SKH St. Simon’s Lui Ming Choi Secondary School
Form 1 Mathematics
Summer Homework Worksheet
Name:
Class:
(
)
Date:
Teacher:
YPC
Chapter 1 Directed Numbers
1.
(a) Mark the following points on the number line.
A  3, B  8, C  2, D  6, E  0
8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8
(b) Arrange the above numbers in ascending order.
2.
Evaluate the following.
(a) ( 3)  ( 2)  ( 7)
(c)
( 7)(3)(9)
(b) ( 8  4)  (2  10)  ( 8  11)
(d)
( 5)( 2)(  4)
( 6)( 3)
1
Chapter 2 Basic Algebra
1.
2.
ab a 2  b 2

Given M 
, find the value of M if a  3, b  4 and c  5.
2
c
Observe the pattern of each of the following sequences, write down the next two terms
of the sequence and determine what kind of sequence it is.
(a) 2, 17, 32, 47, 62, 
3.
(b) 4 096, 1 024, 256, 64, 16, 
Write down two numbers which are both triangular numbers and square numbers.
2
Chapter 3 Basic Geometry
1.
A
Referring to the figure, answer the following questions.
(a) CBD 
(b) ABD 
(c) BCD 
(d)
(e)
(f)
y
B
w
z
xy
E
x
z
w
D
v
C
2.
In the following figures, find the marked angle between the hour-hand and the
minute-hand.
12
9
3
6
3.
Find the unknown in each of the following figures.
(a)
(b)
A
A
a
53
60
b
50
B
4.
C
B
C
Treat point A as the lowest point of each of the following solids, draw the solids on the
isometric grids. (The numbers in the figures are lengths of sides.)
1
1
1
2
2
A
1
3
Chapter 4 Linear Equations in One Unknown
1.
Solve the following equations.
(a) 3x  6  2 x  9
(c)
1
( 2 x  1)  5
3
(b)
x  9  2(6  x)
(d)
4x  6 9  2x

2
5
2.
For two consecutive odd numbers, 4 times the smaller number is 23 less than 5 times
the larger number. Find the two numbers.
3.
**Leo is 20 years older than Benjamin. After 10 years, Leo will be 2 times as old as
Benjamin. Find the current age of Benjamin.
4
Chapter 5 Percentages
1.
Evaluate the following and express your answers in percentages.
(a) 160%  1
(b) 30%  30%
(c)
50  1  40 % 
(d) 60  1  20 % 
2.
A can of cola has a volume of 375 mL. If Wendy has drunk 44% of it, how much cola is
left?
3.
Mike buys an air conditioner for $2 720 with a marked price of $3 200.Find the
percentage discount.
4.
The weight of May decreases by 12% and goes down to 44 kg. Find the original weight
of May.
5
Chapter 6 Statistics in Daily Life
1.
The following stem-and-leaf diagram shows the scores of S1A students in a test.
(a) What is the score of the student
with the best result?
Scores of S1A students in a test
Stem (tens)
_________________________
(b) Which stem do most of the
scores fall into?
Leaf (units)
4
1
2
4
4
5
7
9
5
0
0
2
5
6
6
7
8
6
0
1
2
2
4
5
9
9
9
7
2
2
4
5
5
6
7
8
8
8
0
0
1
4
5
6
9
_________________________
(c) How many students have obtained scores less than 50?
_________________________
2.
The following pie chart shows the allocation of monthly pocket money by Kevin.
Allocation of monthly pocket money by Kevin
Entertainment
Transportation
Food
70
120
60
45 65
Shopping
Savings
(a) What percentage of pocket money does Kevin allocate to transportation each
month?
(b) It is known that Kevin has $1 620 pocket money each month.
i.
How much does he spend on food each month?
ii.
If he also saves his monthly spending on entertainment and shopping, how
much does he save each month?
6
Chapter 7 Algebraic Expressions and Polynomials
1.
2.
Simplify the following.
(a) (a 5 )( 3a 4 )
(b) ( 2a 2 b)( 4ab 3 )
(c)
(a 3 ) 4
(d) ( 2 x 2 y 3 ) 3
(e)
5y
25 y 3
(f)
( 2a 2 b 3 ) 2
8a 3b 5
(g) 7b  3  2b  9
(h) (5 x  6 y 2 )  (3x  2 y 2 )
Expand the following.
(a) 3x( x  2)
(b) (3 y  2)( y  3)
(c)
( x  3) 2
(d) ( x 2  2 x )( 3x 2  5)
7
Chapter 8 Symmetry and Transformation
1.
Complete the following reflectional symmetrical figures by taking the dotted lines as
the axes of symmetry.
(a)
2.
(b)
In each of the following figures, mark the centre of rotation with ‘’ and write down
the number of folds of rotational symmetry.
(a)
________________
3.
(b)
_________________
**In each of the following figures, draw the image according to the given instruction.
(a) Translate 3 units downwards and
(b) Draw the image of rotating the
4 units to the left.
figure about point O
anti-clockwise through 90.
O
8
Chapter 9 Introduction to Coordinates
1.
y
(a) Mark four points A(1, 4), B(5, 2), C(1, 2)
and D(3, 4) on the rectangular coordinate plane.
(b) Join the points according to the order A, B, C, D
and A.
(c) What kind of quadrilateral is ABCD?
________________________________
6
5
4
3
2
1
x
6 5 4 3 2 1 O
1
1
2
3
4
5
6
2
3
(d) Write down the coordinates of the point of
intersection of the two diagonals.
4
5
6
________________________________
2.
120
(a) Mark four points O(0, 0), A(3, 45), B(4, 135) and
C(4, 255) on the polar coordinate plane.
105 90
75
60
135
45
150
30
15
165
(b) Find AOB and BOC.
180
0
I
1 2 3 4 5 6
O
195
345
210
3.
**Find the area of quadrilateral ABCD in the following figure.
330
225
240
315
300
255 270 285
y
5
A
4
3
B
2
1
x
5 4 3 2 1 O
1
1
2
3
4
2 C
3
D
4
5
4.
**The images A' to F' are obtained by transforming the points A to F respectively.
Complete the table.
Point
Transformation
A(1, 4)
Translate 2 units to the left and 3 units downwards
B(
,
)
Translate 4 units to the right and 1 unit downwards
Reflect along the x-axis
C(2, 1)
Image
A'(
,
,
D(
,
)
Reflect along the y-axis
D '(1, 4)
E(
,
)
Rotate about the origin through 180
E '(1, 2)
F(4, 5)
Rotate anti-clockwise about the origin through 90
)
B '(3, 4)
C '(
F '(
,
5
)
)
9
Chapter 10 Statistical Graphs
1.
(a) The following table shows the weights of 40 S2 girls. Complete the table.
Weight (kg)
Class boundaries (kg)
Class mark (kg)
Frequency
26 - 30
2
31 - 35
9
36 - 40
13
41 - 45
8
46 - 50
5
51 - 55
(b) Which class interval has the greatest number of girls? What percentage of girls
belong to this class interval?
The following histogram shows the distribution of the weights of S1A students. It is
known that the first class interval is 45 kg - 49 kg.
Weights of S1A students
(a) What is the class width?
14
____________________________________
12
(b) Which class interval has the fewest students?
How many students are there?
Frequency
2.
10
____________________________________
8
6
4
(c) How many students are there in S1A?
____________________________________
2
0
47
52
57 62 67
Weight (kg)
72
(d) What percentage of students weigh 64.5 kg or more?
10
Chapter 11 Linear Equations in two Unknowns
1.
According to the equation y  2 x  1 , complete the following table and draw the graph
of the equation from x  2 to x  2 on the rectangular coordinate plane given below.
x
2
1
2
1
y
y
5
4
3
2
1
2 1 O
1
x
1
2
2
3
4
5
2.
If A(a, 3) and B(2, b) are points on the graph of the equation 3x  2 y  6 , find the
values of a and b.
11
Chapter 12 Ratio and Rate
1.
Simplify the following ratios.
(a) 28 : 70
(c) 45 seconds : 1 hour
2.
If a : 6  7 : 2 , find the value of a.
3.
**It is given that h : m  5 : 2 and k : m  4 : 9 .
(a) Find h : k : m.
(b) If k  24 , find the value of h.
4.
A car travelled 270 km in 3 hours.
(a) Find the speed of the car in km/h.
(b) Find the speed of the car in m/s.
(b) 2.5 : 0.75
(d) 6 weeks and 3 days : 1 week and 5
days
12
Chapter 13 Angles in Rectilinear Figures
1.
In the figure, ABC is a straight line. Find x.
D
E
x
x4
A
B
2. In the figure, find x.
C
B
3x10
80
O
x
A
x35
C
D
3. In the figure, ABC is a straight line. Find x.
D
34
2x26
A
B
C
4. In the figure, AOD, BOE and COF are straight lines. Find x.
F
E
3x
A
D
x
2x
O
B
C
5. In the figure, AB // CD, EF is their transversal. Find x, y and z.
B
D
E
z
F
y
x
C
125
A
13
6. In the figure, ADC is a straight line. Find x and y.
B
18
y
50
A
x
C
D
7. **Find x in the following figure.
B
35
D
80
C
A
8.
x
E
**In the figure, APB, BQC, DPE and EQF are straight lines, AB // EF. Prove that
ED // CB.
A
D
P
41
B
E
Q
C
41
F
14