More Revision

MORE REVISION 20040201


This sheet should be done entirely without calculators. The idea is to help you remember some conversions, remember some rules and to apply some skills.


1  The number of grammes in a pound is  ____________

2  A mile is  _____________________ metres to 4 sig. fig.(no, not seven)

3  There are __________ litres in a gallon   (probably 3 sig.fig.)

4  An acre, __________ sq yds, is a   c__________ by a    f_______________

5   (-23) ²    = ___________            24 ²    = ______            -(25) ²    = ___________

6  26 ²  - 24 ²   =  50 x ____  = _____                             29 ²  - 21 ²    =  8 x  ______  =

7  The difference of two squares is ……………………     times ………………………

( x ²  -  y ²)    =           (                    )  (                   )

So, without knowing or needing either square, we can work out

8  56²  -  44²  =

9  76²  -  24²    =

10  144²  -  56²  =

and when we do know some squares (up to 30 squared and all ending in 5), then the rule works in reverse, so we can do

11     (29 + 7) (29 - 7)=

12      106  x  94         =

13      88  x  72             =


If you have any time left: treat this as a logical problem, or recognise matrix methods, or both:

14 TRY to fill in the gaps here: 12 x  +   7 y    =   19     so  ( 12     7 )( x )  = (   19)

  3 x  +   2 y   =   -17           (              )( y )     ( )


PREMULTIPLY both   (  2    -7  ) (  12    7 )( x )  =(  2          )  (   19)

sides by the same thing (               ) (  3         )( y ) (              )  (      )


Do matrix multiplication           (           0 ) ( x )  = ()   =   (            )

(I’ve given you enough)           (  0          ) ( y )   ( )        (            )


DIVIDE both sides by                                  ( x )  = (                      )    a pair of

the three                                       ( y )   (                      )   fractions

© David Scoins 2017