Semester 2 Revision

NAME:

TEACHER: Ms Leishman Langley/Cocks Ms Le-Rodda Mr Sinniah(please circle your teacher’s name)

GISBORNE SECONDARY COLLEGEYear 9 Maths Semester Two

Examination 2012

Reading Time: 10 minutesWriting Time: 60 minutes

Section A: Multiple Choice 20 Questions 20 marksSection B: Short Answer 8 Questions 50 marks

TOTAL: 70 marks

Allowed Materials•Scientific Calculator•2 pages (1 x A4 sheet) of revision notes

Formulas Area of a rectangle = l x w Area of a parallelogram = b x h Area of triangle = ½ x b x h Area of a trapezium = ½ (a + b) x h Area of circle = πr2

Circumference = 2πr

Topics

• Trigonometry• Shapes & Solids• Graphs

Graphs

Test ATest B

Shapes & SolidsPerimeterThe distance around the outside of a shape

AreaThe space inside a 2-dimensional (flat) shape

VolumeThe space inside a 3-dimensional solid

PerimeterIs measured in linear unitse.g. mm, cm, m or km

To calculate the perimeter, find the length of all sides then add them together.

The perimeter of a circle is called the circumference.

CircumferenceThe rule for finding the circumference of a circle is:

C = π x d

Where d = diameter (the width of the circle) and π = 3.142

or

C = 2πr

Where r = radius (1/2 the diameter).

AreaIs measured in square unitse.g. mm2, cm2, m2 or km2

To calculate the area use the appropriate formula

You need to be able identify shapes

Arearectangle

triangle

trapeziumparallelogram

circle

Area Area of a rectangle = l x wArea of triangle = ½ x b x hArea of a parallelogram = b x hArea of a trapezium = ½ (a + b) x hArea of circle = πr2

l = lengthw = widthb = base lengthh = heightr = radiusa = side a length and b = side b length

Arearectangle

triangle

circle

A = length x width

A = ½ x base x height

A = π x r2

Area• Area of parallelogram = b x h

• Area of trapezium = ½(a + b) x h

b

h

ha

b

Prisms

A prism is a 3-dimensional solid that has congruent ends

Surface area of a prismThe total surface area of a prism is the sum of the area of each side.

• A rectangular prism has 6 sides• Each side is a rectangle• Each side has an equal and opposite side

Surface area of a prismThe total surface area of a prism is the sum of the area of each side.

• A triangular prism has 5 sides• The 2 ends are triangles• The other 3 sides are rectangles

Surface area of a prismThe total surface area of a prism is the sum of the area of each side.

• A circular prism (cylinder) has 3 sides• The 2 ends are circles• The other side is a ?????

h

2 x π x r

Volume of a prism

Volume of a prism = area of the base x height

height

base

base

height

Trigonometry

Hypotenuse

Opp

osite

Adjacent

θ

Trigonometry

Hypotenuse

Opp

osite

Adjacent

θ

Opposite

Adja

cent

Trigonometry

Hypotenuse = 1

Leng

th o

f op

posi

te=

sine

θ

Length of adjacent= cosine θ

θ

Opp

osite

Adjacent

Trigonometry

1

Sin

θ

Cos θ

θ

Trigonometry

5

Leng

th o

f op

posi

te=

5 x

sine

θ

Length of adjacent= 5 x cosine θ

θ

Trigonometry

5

5 x

Sin

θ

5 x Cos θ

θ

Trigonometry

So

Length of opposite = length of hypotenuse x Sin θ

and

Length of adjacent = length of hypotenuse x Cos θ

Trigonometry

Opposite = Hypotenuse x Sin θ

Adjacent = Hypotenuse x Cos θ

TrigonometryTa

ngen

t θ

Adjacent = 1

θ

Trigonometry7

x Ta

n θ

7

θ

TrigonometryOpposite = Hypotenuse x Sin θAdjacent = Hypotenuse x Cos θOpposite = Adjacent x Tan θ

Sin θ =

Cos θ =

Tan θ =

Trigonometry

SOHCAHTOASin θ =

Cos θ =

Tan θ =

TrigonometryWhat if we want to find the angle (θ)?

Sin θ =

Cos θ =

Tan θ =

θ = Sin-1

θ = Cos-1

θ = Tan-1

Trigonometry

6 x

30o

Example

SOHCAHTOA

Trigonometry

6 x

30o

Example

Use Sine

Trigonometry

6 x

30o

Example

Opposite = hypotenuse x Sin θ

Trigonometry

6 x

30o

Example

x = 6 x Sin 30o

Trigonometry

6 x

30o

Example

x = 6 x 0.5 x = 3

Trigonometry

10 9

x

Example

SOHCAHTOA

Trigonometry

10 9

x

Example

Sin θ =

Trigonometry

10 9

x

Example

Sin x =

Trigonometry

10 9

x

Example

Sin x = 0.9x = Sin-1 0.9

Trigonometry

10 9

x

Example

x = 64.16o

TrigonometryWhat if we want to find the hypotenuse (or adjacent)?

Sin θ =

Cos θ =

Tan θ =

Hyp =

Hyp =

Adj =

TrigonometryThings to remember:

1. Make sure your calculator is in DEG (degrees) mode2. SOHCAHTOA3. Which sides of the triangle are involved in the problem?4. Each rule (Sin, Cos or Tan) can be used in 3 ways:• To find one of the side lengths• To find the length of the hypotenuse (Sin or Cos) or

the adjacent (Tan, given the opposite)• To find the angle (use inverse function on calculator)

The End

Remember to bring to the exam:• 1 page (back and front of revision notes)• Pens, pencils, eraser, ruler• Scientific calculator (ipods & phones not

allowed)

GOODLUCK!