
Yearly Exam, Maths paper I
Page total
4. The bar chart and the pie chart below show the distribution of the numbers of keys owned by the
students in class A . The numbers of students having 2 keys, 3 keys and 4 keys are 12, 17 and k
respectively.
Distribution of the numbers of keys owned by the students in class A
No. of students
16-
2 keys
1 key
18-
1
3
2
Number of keys
153o
3 keys
4
63o
4 keys
(a)
Find the total numbers of students in class A .
(2 marks)
(b)
Find the value of k .
(2 marks)
(c)
Find the number of students in class A with only 1 key.
(2 marks)
(d)
It is given that the numbers of students in class A and class B are the same.
The distributions of the numbers of keys owned by the students in class A and
class B are also the same. The two classes are now combined to form a group.
Do we need to re-draw
(i) the bar chart shown above?
If your answer is ‘yes’, write down the modification/change needed.
(3 marks)
(ii) the pie chart shown above?
If your answer is ‘yes’, write down the modification/change needed.
(9 marks)
1A
total no. of students
= 40
1A
1M
no. of students with 4 keys
=7
1A
no. of students with only 1 key = 40 – 12 – 17 – 7
=4
1M
1A
(i) Yes. We have to double the height of each bar or
1A
reduce the scale of the vertical axis by half
1M
(ii) No.
1A
-4–
u-1 for missing unit
Queen’s College 2009-2010
Yearly Exam, Maths paper I
5.
Page total
The figure below shows a prism.ABCDEFGH.
A
12 m
D
5m
B
2m
F
E
C
7m
13 m
H
G
(a)
Find the total number of faces of the prism
(1 mark)
(b)
Which face is the base of the prism?
(1 mark)
(c)
Find the area of the base of the prism.
(2 marks)
(d)
Find the volume of the prism.
(2 marks)
(e)
Find the total surface area of the prism.
(3 marks)
(9 marks)
(a)
the total number of faces of the prism = 6
1A
(b)
BCGF is the base of the prism
1A
(c)
area of the base =
1A
= 54 m2
1A u-1 for missing unit
(d) the volume of the prism = 54 × 5
1M
= 270 m3
(e)
1A
the total surface area = 54 × 2 + ( 2 + 13 + 7 + 12 ) × 5
1M
= 108 + 32
1A
×
5
= 278 m2
1A
-5–
Queen’s College 2009-2010
Yearly Exam, Maths paper I
Page total
6. In the rectangular coordinate plane below, l is a line parallel to the x-axis and it passes through a
point B ( 1, 2) on the plane. If the coordinates of the point A are (–4 , 5) ,find the coordinates of its
images after the following transformations. (Steps are not required for this question.)
y
A (–4 , 5)
×
B ( 1, 2)
×
l
x
(a) A is translated 6 units to the right and then 5 units downward to a point P.
(1 mark)
(b) A is reflected in the y-axis to a point Q.
(1 mark)
(c) A is reflected in line l to a point R.
(1 mark)
(d) A is rotated clockwise about the origin O through 90o to a point S.
(1 mark)
(e) A is rotated anticlockwise about the origin O through 180o to a point T.
(1 mark)
(f)
Which of the above 5 images (P, Q, R, S, T) lie/lies on the x-axis? Explain your (2 mark)
answer.
(g) Which two of the above 5 images (P, Q, R, S, T) can be joined together to form a (2 mark)
line parallel to the y-axis? Explain your answer.
(9 marks)
(a)
the coordinates of the point P are ( 2, 0)
1A
(b) the coordinates of the point Q are ( 4 ,–1)
1A
(c)
the coordinates of the point R are (–4 , 1)
1A
(d)
the coordinates of the point S are ( 5, 4)
1A
(e)
the coordinates of the point T are ( 4,–5)
1A
(f)
P lies on the x-axis.
1A
because its y-coordinate is 0.
(g)
1A
Q , T can be joined together to form a line parallel to the y-axis.
because their x-coordinates are the same.
-6–
1A
1A
Queen’s College 2009-2010
Yearly Exam, Maths paper I
Page total
7.
The consultation fees charges to a child patient and adult patient by a doctor are $120 and $160
respectively. On a certain day, there were 60 patients consulted the doctor and the total
consultation fee charged was $8 160. Find
(a) the number of child patients consulted the doctor on that day
(8 marks)
(b) the number of adult patients consulted the doctor on that day
(2 marks)
(10 marks)
(a) Let the no. of child patients consulted the doctor on that day be x
1M
then, the no. of adult patients consulted the doctor on that day is (60 – x). 1A
1A
1M
1A
120 x + 160 × (60 – x) = 8160
120 x + 9600 – 160x = 8160
For 120 x
For 160 × (result of last step)
For ….+ …. = 8160
1M For removing ( ) correctly.
1440 = 40x
1A
x = 36
the no. of child patients is 36
(b)
60 – x = 60 – 36
1A
1M For 60 – result from (a)
= 24
the no. of adult patients is 24
-7–
1A
Queen’s College 2009-2010
Yearly Exam, Maths paper I
Page total
8. In the rectangular coordinate plane below, AQ, CP are parallel to the y-axis and BP, CQ are
parallel to the x-axis.
×
Q×
A (–5 , 6)
y
C (–3, 2)
×
l
x
×
R
×
×
B ( 7 –4)
P
(a) Find the coordinates of P and the coordinates of Q.
(2 marks)
(11 marks)
(b) Find the area of ABPCQ.
(13 marks)
(a)
(b)
the coordinates of the point P are (–3,–4)
1A
the coordinates of the point Q are (–5, 2)
1A
Mark R in the figure, such that AR⊥RB
1A
the coordinates of the point R are (–5,–4)
1A
AR = 6 – (–4)
1A
= 10
QR = 2 – (–4)
For using data from R
=6
BR = 7 – (–5)
1
= 12
PR = –3 – (–5)
For using data from R
=2
area of ABPCQ =
1M
= 60 – 6
1A
= 54
1A
-8–
For using data from last step
Queen’s College 2009-2010
Yearly Exam, Maths paper I
Page total
9. There are 600 boys in a school and the number of girls is 20% less than that of boys.
(a) Find the number of girls in the school.
(3 marks)
(b) There are 756 local students in the school.
(i) Find the percentage of local students in the school.
(4 marks)
(ii) It is given that 66% of the boys are local students. If x% of the girls are also (5 marks)
local student, write down the value of x .
(12 ma(12 marks)
number of girls in the school = 600 × (1-20%)
(a)
(b) (i)
(ii)
1A
= 600 × 0.8
1A
= 480
1A
the percentage of local students in the school
For 756 as neratFor 600 + result from (a)
=
11M as denominator
=
1A For 1080 as denominator
= 70%
1A
For ….+ …. = 756%
= 756
= 756
1A
4.8x = 360
x=
x = 75
1A
-9–
Queen’s College 2009-2010
Yearly Exam, Maths paper I
Page total
SECTION B
Long Questions. (40 marks)
Answer ALL questions in this section and write your answers in the spaces provided.
10. In the figure below, TSR and KHM are straight lines
while RP//KM and PH//NM.
T
a. Find ∠SRQ.
30o
S
R
s
r
q
(9 marks)
K
100o Q
h
p
b. Find ∠PHK and ∠RPH.
(9 marks)
H
P
m
c. Is PH // TR? Explain your answer.
(2 marks)
N
M
250o
(20 marks)
a.
∠RQS + 100 o =180o
Adj. ∠s on st. line
∠RQS =80o
1A
∠QSR = 30o
∠SRQ + ∠QSR + ∠RQS =180 o
o
o
∠SRQ + 30 + 80
=180
Vert. opp. ∠s
1A+1A
∠ sum of Δ
1A
o
1A+1M
o
∠SRQ = 70
b.
1A
∠NMH + 250o =360 o
∠s at a pt.
∠NMH =110 o
1A+1A
1A
∠PHK = ∠NMH
corr. ∠s, PH// NM
= 110 o
∠RPH + ∠PHK = 180 o
1A
1M+1A
int. ∠s, PR (PQ) // HK (MK)
∠RPH + 110 o = 180 o
c.
1A+1A
1A
1M
∠RPH = 70 o
1A
∴∠RPH = ∠SRQ = 70 o
1A
alt. ∠s equal.
PH // TR
- 10 –
1A
Queen’s College 2009-2010
Yearly Exam, Maths paper I
11. In the diagram below, JKHN is a straight line and NM // FJ.
Page total
F
f
5
N
H
h
3
4
J
K
6
M
a.
Prove that the 2 triangles in the diagram above are similar; hence
(8 marks)
b.
i. find the area of ΔHNM if ∠FKJ = 90o, explain your steps clearly.
(5 marks)
ii. find the length of KF and JF if KJ = 6.
(7 marks)
(20 marks)
a.
f =h
∠J = ∠N
1A+1A
alt. ∠s, NM // IJ
1A+1A
∴180o – f – ∠J = 180o – h – ∠N
1M
∴∠FKJ = ∠M (∠NMH)
1A
ΔFJK
b. i.
given
～ΔHNM
∠NMH = ∠FKJ
A.A.A.
1A+1A for FJK
Corr. ∠s, ～Δs
1A+1M
= 90o
1A
area of ΔHNM =
1M for
=6
1A
Corr. sides, ～Δs
ii.
1M+1A
1A
KF =
1M for any ratio ×
KF = 4.5
1A
JF =
1M for any ratio ×
JF = 7.5
1A
E N D O F PA P E R
- 11 –
3
3