Algebra wrap-up

We looked at algebra today, specifically at question 3 and 4 on this paper.

Q3
Part a: remember the laws of indices, but check your result on your calculator.
Part b: the first two are straightforward factoring questions. Part iii can be solved by multiplying it out or by observing that it is something (2x-1) squared minus something else (x-1) squared and so can be treated as one big difference of 2 squares.
Part c: find an expression for one gram of powder, then for one gram of powder during the promotion. Then set up an equation which states that the difference between these is = 1.
Q4
Part c: note the key difference between an expression and an equation. To write both expressions as a single fraction, take each fraction and multiply above and below the line by the same thing, in such a way that you get a common denominator in the two fractions. Once you get to part ii you have an equation, so you can now multiply both sides of the equation by the denominator of the LHS to get rid of all the fractions. The a±√b format tells you you'll need to use the quadratic formula to find the roots of the equation - don't waste time looking for factors.


Key points from today:

• An expression squared, like (2x-1)² is (2x-1) multiplied by itself i.e. (2x-1)(2x-1).
• A quick way to do this is to square the first term, square the second term and twice their product. If in doubt, do it out the long way.
• x is an element of Q gives you a hint that the result is going to be a fraction (rational number)

Tomorrow we'll do Trigonometry. It is 2005 Paper 2 Q 5 for homework this evening.