Maths

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  • Created on: 10-05-15 10:48

Algebra

- In algebra, only like terms can be added or subtracted

SIMPLIFY

1) 3m + 8n + 7m - 2n = 10m-6n                       2) pq + 7p - 9q + 5pq = 6pq + 7p - 9q

3) 2a + 4b + c - b + 2c = 5b + 3c + 2a

EQUATION, EXPRESSION AND FORMULA:

1) 3x + 1 = -7   - this is an EQUATION

2) P = 3q + N   - this is a FORMULA

3) x + 3 + 2x -1   - is an EXPRESSION

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Expanding brackets and simplifying

EXAMPLES:

1) 4 ( 2a + 3 ) + 3 ( 5a - 1 ) = 8a + 12 + 15a - 3

             = 23a + 9

2) 5 ( 3a - b + 2 ) + 6 ( a = 4b - 1 ) = 15a - 5b + 10 + 6a +24b - 6

                   = 21a + 19b + 4

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Letters for numbers

EXAMPLES:

1)  Start with n, multiply by 8 subtract 3

     n           8n            8n - 2

2) Start with m, add 7 then multiply by 5

    m           m + 7       5 ( m + 7 )

3) Start with p, subtract q then square the result

 p            p - q           ( p - q )

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Circles

- The perimeter of a circle is known as the circumference

 Image result for circle with radius and diameter  CIRCUMFERENCE =  π ×d

  Image result for circle with radius and diameter r = 7cm 

              d = 14cm

              c = π × d

                = π × 14

               =43. 9822

               = 44.0cm (1dp)                       

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General

1 cm = 10 mm

1m = 100cm

1 km = 1000m

1000m = 100000cm

12 inches = 1 ft

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Area of a circle

Area of circle = π r

EXAMPLE :

A = π×7

     = 153.93804

    = 153.9cm

remember if doing area to square the result and working!

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Averages

The mean:

add all numbers/ data together then divide by number of items

The median:

numbers are in oreder of size its the one in the middle

The mode:

mode is the one that occurs most often

The range:

diffference between largest value and the smallest value

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Averages

The mean:

add all numbers/ data together then divide by number of items

The median:

numbers are in oreder of size its the one in the middle

The mode:

mode is the one that occurs most often

The range:

diffference between largest value and the smallest value

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Bearings

- Bearings are used to give directions.

- 3 figures MUST be used.

- Always start from North and move in a clockwise direction.

- The word "from" indicates where to start the North line.

Image result for bearings maths

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Fractions, percentages and decimals

- To change a fraction into a decimal the numerator is divided by the denominator.

EXAMPLES:

1) 3/20 = 15/100                                      2) 1 2/5 = 1.4

            = 0.15                                                    

3) 1/4 = 0.25                                            4) 4/8 = 0.5

                                                            

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Converting between decimals, percentages and fract

- To convert a decimal to a fraction express it as a fraction out of 10, 100, 1000 etc and then cancel if possible.

EXAMPLES:

1)  0.24 = 24/100                                                 2) 0.6 = 6/10

            = 6/25                                                              = 3/5 

3) 0.375 = 375/1000 

             = 15/40

             = 3/8

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Percentages

- To change a fraction or a decimal to a percentage, multiply by 100

EXAMPLES - CONVERT TO PERCENTAGES: 

1) 0.47                              

    0.47 ×  100                     

            = 47%

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Rotation

- When rotating a shape you need to have the:

- angle of rotation 190° or 180°

- direction

- centre of rotation

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Expanding brackets

EXAMPLES:

1) 3 ( x - 2 ) + 4 ( 2x + 5 ) = 3x - 6 + 8x + 20       2) 2 ( 5x - 1 ) - 3 ( 2x - 6 ) = 10x -2 - 6x + 18

                                      = 11x + 14                                                        = 4x + 16

3) 3 ( x + 4 ) = 3x + 12                            4) 2 ( x + 1 ) + 3 ( x + 3 ) = 2x + 2 + 3x + 9

                                                                                                       = 5x + 11

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Solving equations

MAIN RULE :  DO THE SAME TO BOTH SIDES!

- you may add the same thing to both sides.

- you may subtract the same thing from both side.

- you may multiply both sides by the same thing.

- you may divide both sides by the same thing.    e.g.   1) n + 5 = 12                       2) 2n + 3 = 15    

                                                                                              5      -5                                - 3     - 3

                                                                                               n = 7                                   2n = 12

                                                                                                                                          ÷2   ÷2  

                                                                                                        n = 7

 

 

  

 

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Enlargements

- When a shape is enlarged each length is increased by the same quantity. E.g. if the scale factor is 3 each side is 3 times as long. 

ALWAYS WORK WITH VERTICAL AND HORIZONTAL MOVEMENTS!

Image result for enlargement maths

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Sequences

Finding the nth term:

EXAMPLES:

4n    4   8    12   16    20 

        5,  9,    13,   17,  21

     + 4       +4

nth term = 4n+ 1

find the 50th term = ( 4 × 50 ) + 1

                                        =   201 

                                        

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Pythagoras' theorem

- The area of the square on the hypotenuse is equal to the sum of the squares on the shortest to sides.

 Image result for pythagoras theorem             The longest side of the triangle is called the hypotenuse!

                                

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