Top Banner
1 Press Ctrl-A Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Stage 6 - Year 12 Mathematic (HSC)
23

1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Mathematic (HSC)

Dec 25, 2015

Download

Documents

Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1: 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Mathematic (HSC)

1Press Ctrl-APress Ctrl-A

©G Dear2008 – Not to be sold/Free to use

Stage 6 - Year 12Stage 6 - Year 12

Mathematic(HSC)

Page 2: 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Mathematic (HSC)

2

Types of Angles

1. Acute angles 2. Right Angle

3. Obtuse Angle

4. Straight Angle 5. Reflex Angle

6. Angle of Revolution

(0o < θ < 90o θ = 90o

(90o < θ < 180o)

(θ = 360o)

(θ = 180o)

(180o < θ < 360o)

Page 3: 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Mathematic (HSC)

3

1. Vertically Opposite Angle are equal.

2. Complementary Angles ao

bo add to 90o.

2. Supplementary Angles ao

boadd to 180o.

Pairs of Angles

Page 4: 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Mathematic (HSC)

4

Transversal1. Alternate Angles

2. Corresponding Angles

3. Co-Interior angles

Makes a Z shape.

Makes a F shape.

Makes a C shape.

andare equal.

andare equal.

andAdd to 180o

Angles between Parallel Lines

Page 5: 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Mathematic (HSC)

5

Based on SidesBased on Angles1. Equilateral triangle.

•All sides equal•All angles equal (60O)

2. Isosceles triangle.•Two sides equal•Two base-angles equal

3. Scalene triangle.•No sides equal

•No angles equal

1. Acute angled triangle.

2. Right angled triangle.

•All angles acute

•One angle 90o

•One Obtuse angle.

3. Obtuse angled triangle.

Types of Triangles

Page 6: 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Mathematic (HSC)

6

3. Exterior Angle of a Triangle.

1. Angle Sum of a Triangle

2. Angle Sum of a Quadrilateral

4. Angles at a point.

ao

bo

co

ao + bo + co = 180oao

bo co

do

ao + bo + co + do = 360o

bo

co

ao

ao = bo + coao

bo

co

ao + bo + co = 360o

Angle Sums

Page 7: 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Mathematic (HSC)

7

1. Side, Side, Side. 2. Side, Angle, Side.

4. Right angle, Hypotenuse, Side.3. Angle, Angle, Side.

SSS SAS

AAS RHS

Congruence

Page 8: 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Mathematic (HSC)

8

1. Corresponding angles are all

equal.α

β

αβ

γγ

2. Corresponding sides are in the

same ratio.

a x

ax

b

y

by

= = cz

c z

3. Two pairs of sides are in proportion and their included

angles are equal.

pq

s

φ

pr

= qs

=

Similar Triangles

Page 9: 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Mathematic (HSC)

9

AB : BC = DE : EF

A

F

E

D

C

B

ABBC EF

DE=

Ratio of Intercepts

Page 10: 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Mathematic (HSC)

10

ca

b

c2 = a2 + b2

You need to be able to:1. Find the length of the

hypotenuse.2. Find the length of the shorter side.3. Prove you have a right angle.

Pythagoras Theorem

Page 11: 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Mathematic (HSC)

11

1. Rectangle 2. Square 3. Rhombus

4.Parallelogram 5. Trapezium

6. Kite

You must know their properties

Types of Quadrilaterals

Page 12: 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Mathematic (HSC)

12

1. Triangle 2. Square 3. Pentagon

4. Hexagon 5. Octagon

Types of Regular Polygons

Page 13: 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Mathematic (HSC)

13

1. Angle Sum of a Polygon.

2. Interior angle.

3. Exterior angle

a

f c

b

e d

= (n – 2) x 180(n is the number of angles)

Divide the angle sum by the number of angles.

The exterior angles of add to 360o.

Regular Polygons

Page 14: 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Mathematic (HSC)

14

Area Formulae

1.SquareA = s2 ss

2. RectangleA = LB L

B

3.TriangleA=½bh

b

h 6.TrapeziumA=½(a+b)h

b

a

h

7.CircleA=πr2

r

4. ParallelogramA=bh

b h

5.Rhombus/KiteA=½xyx y

xy

Page 15: 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Mathematic (HSC)

15

1. Rectangular Prism

lb

h

SA = 2(bh + hl + lb)

2. Cube

s

SA = 6s2

3. Sphere

SA = 4 π r2

4. Cylinder

SA = 2 π r (r + h)

5. Cone

h

r

h

r

l

SA = π r (r + l)

Surface Area Formulae

Page 16: 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Mathematic (HSC)

16

1. Rectangular Prism

lb

h

V = lbh

2. Cube

s

V = s3

3. Sphere

V = 4 π r3

34. Cylinder

V = π r2 h

5. Cone

h

r

h

rV = 1 π r2 h 3

V = Ah

Volume Formulae

Page 17: 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Mathematic (HSC)

17

2006 HSC Question 6

Page 18: 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Mathematic (HSC)

18

BCA = CAD [Alternate angles between parallel lines.]

BAC = CAD [Given]

(i) Prove that BAC = BCA 1

BAC = BCA

2006 HSC Question 6

Page 19: 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Mathematic (HSC)

19

BP [Common]

PBA = PBC [Given]

(ii) Prove that ∆ABP ≡ ∆CBP 1

BAC = BCA [See part (i)]

∆ABP ≡ ∆CBP [AAS]

2006 HSC Question 6

Page 20: 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Mathematic (HSC)

20

(iii) Prove that ABCD is a rhombus. 3

APB = BPC [corresponding angles in congruent triangles – part ii]

APB + BPC = 180o [straight angle]

2 x BPC = 180o

BPC = 90o = APB

Diagonals bisect at 90o [ Square or Rhombus ????]

2006 HSC Question 6

Page 21: 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Mathematic (HSC)

21

2005 HSC Question 5

Page 22: 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Mathematic (HSC)

22

2004 HSC Question 2

Page 23: 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Stage 6 - Year 12 Mathematic (HSC)

23

2004 HSC Question 6