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Proper, Improper and Mixed Fractions

Fractional Arithmetic

Changing the Subject of an Expression

Multiplying Expressions

Factorising Quadratic Expressions

Ex. 0:
-3 x2 + 3 x + 0 = 0
=>
(x -
0
-6
) (x -
-1
-1
)
Ex. 1:
8 x2 + -8 x + 2 = 0
=>
(x +
8
16
)2
Ex. 2:
9 x2 + -9 x + 5 = 0
=>
No real roots
(x -
9 + i √99
18
) (x -
9 - i √99
18
)
Ex. 3:
-2 x2 + -9 x + 8 = 0
=>
(x -
9 + √145
-4
) (x -
9 - √145
-4
)
Ex. 4:
2 x2 + -3 x + 4 = 0
=>
No real roots
(x -
3 + i √23
4
) (x -
3 - i √23
4
)
Ex. 5:
4 x2 + 3 x + 0 = 0
=>
(x -
0
8
) (x -
-3
4
)
Ex. 6:
3 x2 + 0 x + 6 = 0
=>
No real roots
(x -
0 + i √72
6
) (x -
0 - i √72
6
)
Ex. 7:
1 x2 + -4 x + -9 = 0
=>
(x -
4 + √52
2
) (x -
4 - √52
2
)
Ex. 8:
-9 x2 + -6 x + -4 = 0
=>
No real roots
(x -
6 + i √108
-18
) (x -
6 - i √108
-18
)
Ex. 9:
-7 x2 + -9 x + -4 = 0
=>
No real roots
(x -
9 + i √31
-14
) (x -
9 - i √31
-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