Maths

Maths

1. Angles

   • Sum of interior angles = 180(n-2)
     • 11 sides = 180(n-2)... 180(11-2) = 1620*
   • Number of sides = sum of interior angles / 180
     • 1980 / 180 = 11 + 2 = 13 sides
   • Angles In Parallel Lines
     • Alternate = Z
       • The same
     • Co - interior = C
       • Add to 180*
     • Corresponding = F
       • The same
     • Angles on a straight line
       • Add to 180*
     • Vertically opposite = X
       • The same
   • Angles in polygons
     • Triangle = 180*
       • Hexagon = 720*
     • Quadrilateral = 360*
       • Heptagon = 900*
         • Nonagon = 1260*
     • Pentagon = 540*
       • Octagon = 1080*

2. Bearings

   • 1) Bearings are a measure of direction taken from the North
   • 2) Bearings are always measured in a clockwise direction
   • 3) Bearings are always written in 3 figures e.g. 079*

3. Inequalities

   • There are 5 inequality symbols
   • Some problems don't have specific answers. Inequalities give a range of possible numbers, but you have to give the whole range of answers by using the inequality signs e.g. x < 3
   • Filled in dots represent greater than and less than
     • Not filled in dots represent greater thank or equal to and less than or equal to
   • Solving inequalities = 4x + 1 > 11... 4x +1 = 11... 4x = 10... x = 2.5... >2.5
   • 3>1 ... 2<7 ... 33>25 ... 110<567

4. Negative Numbers

   • Ordering from S - L -5, -2, 0, 1, 3, 4, 7.
   • -4 + 6 = 2
   • -4 + -7 = -11
   • 6 - - 7 = 13

5. Prime Factors

   • Prime factor trees are used to find the LCM and HCF of 2 numbers
   • Prime numbers = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 etc.

6. HCF And LCM

   • To find the Highest Common Factor and Lowest Common Multiple you can use a venn diagram
   • Example = LCM and HCF of 660 and 252
     • Do the prime factor trees of both numbers and write them out the long way
     • If there is a 2 for example in both of the lists, then put it in the middle. Same with the other numbers the re-occur in both lists
     • Place the rest in the corresponding circle.
     • To find the HCF you multiply all the numbers in the middle.
       • To find the LCM you multiply the numbers in one circle by the number fromthe outside of the other circle, 5x11x252

7. Fractions

   • Top heavy fractions are fractions where the denominator is smaller than the numerator. We solve this problem by changing them into mixed numbers
     • To find a mixed number we divide the numerator by the denominator and write the remainder over the previous denominator.
       • E.g. 22/3 = 7 and 1/3

8. Multiplying and Dividing Decimals

   • Dividing
     • Using short division will come in handy ( bus stop method)
   • Multiplying
     • To multiply decimals, count how many numbers there are after the decimal point and remember it
     • Take out the decimal point(s) and use the Chinese method to solve it
       • Once you have gotten your answer, put the decimal point back where it should be.

9. Recurring Decimals

   • First, change the decimal into a whole number by multiplying it by 10,100,1000 etc.
     • When you have a whole number, and the digits after the decimal are the same as x, then you can take x away from the largest number.
       • Write the whole number as a fraction over the total and simplify it

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