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Proper, Improper and Mixed Fractions

Fractional Arithmetic

Changing the Subject of an Expression

Multiplying Expressions

Factorising Quadratic Expressions

Ex. 0:
6 x2 + -4 x + -2 = 0
=>
(x -
1
1
) (x -
-1
3
)
Ex. 1:
-5 x2 + 7 x + 1 = 0
=>
(x -
-7 + √69
-10
) (x -
-7 - √69
-10
)
Ex. 2:
-5 x2 + 2 x + 6 = 0
=>
(x -
-2 + √124
-10
) (x -
-2 - √124
-10
)
Ex. 3:
9 x2 + -1 x + -1 = 0
=>
(x -
1 + √37
18
) (x -
1 - √37
18
)
Ex. 4:
-7 x2 + -9 x + 8 = 0
=>
(x -
9 + √305
-14
) (x -
9 - √305
-14
)
Ex. 5:
5 x2 + -1 x + 5 = 0
=>
No real roots
(x -
1 + i √99
10
) (x -
1 - i √99
10
)
Ex. 6:
3 x2 + -1 x + -3 = 0
=>
(x -
1 + √37
6
) (x -
1 - √37
6
)
Ex. 7:
9 x2 + 3 x + 0 = 0
=>
(x -
0
18
) (x -
-1
3
)
Ex. 8:
-5 x2 + 9 x + -2 = 0
=>
(x -
-9 + √41
-10
) (x -
-9 - √41
-10
)
Ex. 9:
9 x2 + -2 x + -5 = 0
=>
(x -
2 + √184
18
) (x -
2 - √184
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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