HKDSE Mathematics Compulsory Part
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S5-S6
Revision 4
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Revision 4
1. Trigonometry
2. Equations of circles
3. Locus
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1. Trigonometry
A. Graphs of trigonometric functions
y= sin x
y= cos x
y= tan x
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B. Trigonometric identities
(i)
If n is even:
(ii)
If n is odd:
( ) =
( ) =
( ) =
( ) =
( ) =
( ) =
Using the graph below, we can determine the sign of the identities above.
cos(270 ) =
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tan(90 + ) =
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C. Formula of triangle
Area of ABC:
= = =
Herons formula:
= ( )( )( )
Where =
++
The sine formula:
=
=
The cosine formula:
= +
= +
= +
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D. More about 3D problems
Angle between a straight line and a plane
If line AB intersects the horizontal plane at point B and P is the
projection of A on the plane, then is the angle between AB
and the plane.
Angle between two intersecting planes
If two non-parallel planes intersect at a straight line XY and there
are two lines and intersecting at a point such that
and , then the angle between the two lines is the angle
between the two planes.
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2. Equations of circles
Standard form
( ) + ( ) =
Centre= (, ), radius=
General form
+ + + + =
Centre= ( , ), radius= ( ) + ( )
Possible intersection between a straight line and a circle
{
: = +
: 2 + 2 + + + = 0
No. of
>
<
2 intersections
1 intersection
No intersections
intersection
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3. Locus
When a point moves in a manner satisfying some given conditions,
its path is called the locus.
Distance between (1 , 1 )and (1 , 1 )
= (1 2 )2 + (1 2 )2
Mid-point of the line segment joining (1 , 1 )and (1 , 1 )
=(
1 + 2 1 + 2
,
)
2
2
If AC:CB=m:n, then
1 +2 1 +2
=(
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MC
1.
2.
3.
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4.
5.
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6.
7.
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8.
9.
10.
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11.
12.
13.
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14.
15.
16.
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17.
18.
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19.
20.
21.
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Question
1.
2.
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3.
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4.
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5.
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6.
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7.
The end
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DSE S6 MATHS SPECIAL COURSE
($200 / 1 LESSON, $380 / 2 LESSONS,$570 / 3 LESSONS,$750 / 4 LESSONS)
($200 / 1 , $380 / 2 , $570 / 3 , $750 /4 )
12 23 12 3
(Equations of straight lines and circles, Locus)
- (properties of straight line and circle equation)
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(possible intersection of two straight lines, a straight line and a circle)
- (describe the locus of points with algebraic equations)
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12 24 5 8
1 3 1 4
(Variations, Arithmetic and geometric sequences and their summations)
-
(direct, inverse, joint and partial variations)
(general term of AS and GS)
(sum of AS and GS)
(sum to infinity of GS)
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12 25 1 4
12 30 1 4
(Inequalities and linear programming)
-
(solve linear and quadratic inequalities in one unknown)
-
(represent the graphs of linear inequalities in two unknowns on a plane)
- (solve linear programming problems)
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12 28 3 6
12 29 12 3
(Basic properties of circles)
- (properties of chords and arcs)
- (angle properties)
-
(properties of a cyclic quadrilateral and its test)
-
(properties of tangents to a circle and angles in the alternate segments)
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12 29 5 8
12 26 1 4
(More about trigonometry)
-
(functions, graphs and properties of sine, cosine and tangent)
-
(solve trigonometric equations)
-
(formula for areas of triangles, sine and cosine formulae, Herons formula)
-
(solve 2D and 3D problems)
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12 31 12 3
12 24 12 3
(Probability and Statistics)
-
(understand the concept and notation of permutation and combination)
-
(understand the addition law, multiplication law and conditional probability)
-
(understand exclusive events, complementary events and independent events)
-
(concepts of dispersion, range, inter-quartile range, standard deviation)
-
(construct and interpret the box-and-whisker diagram) (
-
(understand the concept of standard scores and properties of normal
distribution)
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12 23 5 8
(Complex number, Functions and graphs , Exponential and logarithmic functions)
-
(laws of rational indices and properties of logarithms)
(solve exponential equations and logarithmic equations)
(graph of exponential and logarithmic functions)
(addition, subtraction, multiplication and division of complex numbers)
- (feature of the graphs of quadratic functions)
-
(find maximum and minimum value by completing the square)
- (transformation of function)
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