Both at once
Rushing. Marking. Running. Meeting.
These are what engulfs my staff room now. Who says we are free after class. There are many things to be done. Typing and Marking, and picking out common mistakes for notes. All at once. That is what I call simultaneity.
Soon, the 'more thans' and the 'less thans' will be over. It is time we embark on a new journey with A Maths. The land of SiMUltaneous equations, Remainder theorem and Factor theorem (SMURF*).
Firstly, simultaneous equations will be solved. These involve more than 1 variable. Generally, the same number of equations as there are to variables is required to solve completely. (3 variables need 3 equations at least.) It can be both linear ones, or non-linear.
Secondly, algebraic EXPRESSIONS and POLYNOMIALS will be taught. They should be arranged in a specific descending / ascending order, like x² +2x +1 or 1+ 2x + x². x² terms should always add /subtract x² terms. Division of polynomials by other polynomials should always end in the form F(x) / P(x) = Q(x) with remainder R(x).
Also, F(x) = P(x)Q(x) + R(x). Note that the remainder R(x) should always be at least one degree less than P(x), the divisor. (If P(x) is x², R(x) can be bx, or c, but not ax²)
Thirdly, identities will be taught. Recall things like first law of algebra. This is an example of an identity.
Fourthly, Remainder Theorem. It states that when F(x) is divided by a linear divisor ax - b (a not 0), then the remainder is F(b/a). Together with this is the factor theorem, which just states that if F(b/a) = 0, (ax - b) is a factor, and vice versa.
Lastly, factorising cubic expressions. With all that we've learnt before, it is now time to use them.
Lots to teach. So little time! This will really be a tough topic.
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