maths

Area of a Parallelogram

The area of a parallelogram = base x height. The area can also be worked out by making the parallelogram into a rectangle, however this will only work if you have the base and the height of the rectangle.

If you only have the area of the parallelogram and one of either base or height. You will need to divide the area by either the base or the height, whichever one you have.

Imperial and Metric Units

Metric

Mass

1000mg = 1g

1000g = 1kg

1000kg = 1 tonne

Length

10mm = 1cm

100cm = 1m

1000m = 1km

Volume

1000ml = 1l

1ml = 1cm(cubed)

1000cm (cubed) = 1l

Imperial

Length

12 inches = 1foot

3 feet = 1 yard

36 inches = 1 yard

1760 yards = 1 mile

Mass

16 ounces = 1 pound

14 pounds = 1 stone

2240 pounds = 1 ton

Metric to Imperial

Length

1 inch = 2.5 cm

1 foot = 30 cm

1.6 km = 1 mile

8 km = 5 miles

16 km = 10 miles

Mass and Volume

2.2 pounds = 1 kg

1 ounce = 30 g

1 gallon = 4.5 litres

Mean, median, mode and range

Mean : add up all the numbers and divide the result by the amount of numbers.

Median : put the numbers in consecutive order and find the number in the middle.

Mode : the number that occurs most often.

Range : the difference between the highest and lowest number.

Angles in Parallel Lines

Alternate angles are the same size. ( Z shape, angles are inside bends)

Supplementary angles add up to 180 degrees. ( C shape, inside the C)

Correspondind angles are equal. ( F shape, angles are underneath both lines of the F)

Adding, Subtracting, Dividing and Multiplying negative numbers

Same symbols are always equal to +.

Opposite symbols are always equal to -.

Vertical and Horizontal Lines

Any vertical line has an equation in the form = x = ...

Any horizontal line has an equation in the form = y = ...

Diagonal Lines

To work out the equation for any line, you need the equation mx+c.

M, is the gradient, this is the difference between each of the points. The point on the x axis divided by the point on the y axis.

C, is the y intercept, this is where the line intercepts the y axis. This can be a positive number or a negative number. Sometimes you may have to extend the line if it does not touch the y axis, for this use the gradient.

Constructing Triangles

To construct a triangle without the sizes of the angles you need to:

1) Draw your base line however long it needs to be.

2) Open your compass to the size of the side connected to the left edge of your straight base line.

3) Place the metal part of the compass of the left edge of the base line.

4) Draw an arc shape with the compass.

5) Re-do steps 2-4 but this time on the right edge of the base line.

6) Where the arc meet will be the final point of your triangle. Join it all together.

Remember to leave the arcs. NO ARCS, NO MARKS!!