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Proper, Improper and Mixed Fractions

Fractional Arithmetic

Changing the Subject of an Expression

Multiplying Expressions

Factorising Quadratic Expressions

Ex. 0:
-4 x2 + 3 x + -1 = 0
=>
No real roots
(x -
-3 + i √7
-8
) (x -
-3 - i √7
-8
)
Ex. 1:
-2 x2 + -2 x + -9 = 0
=>
No real roots
(x -
2 + i √68
-4
) (x -
2 - i √68
-4
)
Ex. 2:
8 x2 + -7 x + -6 = 0
=>
(x -
7 + √241
16
) (x -
7 - √241
16
)
Ex. 3:
8 x2 + 1 x + 0 = 0
=>
(x -
0
16
) (x -
-1
8
)
Ex. 4:
-7 x2 + 7 x + 9 = 0
=>
(x -
-7 + √301
-14
) (x -
-7 - √301
-14
)
Ex. 5:
5 x2 + 8 x + 6 = 0
=>
No real roots
(x -
-8 + i √56
10
) (x -
-8 - i √56
10
)
Ex. 6:
-4 x2 + -5 x + 5 = 0
=>
(x -
5 + √105
-8
) (x -
5 - √105
-8
)
Ex. 7:
1 x2 + 3 x + 4 = 0
=>
No real roots
(x -
-3 + i √7
2
) (x -
-3 - i √7
2
)
Ex. 8:
7 x2 + 1 x + 7 = 0
=>
No real roots
(x -
-1 + i √195
14
) (x -
-1 - i √195
14
)
Ex. 9:
9 x2 + 7 x + 2 = 0
=>
No real roots
(x -
-7 + i √23
18
) (x -
-7 - i √23
18
)

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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