Algebra & Numeracy 2

ALGEBRA AND NUMERACY 20040307


An answer to one question may well help in another. You are presumed able to think. And to work without a calculator. Working and answers in your exercise book for this one, please.


1  Find two answers to       (x + 3)²  - 9  =  16

2  If $1.60 = £1 and €1 = 71p what is $100 in €uros?

3  If x² – 5x + 6  is odd, is x odd or even? Any idea why?

4  If 3 < 2x - 5 ≤ 17  then what values might x have?.

5  Sketch y = 2x – 5 with –5 ≤ y ≤ 20 and on the same pair of axes, draw y = 3, y = 17 and y + 2x = 17 Mark all six intercepts and the intersection of the two sloping lines.


6a) How do you tell if a number is divisible by three?  Is 2047?

b) The four digit number 20x8 is divisible by 3 exactly. Find values for x.

c) Can you find a x so that 20x8 is divisible by nine?

d) Is 2e + 3e + e divisible by 3, even if e = √5 ??

e) If the three digit number pqr is divisible by 9, is √pqr divisible by 3? Evidence?

f) A 3 digit number is divisible by 3 5 and 7. Find several answers, and

g) find the one closest to being a perfect square (an integer squared)


Homework should be 30 minutes of effective work, which is not the same as sitting with this page for half an hour. There are two consequences to this: if you have spent the time struggling (probably not so with this sheet)  then write me a note so to tell me you have struggled (but that should be visible on the page already). The other consequence is that I make a judgement about how much you can do; if this is particularly small (or particularly large), you affect my opinion of your abilities – which is what I write about in reports and is the basis for judgements on your ability and effort. Difficult, isn’t it?

I want you to do 30 minutes effective work. However, if you pass 30 minutes significantly, it would help to know where the 30 minutes was up (draw a line, write a note in the work). Working much further than the 30 minutes is your choice, not my demand; it would be sensible, anyway, to stop working on maths at the half-hour and do other homework. By all means come back to it because you’re interested, but don’t put us both in a position where other work isn’t being done because you’re interested, obligated or just plain obstinate. Don’t be frightened to ask!

© David Scoins 2017