Maths - Algebra 1, 2, 3, 4 & 5

Sequences, Functions, Expressions, Equations, Simultaneous equations, Square and Cube roots, Graphs, Powers, Brackets, Quadratic Expressions.

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Sequences

2, 5, 8, 11, 14, 17, 20, 23   9, 16, 23, 30, 37, 44, 51

nth term - 3n-1                   nth term - 7n+2

50th term - 149                   50th term - 352

Squares - 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 156, 196, 225

Is 225 in this sequence?

7n+2 = 225                             2, 5, 10, 17, 26, 37

 7n = 227                                nth term - n2+1

 n = 32.4    -   No, it isn't!         12th term - 145

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Brackets

Single Brackets -  3(2x-3) = 6x - 9

x(x+2) = x"+2x

3a(2a+4b-5c) = 6a"+12ab-15ac

Fractional Equations - x+2/5 = 3-x/4

x5 x+2    = 5(3-x)/4

                                x4 4(x+2)= 5(3-x)

4x+8  = 15-5x

9x+8  = 15

9x      = 7

x        = 7/9

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Simultaneous Equations 

3x-y = -10

   -   5x-y = -14

________________  Change the Subject in this from t to b 

       -2x = 4 t = a+b x

   x  = -2 t-a = b

________________ t-a/y = b

3x-2-y=-10 b= t-a/y

      -6-y=-10

    y=4

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Substitution of Simultaneous equations

5x-y = 31 Rules, 1. Re-arange easiest equation to y/x = subject

2x+y = 18    2. Substitute into other equation

y= 18-2x    3. Solve

5x - (18-2x) = 31

5x-18+2x = 31 y=18-(2 x 7)

     7x-18 = 31 y=4

          7x = 49

            x = 7

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Square roots and Squares

1;1 2; 4 3;9 4;16 5;25 6;36 7;49 8;63 9;81 10;100 11;121 12;144 13;156 14;196 15;225

Cube roots and Cubes

1;1 2;8 3;27 4;64 5;125 10;1000

2(3x+2)+3(x+1) 3(2y+1)-2(y-3)

=6x+4+3x+3 =6y+3-2y+6

=9x+7 =4y+9

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