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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