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Proper, Improper and Mixed Fractions

Fractional Arithmetic

Changing the Subject of an Expression

Multiplying Expressions

Factorising Quadratic Expressions

Ex. 0:
5 x2 + -5 x + 6 = 0
=>
No real roots
(x -
5 + i √95
10
) (x -
5 - i √95
10
)
Ex. 1:
6 x2 + 2 x + 4 = 0
=>
No real roots
(x -
-2 + i √92
12
) (x -
-2 - i √92
12
)
Ex. 2:
9 x2 + 0 x + -2 = 0
=>
(x -
0 + √72
18
) (x -
0 - √72
18
)
Ex. 3:
-2 x2 + -4 x + -4 = 0
=>
No real roots
(x -
0
-4
) (x -
0
-4
)
Ex. 4:
-4 x2 + -4 x + 2 = 0
=>
(x -
4 + √48
-8
) (x -
4 - √48
-8
)
Ex. 5:
-8 x2 + 5 x + -1 = 0
=>
No real roots
(x -
-5 + i √7
-16
) (x -
-5 - i √7
-16
)
Ex. 6:
-7 x2 + -8 x + -3 = 0
=>
No real roots
(x -
8 + i √20
-14
) (x -
8 - i √20
-14
)
Ex. 7:
3 x2 + -8 x + 8 = 0
=>
No real roots
(x -
8 + i √32
6
) (x -
8 - i √32
6
)
Ex. 8:
1 x2 + -5 x + -8 = 0
=>
(x -
5 + √57
2
) (x -
5 - √57
2
)
Ex. 9:
7 x2 + 5 x + 4 = 0
=>
No real roots
(x -
-5 + i √87
14
) (x -
-5 - i √87
14
)

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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