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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 + -5 x + -8 = 0
=>
(x -
8
3
) (x -
-1
1
)
Ex. 1:
2 x2 + -5 x + -9 = 0
=>
(x -
5 + √97
4
) (x -
5 - √97
4
)
Ex. 2:
9 x2 + 7 x + 3 = 0
=>
No real roots
(x -
-7 + i √59
18
) (x -
-7 - i √59
18
)
Ex. 3:
1 x2 + 9 x + -1 = 0
=>
(x -
-9 + √85
2
) (x -
-9 - √85
2
)
Ex. 4:
-5 x2 + -1 x + -1 = 0
=>
No real roots
(x -
1 + i √19
-10
) (x -
1 - i √19
-10
)
Ex. 5:
-2 x2 + 4 x + 7 = 0
=>
(x -
-4 + √72
-4
) (x -
-4 - √72
-4
)
Ex. 6:
-5 x2 + 6 x + -6 = 0
=>
No real roots
(x -
-6 + i √84
-10
) (x -
-6 - i √84
-10
)
Ex. 7:
7 x2 + 9 x + 2 = 0
=>
(x -
-2
7
) (x -
-1
1
)
Ex. 8:
-4 x2 + -3 x + 0 = 0
=>
(x -
3
-4
) (x -
0
-8
)
Ex. 9:
7 x2 + 3 x + 7 = 0
=>
No real roots
(x -
-3 + i √187
14
) (x -
-3 - i √187
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