Relative frequency = number of times the event happens ÷ total number of trials
For example, if you observed 100 passing cars and found that 23 of them were red, the relative frequency is 23/100.
Recurring Fractions and Decimals
Converting a fraction to a decimal
To change a fraction to a decimal, you divide the top number by the bottom number (divide the numerator by the denominator).
Converting a decimal into a fraction
When you change a terminating decimal to a fraction, the denominator will be 10, or 100, or 1000 or… (depending on the number of decimal places).
0.5 means 'five tenths', so 0.5 = 5/10 = 1/2
0.45 means '45 hundredths', so 0.45 = 45/100 = 9/20
0.240 means '240 thousandths', so 0.240 = 240/1000 = 6/25
Inverse proportion is when one value increases as the other value decreases
y is inversely proportional to x. When y = 3, x = 12 .
Find the constant of proportionality, and the value of x when y = 8.
- y ∝ 1/x
- y = k/x
- So xy = k
- Substitute the values x = 12 and y = 3 into xy = k
- 3 × 12 = 36
- So k = 36
- To find the value of x when y = 8, substitute k = 36 and y = 8 into xy = k
- 8x = 36
- So x = 4.5
Rationalising the Denominator
Angles in Polygons
The formula for calculating the sum of the interior angles of a regular polygon is: (n - 2) × 180° where n is the number of sides of the polygon.
The exterior angle of a polygon and its corresponding interior angle always add up to 180° (because they make a straight line).
Angles in Circles
The angle made at the centre of the circle is exactly double the angle made at the edge of the circle from the same points.
Mean from Grouped Data
We already know how to find the mean from a frequency table. Finding the mean for grouped or continuous data is very similar
- Find mid-points and find the mean from there...
The mean is
Area of a sector
Area of Sector = ½ × θ × r2 (when θ is in radians)