CHAPTER 1- ALGEBRA AND FUNCTIONS
1. Simplifying fractions by division:
When dividing an algebraic fraction including x's, you take the powers away depending on what you divide by.
When simplifying fractions by factorisation, you get rid of similar expressions on the top and bottom.
2. Dividing polynomials:
3. Factorising polynomials using the factor theorem: e.g. show that (x-2) is a factor of x³+x²-4x-4 by the factor theorem:
f(2)=(2) ³+(2)²-4(2)-4=0 therefore (x-2) is a factor of x³+x²-4x-4.4.
4. Using the remainder theorem to find the remainder when dividing polynomials: just use normal division of polynomials as shown above.
CHAPTER 2-SINE AND COSINE RULE
1. Use the sine rule to find a missing side:
When you know two angles and one of the opposite sides.
2. Use the sine rule to find a missing angle:
When you know two sides and one of their opposite angles.
Note that sometimes you can have two solutions for a missing angle, because when the angle you are finding is larger than the given angle, there are two possible results. This is because you can draw two possible triangles with the data.
3. Use the cosine rule to find a missing side:
You can use the cosine rule to find an unknown side in a triangle when you know the lengths of two sides and the angle between the sides. The cosine rule is: