Semester 2 Revision
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Transcript of Semester 2 Revision
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Semester 2 Revision
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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
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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
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Topics
• Trigonometry• Shapes & Solids• Graphs
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Graphs
Test ATest B
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Shapes & SolidsPerimeterThe distance around the outside of a shape
AreaThe space inside a 2-dimensional (flat) shape
VolumeThe space inside a 3-dimensional solid
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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.
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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).
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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
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Arearectangle
triangle
trapeziumparallelogram
circle
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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
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Arearectangle
triangle
circle
A = length x width
A = ½ x base x height
A = π x r2
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Area• Area of parallelogram = b x h
• Area of trapezium = ½(a + b) x h
b
h
ha
b
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Prisms
A prism is a 3-dimensional solid that has congruent ends
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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
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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
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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
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Volume of a prism
Volume of a prism = area of the base x height
height
base
base
height
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Trigonometry
Hypotenuse
Opp
osite
Adjacent
θ
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Trigonometry
Hypotenuse
Opp
osite
Adjacent
θ
Opposite
Adja
cent
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Trigonometry
Hypotenuse = 1
Leng
th o
f op
posi
te=
sine
θ
Length of adjacent= cosine θ
θ
Opp
osite
Adjacent
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Trigonometry
1
Sin
θ
Cos θ
θ
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Trigonometry
5
Leng
th o
f op
posi
te=
5 x
sine
θ
Length of adjacent= 5 x cosine θ
θ
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Trigonometry
5
5 x
Sin
θ
5 x Cos θ
θ
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Trigonometry
So
Length of opposite = length of hypotenuse x Sin θ
and
Length of adjacent = length of hypotenuse x Cos θ
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Trigonometry
Opposite = Hypotenuse x Sin θ
Adjacent = Hypotenuse x Cos θ
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TrigonometryTa
ngen
t θ
Adjacent = 1
θ
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Trigonometry7
x Ta
n θ
7
θ
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TrigonometryOpposite = Hypotenuse x Sin θAdjacent = Hypotenuse x Cos θOpposite = Adjacent x Tan θ
Sin θ =
Cos θ =
Tan θ =
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Trigonometry
SOHCAHTOASin θ =
Cos θ =
Tan θ =
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TrigonometryWhat if we want to find the angle (θ)?
Sin θ =
Cos θ =
Tan θ =
θ = Sin-1
θ = Cos-1
θ = Tan-1
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Trigonometry
6 x
30o
Example
SOHCAHTOA
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Trigonometry
6 x
30o
Example
Use Sine
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Trigonometry
6 x
30o
Example
Opposite = hypotenuse x Sin θ
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Trigonometry
6 x
30o
Example
x = 6 x Sin 30o
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Trigonometry
6 x
30o
Example
x = 6 x 0.5 x = 3
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Trigonometry
10 9
x
Example
SOHCAHTOA
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Trigonometry
10 9
x
Example
Sin θ =
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Trigonometry
10 9
x
Example
Sin x =
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Trigonometry
10 9
x
Example
Sin x = 0.9x = Sin-1 0.9
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Trigonometry
10 9
x
Example
x = 64.16o
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TrigonometryWhat if we want to find the hypotenuse (or adjacent)?
Sin θ =
Cos θ =
Tan θ =
Hyp =
Hyp =
Adj =
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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)
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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!