HSC General Mathematics m5backdrop - ccsyr12-2009

```M5: Applications of area and volume
Areas of ellipses,
annuluses and parts
of a circle
Errors in
calculations
M5: Further applications of
area and volume
Volume of
composite
solids
Surface
area of
spheres
Surface area of
Cylinders
Calculating
areas of
composite
figures
Applying
Simpson’s Rule
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Pythagoras theorem
Circumference of circle
Area of circle
Area of triangle
Area of rectangle
Area of parallelogram
Area of trapezium
Area of rhombus
Volume of Prism
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Pythagoras
c²=a²+b²
(The square on the
hypotenuse is equal to the sum of the squares on the other two sides.)
Circumference of a circle
C=2Πr
Area of a circle
A = Πr²
Area of a triangle
A = ½bh OR
A =bh/2
Area of a rectangle
A =bh
Area of a parallelogram
A = bh
Area of a trapezium
A=h/2 (a+b)
Area of a rhombus
A=Dd/2
Volume of a prism
V=Ah
(Area of the cross-section x height)
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Determining appropriate units to use
Conversion between commonly used units
Accuracy in measurement
Error in measurement
Significant figures, scientific notation
Rates and ratios
Field diagrams
Classifying polyhedra
Surface area
Volume and capacity
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Area of annulus
=area of big circle – area
of small circle
= Π(R² – r²)
Area of an ellipse = Πab
◦ Where a=length of semi-major axis
◦ And b=length of semi-minor axis
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Area of a sector = Θ/360 x Πr²
Arc length
ℓ= Θ/360 x 2Πr
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Remember that more than one method may
be used, adding or subtracting are both
acceptable.
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Simpson’s rule is used to find the area of an
uneven field where one side is a curved
boundary.
A=h/3(d₁ + 4.d₂ + d₃)
where h= width of strip (between
successive measurements)
d₁ = first distance
d₂ = middle distance
d ₃ = last distance
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You can either do two or more separate
applications or you can put the first and last
in brackets and then 4 times the even slotted
distances and 2 times the odd slotted
distances.
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Read the question carefully to determine whether
it is open or closed and whether it is open both
top and bottom
If open and asking for the surface area of the
curved surface only, then
 SA = 2Πrh (if you cut longways through the cylinder you
would have a rectangle with the breadth being the
circumference of the circle , thus 2Πr, and the height of the
cylinder being h.)
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If a closed cylinder then you have to find the area
of the circular base and add that in.
i.e. A closed cylinder with top and bottom is
SA = 2Πrh + 2 x Πr²
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Surface area of a sphere
SA = 4Πr²
Volume of a sphere
V = 4/3Πr³
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Volume of composite figures can be found by
adding the volume of multiple different solids
or subtracting the volume of one solid from
another if looking for remaining spaces.
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The accuracy of measurement is ± the
smallest unit of the measuring instrument.
(If it is a ruler measuring in cm’s then the
error is 0.5cm or 5 mm. If it is a set of scales
measuring in 100gram increments then the
error is ±50 gram.)
Percentage error
% error = (difference ÷ original) x 100%
Or
% error = (½ the smallest unit ÷ actual
measurement) x 100%
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When answering questions do not round off
during a calculation. Continue to use full
calculator display and write down this as
your solution before writing a concluding
statement with a rounded answer. Rounding
off too early causes significant differences in
the final result. You can obtain marks for