S-Cool Revision Summary
S-Cool Revision Summary
Shape: | Area: |
Square | Length x Length |
Rectangle | Length x Width |
Triangle | ½ x Base x Perpendicular Height |
Parallelogram | Base x Perpendicular Height |
Trapezium | Average of parallel sides x distance between them |
Cylinder (curved surface) | 2π rh |
Cone (curved surface) | π rl |
Sphere (surface area) | 4π r^{2} |
Volume
Cube | Length^{3} |
Cuboid | Length x Width x Height |
Prism | Area of cross-section x Length |
Cylinder | |
Sphere | |
Cone | |
Dimensions: note that the area formulae all have a length squared in them and the volume formulae all have a length cubed. Constants (numbers) have no dimensions.
Remember: Measurement is only approximate. It can be up to half the rounded unit up or down!
Metric/Imperial
- 1cm = 10mm
- 1m = 100cm
- 1km = 1000m
- 1kg = 1000g
- 1 tonne = 1000kg
- 1 litre = 1000ml = 1000cm^{3}
Note: Although 1m = 100cm, remember 1m^{2} = 10,000cm^{2} and 1m^{3} = 1,000,000cm^{3}
- 1 foot = 12 inches
- 1 yard = 3 feet
- 1 mile = 1760 yards
- 1 pound = 16 ounces
- 1 stone = 14 pounds
- 1 ton = 160 stones (or 2240 pounds)
Note the different spellings of tonne (metric) and ton (imperial).
- 1 gallon = 8 pints
Kilometres and Miles:
- km to miles - Multiply by 5 and divide by 8
- miles to km - Multiply by 8 and divide by 5
Kilometres and Pounds:
- 1kg = 2.2 pounds
- 1 pound = 0.454kg
- So basically there's about 2 pounds in a kilogram
Litres, Pints and Gallons:
- 1 pint is about half a litre (1 pint = 0.568 litres)
- 1 litre = 0.22 gallons
Metres, Centimetres, Feet and Inches:
1 inch is about 2.5cm so a 30cm ruler is about 12 inches (which is a foot!)
1 metre is about 40 inches which is just over 3 feet so 1 metre is slightly bigger than 1 yard!
Lotus
A locus is simply a set of points that satisfy some sort of condition.
Distance from a point
A circle around the point!
Distance from two points
A perpendicular line straight down the middle of the points:
- Set your compasses so that they are roughly the same as the distance between the points (or less if you don't have a lot of room!).
- Put the point of the compasses on the first cross and do two arcs - one above the points and one below.
- Put the point on the second cross and do the same thing so that you cross the first arcs (making sure you keep the compasses the same distance apart).
- Now simply draw a line straight down the middle through the points where the arcs cross.
Distance from two lines
The set of points that are the same distance from two lines is a straight line down the middle which bisects the angle (cuts it in half):
- Get a pair of compasses and place the point where the two lines meet. Draw little arcs that cross each of the lines.
- Now, keeping the compasses set, put the point on each line where your arc has crossed it and draw another little arc in-between the two lines. You should now have another two little arcs in the middle.
- Draw a straight line from the angle through the point where your little arcs cross and you've done it!