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Proper, Improper and Mixed Fractions

Fractional Arithmetic

Changing the Subject of an Expression

Multiplying Expressions

Factorising Quadratic Expressions

Ex. 0:
-6 x2 + -6 x + -7 = 0
=>
No real roots
(x -
6 + i √132
-12
) (x -
6 - i √132
-12
)
Ex. 1:
-3 x2 + 3 x + 0 = 0
=>
(x -
0
-6
) (x -
-1
-1
)
Ex. 2:
1 x2 + 6 x + -8 = 0
=>
(x -
-6 + √68
2
) (x -
-6 - √68
2
)
Ex. 3:
-3 x2 + 7 x + -6 = 0
=>
No real roots
(x -
-7 + i √23
-6
) (x -
-7 - i √23
-6
)
Ex. 4:
-6 x2 + 9 x + 6 = 0
=>
(x -
1
-2
) (x -
-2
-1
)
Ex. 5:
5 x2 + 3 x + -4 = 0
=>
(x -
-3 + √89
10
) (x -
-3 - √89
10
)
Ex. 6:
2 x2 + 8 x + -2 = 0
=>
(x -
-8 + √80
4
) (x -
-8 - √80
4
)
Ex. 7:
-6 x2 + 9 x + 0 = 0
=>
(x -
0
-12
) (x -
-3
-2
)
Ex. 8:
-4 x2 + -2 x + -9 = 0
=>
No real roots
(x -
2 + i √140
-8
) (x -
2 - i √140
-8
)
Ex. 9:
-4 x2 + 1 x + 4 = 0
=>
(x -
-1 + √65
-8
) (x -
-1 - √65
-8
)

Solving Linear Equations

Rationalising the Denominator

Solving Simultaneous (Linear) Equations

Solving Simultaneous Quadratic Equations

2 and 3 Part Ratios

Completing the Square

Sequences and Series

Polynomial Long Division

Factor and Remainder Theorem

Roots of a cubic

Differentials

Finding Turning Points

Pythagorus

Sine and Cosine Rules

Vectors

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