Revision 4 Eng

8/10/2019 Revision 4 Eng

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HKDSE Mathematics Compulsory Part

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TEL3428 5444WHATSAPP5160 6464FB// Dr. Chiu Education Centre1

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=sinx

y=cosx

y=tanx


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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)= tan(9 0 ) =


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C.Formula of triangle

Area ofABC:= =

=

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 ABand 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 anglebetween 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

{: = : = 0

> = < No. of

intersection

2 intersections 1 intersection No intersections


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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 ) (1 )

Mid-point of the line segment joining (1, 1)and (1, 1)= ( 1

2

, 1

2

)

If AC:CB=m:n, then

= (++ , ++ )


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MC1.

2.

3.


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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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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)-

(possible intersection of two straight lines, a straight line and a circle)

- (describe the locus of points with algebraic equations)_____________________________________________________________________________________________

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)_____________________________________________________________________________________________

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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TEL3428 5444

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31

12

3

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(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)

Documents

Revision 4 Eng