M1: Units of Measurement
M1: Units of Measurement
M2: Applications of Area and Volume
M3: Similarity of 2-Dimensional Figures
M4: Right-angled Triangles
M5: Further Applications of Area and Volume
M6: Applications of Trigonometry
M7: Spherical Geometry
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With the unitary method, divide first to find one part, and then multiply to find the whole amount
Percentage error = absolute error/measurement x 100%
Surface area of a solid = sum of the areas of its faces
1 cm³ = 1mL 1L = 1000mL
Similar figures are the same shape but not necessarily the same size
The matching angles in similar figures are equal to preserve the same shape
Two similar figures that have a scale factor of 1 are said to be congruent
Similar figures have all matching angles equal
Similar figures have matching sides in the same ratio
a² = b² + c²
sin = opposite/hypotenuse cos = adjacent/hypotenuse tan = opposite/adjacent
Length of an arc = l = ¸/360 × 2Àr
Area of a sector = A = ¸/360 × Àr²
Area of an Ellipse = A = Àab
Simpson s Rule
Cosine Rule
[pic]
Sine Rule
[pic]
Area of a triangle
[pic]
Obtuse Angles
sin (180 – θ) = sin θ
cos (180 – θ) = -cos θ
tan (180- θ) = -tan θ
Great circle –The radius is the same as that of the sphere.
Small circle –radius is smaller than that of a great circle.
Latitude – imaginary lines which rule out north and south. All small circles except the Equator. Parallels of latitude vary from 90˚N to 90˚S.
Equator – 0˚ divides the world into the north & south hemispheres
Angle of latitude – the angle that a line from the centre of earth, to a parallel of latitude makes with the equator.
Longitude – imaginary lines which rule out east and west. They are all great circles. The main meridian of longitude is the Greenwich meridian. Meridians range from 180˚W to 180˚E. 180˚W and 180˚E are the same meridian. All meridians meet at the poles.
Angle of longitude – the angle a meridian makes with the Greenwich meridian.
International Date Line - 180˚ meridian and runs through the Pacific Ocean. Those countries west of the Date Line receive the date first, those east get the day 24hours later.
Arc length of a circle -
Θ
l = ---- x 2 ∏ r
360
Earth’s radius – 6400km or 6367.4km
Nautical miles – used instead of km for sea and air travel (M)
Knots – nautical and air speed
Speed = distance ÷ time
1M = 1.852km 1knot = 1M/h
= 1.852km/h
1` = 1M 1˚ = 60M
1˚ = 4 minutes (longitude) 15˚ = 1 hour (longitude)
Conversion - km to M = multiply
- M to km = divide
GMT = Greenwich meridian = (Greenwich Mean Time)
IDL = International Date Line
AEST = Australian Eastern Standard Time
ACST = Australian Central Standard Time
AEST = Australian Western Standard Time
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