Maths Key Revision Points

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Relative Frequency

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.

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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).

For example:

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

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Inverse Proportion

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
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Rationalising the Denominator

 

"Rationalising the denominator" is when we move a root (like a square root or cube root) from the bottom of a fraction to the top.

  • Numbers like 2 and 3 are rational.
    But many roots, such as √2 and √3, are irrational.

PRACTICE THESE!

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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).

 image: interior and exterior angles of a pentagon (http://www.bbc.co.uk/staticarchive/82a56d3ecb76f219428589e69d71b9b8c0b1cff5.gif)

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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.

(http://www.bbc.co.uk/staticarchive/c916f4b89ce6e9ca185f5d9a01b802c79e416a3e.gif)

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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 20 + 82 + 72 + 34 over 10 + 12 + 6 + 2 = 210 over 30 = 7 (http://www.bbc.co.uk/staticarchive/9e623840b5310fd0449d057f59b138f3173ca9ae.png)

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Area of a sector

Area of Sector = ½ × θ × r2   (when θ is in radians)

circular sector area (http://www.mathsisfun.com/geometry/images/circle-sector-area.gif)

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