Effective Learning Mathematics | S4A
The figure shows the rectangle ABCD, where AB BC . Its perimeter is 36 cm. Let AB x cm.
A
x cm
D
B
C
(a) Find the area of ABCD in terms of x.
(b) Given that the ar
Effective Learning Mathematics | S5A
In the figure, the circle C : x 2 y 2 10 y 5 0 touches the straight lines L1 and L2 at P and Q
respectively. L1 and L2 meet at the origin O.
y
L2
L1
Q
O
x
P
C
(a)
Chapter Test 7D
[Multiple Choice questions]
Time allowed : 40 minutes
Full marks : 98
(T3-07-27)
1. Find the slope of the line segment
joining the points (0 , 1) and (-1 , 3).
A. -4
B. -2
1
2
1
2
C. D
Diagnostic Test 8
( T2-08-01 )
1. In each of the following figures, find the value of the unknown.
a
13
12
(a)
b
12
(b)
9
( T2-08-02 )
2. Find the value of each of the following :
(a) 4 (8)
(c)
(b) (7
Chapter 14
(b) Number of students who got 60.5 marks or more
Uses and Abuses of Statistics
50 number of students who got marks less
than 60.5
50 35
15
(T3-14-01)
is a pictogram.
1. (a) This Test
Diagn
Diagnostic Test 7
(T3-07-01)
1. The figure shows four points A(1 , 0), B(6 , 0), C(9 , 4) and D(4 , 4).
y
C(9,4)
D(4,4)
O
A(1,0)
B(6,0)
x
(a) Calculate the lengths of AB and BC. Are they equal?
(b) Ca
Diagnostic Test 14
(T3-14-01)
1.
Annual sales of cars
1995
1996
represents 1 000 cars
(a) What kind of statistical diagrams is this?
(b) What is the annual sale of cars in 1996?
(T3-14-02)
2.
Sales of
Chapter Test 12D
[Multiple Choice questions]
Time allowed : 40 minutes
Full marks : 98
(T3-12-29)
1. What is the probability of getting an
even prime number in throwing a die
once?
1
6
1
B.
3
1
C.
2
2
Chapter Test 8D
[Multiple Choice questions]
Time allowed : 40 minutes
Full marks : 98
(T2-08-28)
1. The distance between A(2 , 5) and
B(6 , 10) is
A.
B.
C.
D.
E.
89
4. In the figure, find the slope of
Chapter 7
(c)
Coordinate Geometry of
Straight Lines
x y
1
3 2
x
y
6 6 6(1)
3
2
2 x 3 y 6
(T3-07-01)
2 x 3 y 6 0
1. (a)
Diagnostic
Teston
7 the x-axis.
AB lies
AB 6 1
5
BC
(T3-07-03)
3. (a)
9 6
Chapter Test 14D
[Multiple Choice questions]
Time allowed : 35 minutes
Full marks : 98
(T3-14-16)
1.
(T3-14-18)
Living areas of Tom, John and Paul
3.
Monthly expenditure of Mr. Chan
25
Others
20
Rent
1
F.1 Mathematics Chapter Summary 6
Chapter 6
Introduction to Geometry
6.1 Points, Lines and Planes
Points
a point represents a position in space.
Lines
Planes
Intersection
it has no size.
usually use
1
F.1 Mathematics Chapter Summary 5
Chapter 5
Estimation in Numbers and Measurement
5.1 Meaning of Estimation
When there is no calculating tools on hand, we can use certain methods to simplify calcula
1
F.1 Mathematics Chapter Summary 4
Chapter 4
Using Algebra to Solve Problems (II)
4.1 Formulas
A formula is an equality () that shows the relationship () between two or more variables.
e.g. the formu
Effective Learning Mathematics | S5A
(a) Find the range of values of x which satisfy both the inequalities
x
7x
2 and 3 5 .
2
4
(b) How many integers satisfy both the inequalities in (a)?
(4 marks)
S
(page EP6.5)
1. (a)
2x2 2kx 3k 8 0 for all real values of x.
The graph of y 2 x2 2kx 3k 8 does not
cut the x-axis.
0
(2k ) 2 4(2)(3k 8) 0
4k 2 24k 64 0
k 2 6k 16 0
(k 2)(k 8) 0
2 k 8
(b) The intege
(b) When y 9 and z
(page EP7.5)
1. (a) Let y k1 x k 2 x , where k1 and k 2 are non-zero
constants.
9
12 x 2
1
3
1A
When x 1, y 6 .
1
,
3
1
4
1
1
or (rejected)
x
2
2
x2
6 k1 k 2 . (1)
When x 4, y 18
(b) f ( x) x 2 2
(page EP1.3)
1.
2(k 1)2 (k 1) 19 k 2
g ( x) x 2
1M
g (1) 1 2
1
2(k 2 2k 1) k 1 19 k 2
f (1) 12 2
3
g (1) f (1) 1 3
4
2k 2 3k 18 k 2
k 2 3k 18 0
(k 3)(k 6) 0
k 3 or 6
1M
1A
1A
(4)
(3
y 2 x 2 + 3x - k + 5 cuts the x-axis at
two distinct points.
0
4. (a)
(page EP2.4)
1. (a) When f (x) is divided by x - 3 , the remainder
is 81.
f (3) 81
32 - 4(2)(- k + 5) 0
9 + 8k - 40 0
1M
a(3)3 -
Effective Learning Mathematics | S4A
Let f (x) be a polynomial. When f (x) is divided by x 1, the quotient is 3x 2 x 6. It is given that
f (1) 8.
(a) Find f (1) .
(3 marks)
(b) Factorize f (x) .
(3 ma
(a) Add the straight line y 2 to the graph of
y x3 5 x .
(page EP8.5)
1. (a) The period of the function is 180 .
1A
(b) When x 0, y 2 .
2 a sin 2(0) b
b2
1A
When x 45, y 5.
5 a sin 2(45) 2
a3
1A
(3)
F
Effective Learning Mathematics | S5B
There are two cubic tanks A and B of sides x m and ( x 1) m respectively.
(a) Show that the total capacity of tanks A and B is (2 x3 3x 2 3x 1) m3 .
(2 marks)
(b)
Effective Learning Mathematics | S6
It is given that the number of visitors to a place in 2010 was 800 000. In subsequent years, the number
of visitors is expected to increase by 5% each year compared
6. (log x y 5 ) log
(page EP3.3)
2 3
1.
2 3
a b
a b
( 14 ab 5 ) 2 (41 ) 2 a 2b10
a 2 2b3 1 0
42
b7
16
1
16b 7
y
1
1 log y 5 log x 3
x3 log x log y
1M
log y 5 log x 3
1
log x
log y 2
5 log y 3 log x
l
Effective Learning Mathematics | S5B
In a shopping mall, the rent of a shop of area x m 2 is $R, where 0 x 30 . It is given that R is the sum
of two parts, one part varies as x and the other part vari
Effective Learning Mathematics | S4B
Solve the equation 2 x 2 2 x 40.
(3 marks)
Suggested Solution
Marks
Remark
2 x 2 2 x 40
4(2 x ) 2 x 40
5(2 x ) 40
1M
2x 8
2 x 23
1M
x3
1A
(3)
Express 2 x 2 in term
(page EP4.4)
1.
sin 2 (90 ) cos(270 ) cos2 ( sin )
tan 2 (270 )
( tan1 ) 2
42 sin 30 cos 77 sin 42 cos
12 cos 35 sin
12
tan
35
2M
cos2 sin tan 2
sin
3
7 sin 5 cos 7
11sin 6 cos 6
1A
1A
(3)
(b)
For 5 y 8 9,
5 y 8 9
5 y 1
1
y
5
(page EP5.4)
1. For 6 7 x 5x 6,
6 7 x 5x 6
12 x 12
x 1
1A
For 5 y 8 12 ,
5 y 8 12
5 y 20
y4
For 12x 9 0 ,
12 x 9 0
12 x 9
3
x
4
1A
The solutions of the inequality are
(page EP9.5)
1. (a)
1A
2
(b) Tr 9r 12
3(3r 2 4)
1M
3 is a factor of Tr .
Tr is a multiple of 3.
1A
(3)
2. (a) T1 7
1M
The first term and the common ratio are 544
a(1) 2 b(1) 7
a b 7 . (1)
and
T3