1994-2007 CE Math Paper 1 Questions
Chapter 9: Deductive Geometry in Circles
1.
[07 Q17]
(a)
In Figure 7(a), AC is the diameter of the semi-circle ABC with centre O. D is a point lying on
AC such that AB = BD. I is the in-centre ofABD. AI is produced to m
HKDSE
MATH CP
PAPER 2
HONG KONG DIPLOMA OF
SECONDARY EDUCATION EXAMINATION
MATHEMATICS Compulsory Part
MOCK EXAM 2 (2014)
PAPER 2
Time allowed: 1 1 4 hours
1.
2.
3.
4.
5.
6.
Read carefully the instructions on the Answer Sheet. After the announcement of
th
HKDSE
MATH CP
PAPER 2
HONG KONG DIPLOMA OF
SECONDARY EDUCATION EXAMINATION
MATHEMATICS Compulsory Part
MOCK EXAM 1 (2014)
PAPER 2
Time allowed: 1 1 4 hours
1.
2.
3.
4.
5.
6.
Read carefully the instructions on the Answer Sheet. After the announcement of
th
Quadratic Equations
mc-TY-quadeqns-1
This unit is about the solution of quadratic equations. These take the form ax2 + bx + c = 0. We
will look at four methods: solution by factorisation, solution by completing the square, solution
using a formula, and so
The sum of an innite
series
mc-TY-convergence-2009-1
In this unit we see how nite and innite series are obtained from nite and innite sequences.
We explain how the partial sums of an innite series form a new sequence, and that the limit
of this new sequen
The scalar product
mc-TY-scalarprod-2009-1
One of the ways in which two vectors can be combined is known as the scalar product. When
we calculate the scalar product of two vectors the result, as the name suggests is a scalar, rather
than a vector.
In this
Transposition of
formulae
mc-TY-transposition-2009-1
In mathematics, engineering and science, formulae are used to relate physical quantities to each
other. They provide rules so that if we know the values of certain quantities, we can calculate
the value
The vector product
mc-TY-vectorprod-2009-1
One of the ways in which two vectors can be combined is known as the vector product. When
we calculate the vector product of two vectors the result, as the name suggests, is a vector.
In this unit you will learn
Triangle formulae
mc-TY-triangleformulae-2009-1
A common mathematical problem is to nd the angles or lengths of the sides of a triangle when
some, but not all of these quantities are known. It is also useful to be able to calculate the area
of a triangle
Trigonometric
functions
mc-TY-trig-2009-1
The sine, cosine and tangent of an angle are all dened in terms of trigonometry, but they can
also be expressed as functions. In this unit we examine these functions and their graphs. We
also see how to restrict t
Trigonometric
Identities
mc-TY-trigids-2009-1
In this unit we are going to look at trigonometric identities and how to use them to solve
trigonometric equations.
In order to master the techniques explained here it is vital that you undertake plenty of pra
Trigonometric
equations
mc-TY-trigeqn-2009-1
In this unit we consider the solution of trigonometric equations. The strategy we adopt is to nd
one solution using knowledge of commonly occuring angles, and then use the symmetries in the
graphs of the trigon
Trigonometrical ratios
in a right-angled
triangle
mc-TY-trigratios-2009-1
Knowledge of the trigonometrical ratios sine, cosine and tangent, is vital in very many elds of
engineering, mathematics and physics. This unit introduces them and provides examples
The geometry of a
circle
mc-TY-circles-2009-1
In this unit we nd the equation of a circle, when we are told its centre and its radius. There are
two dierent forms of the equation, and you should be able to recognise both of them. We also
look at some prob
The gradient of a
straight line segment
mc-TY-gradstlnseg-2009-1
In this unit we nd the gradient of a straight line segment, and the relationships between the
gradients of parallel lines and of perpendicular lines.
In order to master the techniques explai
Trigonometric ratios
of an angle of any size
mc-TY-trigratiosanysize-2009-1
Knowledge of the trigonometrical ratios sine, cosine and tangent, is vital in very many elds of
engineering, mathematics and physics. This unit explains how the sine, cosine and t
Surds, and other roots
mc-TY-surds-2009-1
Roots and powers are closely related, but only some roots can be written as whole numbers.
Surds are roots which cannot be written in this way. Nevertheless, it is possible to manipulate
surds, and to simplify for
Substitution
& Formulae
mc-subsandformulae-2009-1
In mathematics, engineering and science, formulae are used to relate physical quantities to each
other. They provide rules so that if we know the values of certain quantities, we can calculate
the values o
Solving inequalities
mc-TY-inequalities-2009-1
Inequalities are mathematical expressions involving the symbols >, <, and . To solve an
inequality means to nd a range, or ranges, of values that an unknown x can take and still satisfy
the inequality.
In thi
Tangents and normals
mc-TY-tannorm-2009-1
This unit explains how dierentiation can be used to calculate the equations of the tangent and
normal to a curve. The tangent is a straight line which just touches the curve at a given point.
The normal is a strai
The addition formulae
mc-TY-addnformulae-2009-1
There are six so-called addition formulae often needed in the solution of trigonometric problems.
In this unit we start with one and derive a second from that. Then we take another one as given,
and derive a
The Chain Rule
mc-TY-chain-2009-1
A special rule, the chain rule, exists for dierentiating a function of another function. This unit
illustrates this rule.
In order to master the techniques explained here it is vital that you undertake plenty of practice
The Product Rule
mc-TY-product-2009-1
A special rule, the product rule, exists for dierentiating products of two (or more) functions.
This unit illustrates this rule.
In order to master the techniques explained here it is vital that you undertake plenty o
The double angle
formulae
mc-TY-doubleangle-2009-1
This unit looks at trigonometric formulae known as the double angle formulae. They are called
this because they involve trigonometric functions of double angles, i.e. sin 2A, cos 2A and tan 2A.
In order t
The Quotient Rule
mc-TY-quotient-2009-1
A special rule, the quotient rule, exists for dierentiating quotients of two functions. This unit
illustrates this rule.
In order to master the techniques explained here it is vital that you undertake plenty of prac
Please stick the barcode label here.
HKDSE
MATH CP
PAPER 1
6.
The diagrams in this paper
are not necessarily drawn to
Candidate Number
scale.
HONG KONG DIPLOMA OF
SECONDARY EDUCATION EXAMINATION
7.
MATHEMATICS Compulsory Part
Mock Exam 1 (2014)
PAPER 1
Qu
Please stick the barcode label here.
HKDSE
MATH CP
PAPER 1
6.
The diagrams in this paper
are not necessarily drawn to
Candidate Number
scale.
HONG KONG DIPLOMA OF
SECONDARY EDUCATION EXAMINATION
7.
MATHEMATICS Compulsory Part
Mock Exam 2 (2014)
PAPER 1
Qu
HndMgthevmueofavaabbinafbnnMa
ChanwngsumectofafonnMa
l
3 i.e.
1 _ = _9
B. . a
9
1 a=_l
Q .
9 _9
1 The answer IS B.
D 3
ggvmmAigi
1
Sf Example2
IfP =g+ 3, then R =
S
A. 535. C. 3(53].
Q Q
3 L3. a EQ;2.
Q Q
Solution
QR=S(P3)
R:S(P3)
Q
The answer is
7%
lua
S? 505%!
Basic concept
Percentage change *
Proﬁt and loss
Discount
Simple and compound interests
Growth and depreciation *
Successive and component changes *
Taxaﬁon
X=(1 +20%) Y
t X: 1.2 Y . (i)
i Example 1 3
‘u
Angles and parallel lines
Angles of a triangle and a convex polygon
Similar triangles and congruent triangles
Special quadrilaterals
Pythagoras’ theorem
Mid—point theorem and intercept theorem
Triangle inequality
-‘ Centres of a triangle
Example 1
Acc