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KIANGSU-CHEKIANG COLLEGE (SHATIN)
Form One
Mathematics
Final Examination 2006/2007
Date: June 28, 2007
Time: 8:30 a.m. – 10:00 a.m.
Total marks: 100
Time allowed: 90 minutes
Name: ______________________ Class: 1(__) Class No. (__)
Index No.:
Instructions
1. This paper consists of THERE sections.
2. Answer ALL the questions.
3. Write down all your answers in the space provided.
4. Calculator is not allowed.
Section A (40 marks)
1.
It is given that C 
5
( F  32) .
9
(a) If F  212 , find the value of C.
(b) If C  80 , find the value of F.
(2 marks)
2.
Complete the following table.
Polynomial
(4 marks)
Number of Coefficient of
terms
x3
x2
x
(a) 4x3 – x4 + 2x2 + 8
(b)
x3 
1 2
x
x  9x 2 
6
3
Page 1 of 20
Constant term
Degree of
polynomial
3.
Simplify the following expressions.
(4 marks)
(a) (2 x 2  6 x  5)  ( x  x 2  2)
(b) (m) 3  (n) 2
4.
Expand the following expressions.
(4 marks)
(a)  3x 2 ( x 3  6 x 2  1)
(b) (2a  b) 2
5.
Express the following statements in algebraic expressions.
(a) Subtract b from the product of 4 and a.
(b) Divide the sum of a and three times b by – c.
Page 2 of 20
(2 marks)
6.
Solve the following equations.
(a) 10 
(b)
7.
(4 marks)
x
3
4
( y  3) 5  2 y

4
3
6, 11, 16, 21, 26 are the first 5 terms of a sequence that follows a certain pattern.
(a) Find the 6 th , 7 th terms of the sequence.
(b) Write down the general term of the sequence.
(4 marks)
8.
Estimate the value of the following expressions by appropriate estimation strategies.
(a) 1397  1403  1391  1412  1400  1398
(b) 24.7  4.03  9.12
(2 marks)
Page 3 of 20
9.
If p  100  (1  35%  70%) , find p.
(2 marks)
10. Express the following angles in degrees.
(a)
5
straight angle.
9
(b)
1
round angle.
4
(4 marks)
11. Measure the length of the line segment AB with a ruler
(a) correct to the nearest cm,
A
B
(b) correct to the nearest mm.
(2 marks)
12. For each of the following figure,
(a) draw all the axes of reflectional symmetry,
(b) state the order of rotational summetry.
(6 marks)
Page 4 of 20
Section B (50 marks)
13. Find all the unknowns in the following figure.
(6 marks)
z
65∘
70∘
55∘
y x
60∘
14. Peter has 130 coins in his bag, which includes $5-coins, $2-coins and $1-coins.
The number of $2-coins is 8 more than twice the number of $5-coins.
(a) Let x be the number of $5-coins. Use an algebraic expression to represent the
number of $2-coins and $1-coins.
(b) Given that the total value of the coins is $258, set up an algebrai c equation in x
and find the number of $5-coins, $2-coins and $1-coins.
(6 marks)
Page 5 of 20
15. Name all the similar triangles and give reasons.
5 cm
K
A
D
J
F
3.5 cm
2.5 cm
B
(6 marks)
C
3 cm
7 cm
E
M
6 cm
P
L
9 cm
H
G
4 cm
4.5 cm
I
O
8 cm
R
Q
N
16. (a) Draw the 2-D representation of the prism on an oblique grid paper.
(2 marks)
E
F
4
H
4
G
5
D
C
6
A
7
B
Page 6 of 20
16. (b) Draw the uniform cross-sections of the prism.
(1 mark)
(c) Find the volume of the prism.
(3 marks)
(d) Find the total surface area of the prism.
(4 marks)
Page 7 of 20
17. (a) PQRS is transformed to ABCD by the following way:
(1) P is translated to the right by 6 units to A.
(2) Q is reflected about the y-axis to B.
(3) S is rotated through 90 ∘ clockwise about O to C.
(4) R is reflected about the x-axis to D.
Draw the quadrilateral ABCD in the figure and write down the coordinates
of point A, B, C and D in the box provided.
(4 marks)
y
7
A=
6
5
P
B=
4
3
2
C=
1
–7 –6 –5 –4 –3 –2 –1–10
–2
Q
–3
–4
R
–5
–6
–7
x
1
2
3
4 5
6
D=
7
S
(b) Find the area of ABCD or PQRS. Which quadrilateral is bigger?
Page 8 of 20
(4 marks)
18. The following stem-and-leaf diagram shows the Mathematics Examination marks of 1F class
students.
Marks
Class boundaries
Class
mark
Frequency
3
4
5
6
7
8
30-39
40-49
39.5–49.5
44.5
49.5–59.5
54.5
Stem
Leaf
(10 marks) (1 mark)
60-69
69.5–79.5
6679
146667789
012345666778
0014566
111279
257
84.5
(a) Complete the above table.
(4 marks)
(b) Draw a histogram to present the above data.
(5 marks)
Page 9 of 20

x
19. If x is an unknown, solve the literal equation b 8    x .
y

(5 marks)
Section C (10 marks)
20. (a) According to the following figures, find the value of
(1) a  b  c  d ,
(2) e  f  g  h  i ,
j  k  l  m  n  o.
(3)
Hint:
Divide the polygons into triangles.
(3 marks)
f
b
a
c
n
g
m
o
l
e
h
d
i
Page 10 of 20
j
k
(b) Find the sum of the interior angles of
(1) a heptagon (7-sided polygon),
(2) an octagon (8-sided polygon),
(3) a nonagon (9-sided polygon).
Hint:
The sum of the interior angles of polygons follows a certain pattern,
try to find the pattern by question 20(a).
(3 marks)
(c) Find the sum of the interior angles of an n-sided polygon in term of n.
(2 marks)
(d) Find the number of sides of a polygon if the sum of its interior angles is equal to
6840 ∘.
(2 marks)
End of paper
Page 11 of 20
Section A (40 marks)
1.
C
5
(212  32)  100
9
(1M+1A)
80 
5
( F  32)  F  176
9
(1M+1A)
(4 marks)
2.
Complete the following table.
Polynomial
(a) 4x3 – x4 + 2x2 + 8
(b)
x3 
1 2
x
x  9x 2 
6
3
Number of Coefficient of
terms
X3
x2
x
4
4
3
1
2
0
53/6 1/3
Constant term
Degree of
polynomial
8
4
0
3
Deduct 1 mark for each mistake, maximum 4 marks.
(4 marks)
3.
(a) (2 x 2  6 x  5)  ( x  x 2  2)  x 2  5x  3
(b) (m)3  (n)2  m3  n2  m3n2
(2A)
(1M+1A)
(4 marks)
4.
(a)  3x 2 ( x3  6 x 2  1)  3x5  18x 4  3x 2
(b) (2a  b)2  (2a  b)(2a  b)  4a 2  2ab  2ba  b2  4a 2  4ab  b2
(2A)
(1M+1A)
(4 marks)
5.
(a) 4a  b
(b)
(1A)
a  3b
or (a  3b)  (c)
c
(1A)
(2 marks)
Page 12 of 20
6.
Solve the following equations.
(a) 10 
(b)
(4 marks)
x
x
 3  7   x  28
4
4
(1A)
( y  3) 5  2 y

 3( y  3)  4(5  2 y )
4
3
(1M)
 3 y  9  20  8 y
(1M)
 11y  11  y  1
(1A)
(4 marks)
7.
(a) 6 th terms = 31, 7 th terms = 36
(1A+1A)
(b) the general term =5n+1
(2A)
(4 marks)
8.
(a) 1397  1403  1391  1412  1400  1398  1400  6  8400
(1M+1A)
(b) 24.7  4.03  9.12  25  4 10  10
(1M+1A)
(2 marks)
9.
p  100  (1  35%  70%)  p  100  65%
(1M)
 p  65
(1A)
(2 marks)
10. (a)
(b)
5
5
180
straight angle =
9
9
(1M)
 100
(1A)
1
1
 360
round angle =
4
4
(1M)
 90
(1A)
(4 marks)
11. (a) The length of AB = 5 cm
(1A)
(b) The length of AB = 47 mm.
(1A)
(2 marks)
Page 13 of 20
12. For each of the following figure,
(a) draw all the axes of reflectional symmetry,
2A+2A
(b) state the order of rotational symmetry.
1A+1A
(6 marks)
2-fold rotational symmetry
5-fold rotational symmetry
Section B (50 marks)
13. 55  65  x  180  x  60
(1M+1A)
60  70  y  180  y  50
(1M+1A)
50  60  z  180  x  70
(1M+1A)
(6 marks)
14. (a) The number of $2-coins = 2x  8
The number of $1-coins = 130  x  (2 x  8)  130  3x  8  122  3x
(b) 5x  2(2x  8)  1122  3x  258
(1A)
(1M+1A)
(1M)
138  6x  258  x  20
(1M)
So the number of $5-coins, $2-coins and $1-coins
are 20, 48 and 62 respectively.
(1A)
(6 marks)
15. ABC ~ KJL (3 sides proportional)
(1A+1A)
DEF ~ QRP (A.A.A.)
(1A+1A)
GHI ~ MNO (ratio of 2 sides, inc  )
(1A+1A)
(6 marks)
Page 14 of 20
16. (a) Correct shape + Correct label
(1A+1A)
H
E
G
F
C
D
B
A
16. (b) Correct shape
(1A)
(c) The volume of the prism

(4  7)  4
6
2
(1M)
= 132 (cubic units)
(2A)
(d) The total surface area of the prism

( 4  7)  4
 2  (4  7  5  4)  6
2
 44  120  164 (square units)
Page 15 of 20
(2M)
(2A)
17. (a) Drawing
2A
Coordinates – Deduct 1 mark for each mistake, max. 2marks)
2A
(4 marks)
y
7
D
P
A = (4 , 1)
6
5
B = (4 , -2)
4
3
2
C = (-4 , -1)
A
1
x
–7 –6 –5 –4 –3 –2 –1–10
C
–2
Q
–3
R –4
–5
–6
–7
1
2
3
4 5
6
D = (-2 , 4)
7
B
S
3 5 2  3 2  2


 12.5
2
2
2
(b) Area of PQRS =  5  5 
Area of ABCD =  6  8 
(1M+1A)
6  3 2  5 1 8


 30
2
2
2
(1A)
So ABCD is bigger
(1A)
(4 marks)
18. The following stem-and-leaf diagram shows the Mathematics Examination marks of 1F class
students.
Marks
Class boundaries
Class
mark
Frequency
30-39
29.5-39.5
34.5
4
40-49
39.5–49.5
44.5
9
50-59
49.5–59.5
54.5
12
60-69
59.5-69.5
64.5
7
70-79
69.5–79.5
74.5
6
80-89
79.5-89.5
84.5
3
Page 16 of 20
Stem
Leaf
(10 marks) (1 mark)
3
4
5
6
7
8
6679
146667789
012345666778
0014566
111279
257
(a) 1 mark for each column, mark should not be given
(4A)
(4 marks)
unless whole column is correct..
(b) Label (Deduct 1 mark for each mistake, max 2 marks)
(2A)
Shape (Deduct 1 mark for each mistake, max 3 marks)
(3A)
(5 marks)
The Mathematics Examination marks of 1F class students.
12
10
8
Frequencey
6
4
2
34.5
44.5
54.5
64.5
74.5
84.5
Marks

19. b 8 

8
x
x x
  x  8  
y
y b
x x
 8
b y
(1M)
1 1
x  
b y
(1M+1M)
 y b
8by
  x 
 8  x
y b
 by 
(1M+1M)
(5 marks)
Page 17 of 20
Section C (10 marks)
20. (a) (1) a  b  c  d  2 180  360
(2) e  f  g  h  i  3  180  540
(3)
j  k  l  m  n  o  4  180  720
(1A)
(1A)
(1A)
(3 marks)
(b) Find the sum of the interior angles of
(1) the sum of the interior angles of a heptagon  5 180  900
(1A)
(2) the sum of the interior angles of an octagon  6 180  1080
(1A)
(3) the sum of the interior angles of a nonagon  7 180  1260
(1A)
(3 marks)
(c) the sum of the interior angles of an n-sided polygon  (n  2)  180
(2A)
(1 A for value, 1A for unit)
(2 marks)
(d) (n  2)  180  6840  n  40
(1M+1A)
The number of sides is 40.
(2 marks)
Page 18 of 20
General Performance of Students
1.
Very Good
2.
(a) Good
(b) Fair, Some students just count the “terms” without simplify it first. Also they wrote
-1/6, +9 in coefficient of x 2 .
3.
(a) Very good.
(b) Fair. Some students wrote (n) 2  n 2
4.
(a) Very good
(b) Fair, some students still write (2a  b) 2  4a 2  b 2 or (2a  b) 2  2a 2  b 2
5.
(a) Good.
(b) Good.
6.
(a) Good.
(b) Poor. They do not know the cross multiplying method. Many of them try to break
down in fraction and make the equation more difficult to solve.
7.
(a) Good
(b) Fair. Some students cannot write down the general term.
8.
Fair. Some students just calculate the exact value of the expression.
9.
Good
10. (a) Good
(b) Fair, some of them do not know the meaning of round angle.
11
(a) Good
(b) Poor. Many of them do not realize that the unit has changed. They wrote 4.7cm, or
47cm.
12. Good. They can draw the reflectional symmetry. For rotational symmetry, they just write
down the number instead of 2-folds of rotational symmetry.
13. Fair. Some of them cannot recognize the triangle in the figure. So they cannot find the
answer.
14. (a) Poor, Many students are weak in understanding mathematical problems
(b) Poor. Even a few students can find the value of x, they haven’t answer the problem.
15. Unsatisfactory. Since the question put all the triangle together, they need to find which
pair of triangles are similar but they fail to find them. Also, some students write down
wrong reasons and wrong corresponding angles of the triangle.
Page 19 of 20
16. (a)(b) Poor. Many students do not know what the question ask. Some students forgot to
label the prism.
(c) Good
(d) Poor. Many students have not counted the upper base or lower base.
17. (a) Fair, Students are weak in rotation, some of them forgot to label the vertices.
(b) Fair, many students got the answer wrongly as they draw the figure in (a) wrongly.
18. (a) Very Good.
(b) Poor. Many students cannot distinguish histogram and bar chat.
19. Poor. Students are weak in changing subject. All they cannot tackle complicated
formulae.
20. (a) Good.
(b) Fair. A few students do not know the name of the polygon.
(c) Poor. Many students cannot guess the expression.
(d) Fair. Since they cannot guess the expression, they cannot find the value of n.
End of Report
Page 20 of 20