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Proper, Improper and Mixed Fractions

Fractional Arithmetic

Changing the Subject of an Expression

Multiplying Expressions

Factorising Quadratic Expressions

Solving Linear Equations

Rationalising the Denominator

Solving Simultaneous (Linear) Equations

Solving Simultaneous Quadratic Equations

2 and 3 Part Ratios

Completing the Square

Ex. 0:
-7 x2 + 6 x + -10 =>
-7 (x
+
3
-7
)2
+
61
-7
Ex. 1:
16 x2 + -4 x + 2 =>
16 (x
+
-1
8
)2
+
7
4
Ex. 2:
9 x2 + 6 x + 17 =>
9 (x
+
1
3
)2
+
16
1
Ex. 3:
-1 x2 + -18 x + 7 =>
-1 (x
+
-9
-1
)2
+
-88
-1
Ex. 4:
18 x2 + 16 x + 3 =>
18 (x
+
4
9
)2
+
-5
9
Ex. 5:
-17 x2 + 6 x + -19 =>
-17 (x
+
3
-17
)2
+
314
-17
Ex. 6:
19 x2 + 1 x + -15 =>
19 (x
+
1
38
)2
+
-1141
76
Ex. 7:
-15 x2 + -17 x + -3 =>
-15 (x
+
-17
-30
)2
+
-109
-60
Ex. 8:
9 x2 + -14 x + -14 =>
9 (x
+
-7
9
)2
+
-175
9
Ex. 9:
-1 x2 + 12 x + 7 =>
-1 (x
+
6
-1
)2
+
-43
-1

Sequences and Series

Polynomial Long Division

Factor and Remainder Theorem

Roots of a cubic

Differentials

Finding Turning Points

Pythagorus

Sine and Cosine Rules

Vectors