List of public pages created with Protopage

Estimation

Generally, you should round each number involved to one significant figure and then it's easy to estimate by using the single digits and moving the point around.

It is important to remember that...

..most measurement is approximate! - If you say your garden is 8 metres long you are rounding to the nearest metre and it could be anything from 7.5 to 8.5 metres long!

Lower & Upper Bounds

The real value can be as much as half the rounded unit above or below the value given. So, if you are given 5.4cm the upper bound is 5.45cm and the lower bound is 5.35cm. For 6.0kg you need to go 0.05kg either way so the upper bound is 6.05kg and the lower bound is 5.95kg.

Video example ↓

Area of Triangles

Heron's formula

The height is called the perpendicular height because it is at a right-angle to the base. Below is an example of the formula being used to find the area of a triangle.

Vectors

A vector is a way to represent a movement between two places.

↓ Video examples

We visualise vectors by using straight lines with arrows on.

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Graphs

Cubic ↓

Quadratic ↓

Straight Line ↓

An example of a straight line graph is: y=x+7 X -2 -1 0 1 2 3 4 5 6 7 8 9 10 Y 5 6 7 8 9 10 11 12 13 14 15 16 17 This is shown, plotted, below.

Histograms

Histograms can have bars of different widths.

Videos ↓

Formulas →

FD = F ÷ CW CW = F ÷ FD F = FD x CW

Circle Theorems

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Sectors & Arcs

Sectors

Arcs

Circumference = πd or 2πr

circumference = 10π cm area = 25 π cm2 and the angle 72° is 1/5 of 360° Arc length = 1/5 of 10 π = 2 π = 6.283cm (3 d.p.) Sector area = 1/5 of 25 π = 5 π = 15.708cm2 (3 d.p.)

Probability Trees

This shows the toss of a coin..

The two possible outcomes (Heads and Tails) are AT THE END of the branches The probability of each branch is written ON the branch

This can be extended to two tosses of a coin..

You multiply probabilities along the branches Head, Head = 0.5 x 0.5 = 0.25 Head, Tails = 0.5 x 0.5 = 0.25 Tails, Head = 0.5 x 0.5 = 0.25 Tails, Tails = 0.5 x 0.5 = 0.25

The probability of getting at least one Head from two tosses is: 0.25+0.25+0.25 = 0.75