Bar Graphs 23/10/2015

Types of bar chart

Bar charts or bar graphs represent data as vertical blocks or columns.
The X axis shows what type of data each column represents, and the Y axis shows a value for that type of data. For example, in a rainfall graph, each column on the X axis represents a month of the year, with the height of each column on the Y axis showing the amount of rainfall in that month.

Compound

It is possible to split each column into sections to show the breakdown of data. For example, the employment data shown on the previous page could have been represented as three columns on a bar chart. The three columns would represent the three countries, with each column subdivided into sections showing primary, secondary and tertiary in different colours. This type of bar chart is sometimes called a compound bar chart.

Comparative

It is also possible to compare two sets of data on a bar chart - for example, measuring rainfall in two countries over the same period. This type of bar graph is called a comparative bar graph.
The chart below compares the tourism data for the UK in October 2001 with October the previous year. The graph shows how tourism declined after the terrorist attack in America in September 2001.

Bar chart showing decline in tourism to the UK

3D Shapes

3D solid shapes

Here are some common solid shapes.

Prisms and pyramids

A prism is a 3D shape which has a constant cross section - both ends of the solid are the same shape and anywhere you cut parallel to these ends will give you the same shape.

For example, in the prism below, the cross section is a hexagon.

This is called a hexagonal prism.

A pyramid has sloping faces that meet at a vertex.

Square-based pyramid

Tetrahedron

Drawing 3D shapes on isometric paper

You can use isometric paper to draw 3D shapes.

Remember to hold the isometric paper so that you can see vertical rows of dots!

This cube has been drawn using the dots as guides. The vertical lines are always vertical, but the horizontal lines are drawn at an angle, when drawn on isometric dotted paper. You could get some isometric paper and draw the cube yourself.

Perimeter 9th October Compund shapes

Compound shapes

Sometimes the shape is more complicated. In this case you need to calculate 'missing' lengths and be particularly careful to include all the sides.

Perimeter = 2 + 2 + 3 + 3 + 5 + 5 = 20 cm

Question

A plan of a play area is shown below:

Perimeter 9th october Simple shapes

Simple shapes

The perimeter of a shape is the length of its boundary.
Think of an ant starting from one corner of a small box, measuring 3 cm by 4cm. Imagine it walks all the way around the edge of the box. What distance will it have walked?

Perimeter = 4 + 3 + 4 + 3 = 14 cm

Straight Line Graphs 10th November 2015

When X= 0
Y is whatever the intercept of the line is.

The gradience tells us how much to go up in each time

Sometimes you are given a graph of a straight line and you need to find its gradient.
To find the gradient of a straight line:

• choose any two points on the line
• draw a right-angled triangle with the line as hypotenuse
• use the scale on each axis to find the triangle's:
  • vertical length
  • horizontal length
• work out the vertical length ÷ horizontal length
• the result is the gradient of the line

The following graph shows the exchange rate for euros € and United States dollars $ in March 2011.

There are two marked points at (0, 0) and (70, 98).
By working out the gradient of the graph, we can find the exchange rate from euros to United States dollars.

• The vertical distance between (0, 0) and (70, 98) is 98.
• The horizontal distance between (0, 0) and (70, 98) is 70.
• 98 ÷ 70 = 1.4

This means that 1 euro is equal to 1.4 United States dollars.

Inequalities

Solve the expression 3x - 7 < 8.

• First, write down the inequality:
• 3x - 7 < 8

• Then add 7 to both sides, to cancel out the -7:
• 3x < 15

• Next, simplify the inequality by dividing both sides by the number in front of x - in this case 3.
• x < 5

So the inequality in 3x - 7 < 8 is satisfied when x is less than 5. (Note that this does not include 5 itself.)

Ratio's

Write the ratio in its simplest form.

To work this out, look for a number that will divide into and .

divides into both numbers, so can be written as .

You can divide these by , so the simplified ratio is .

No number divides into and exactly, so is the simplest form of the ratio.

 

If you are making orange squash and you mix one part orange to four parts water, then the ratio of orange to water will be ( to ).

• If you use litre of orange, you will use litres of water .
• If you use litres of orange, you will use litres of water .
• If you use litres of orange, you will use litres of water .

These ratios are all equivalent:

Both sides of the ratio can be multiplied or divided by the same number to give an equivalent ratio.

Negative number 23/10/15

a) 5 × -4
b) -40 ÷ -8

a) We have +5 and -4. The signs are different, so the answer will be negative. So, +5 × -4 = -20

b) We have -40 and -8. The signs are the same, so the answer will be positive. So, -40 ÷ -8 = 5

brackets anf factorisation 9th/10/2015

Factorise the expression: c²- 3c - 10

Write down the expression: c²- 3c - 10
Remember that to factorise an expression we need to look for common factor pairs. In this example we are looking for two numbers that:

• multiply to give -10
• add to give -3

Think of all the factor pairs of -10:

• 1 and -10
• -1 and 10
• 2 and -5
• -2 and 5

Which of these factor pairs can be added to get -3?
Only 2 + (-5) = -3
So the answer is:
c² - 3c - 10 = (c + 2)(c - 5)

Index Laws 8th Sept

Golden rules of index laws (multiplication):


when the big numbers or letters are the same in a multiplication questions you can just add the powers together.

Task
1) A2 x A5= A7
2) B3 x B8= B11
3) C12 x C6= C18
4) D2 x D100= D102
5) E5 x E5= E10

Golden Rules Of Index Laws (Division):



when the big numbers or letters are the same in a division questions you can just subtract the
powers together

1) A5 / A2= A3
2) B7/ B3=B4
3)C3/C5=C-2
4)66/ 62=64
5)712/73=79

Ratio sharing Friday 18th September 2015

Ratio sharing

Example: 
Dave and Lisa win £500 between them. They agree to divide the money in the ratio 2:3.
How much does each person receive?

Method
The ratio 2:3 tells us that for every 2 parts Dave receives, Lisa will receive 3 parts. There are 5 parts in total.
£500 represents 5 parts. Therefore, £100 represents 1 part.
Dave receives 2 parts: 2 × £100 = £200
Lisa receives 3 parts: 3 × £100 = £300




 Example                                 £40    3:5

*3+5=8
*40/8=5
*3x5=15    *5x5= 25