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Proper, Improper and Mixed Fractions

Fractional Arithmetic

Changing the Subject of an Expression

Multiplying Expressions

Factorising Quadratic Expressions

Ex. 0:
8 x2 + 7 x + -6 = 0
=>
(x -
-7 + √241
16
) (x -
-7 - √241
16
)
Ex. 1:
5 x2 + 0 x + 9 = 0
=>
No real roots
(x -
0 + i √180
10
) (x -
0 - i √180
10
)
Ex. 2:
3 x2 + -6 x + -4 = 0
=>
(x -
6 + √84
6
) (x -
6 - √84
6
)
Ex. 3:
8 x2 + -1 x + -7 = 0
=>
(x -
1
1
) (x -
-7
8
)
Ex. 4:
-6 x2 + -5 x + 8 = 0
=>
(x -
5 + √217
-12
) (x -
5 - √217
-12
)
Ex. 5:
4 x2 + 2 x + -8 = 0
=>
(x -
-2 + √132
8
) (x -
-2 - √132
8
)
Ex. 6:
-7 x2 + 2 x + 1 = 0
=>
(x -
-2 + √32
-14
) (x -
-2 - √32
-14
)
Ex. 7:
9 x2 + -3 x + -6 = 0
=>
(x -
1
1
) (x -
-2
3
)
Ex. 8:
6 x2 + -2 x + -8 = 0
=>
(x -
4
3
) (x -
-1
1
)
Ex. 9:
1 x2 + 7 x + -5 = 0
=>
(x -
-7 + √69
2
) (x -
-7 - √69
2
)

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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