# 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 r2

## Volume

 Cube Length3 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 = 1000cm3

Note: Although 1m = 100cm, remember 1m2 = 10,000cm2 and 1m3 = 1,000,000cm3

• 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:

1. 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!).
2. Put the point of the compasses on the first cross and do two arcs - one above the points and one below.
3. 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).
4. 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):

1. Get a pair of compasses and place the point where the two lines meet. Draw little arcs that cross each of the lines.
2. 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.
3. Draw a straight line from the angle through the point where your little arcs cross and you've done it! 