UNIT+3+Chapter+2+Bounds

__**Bounds**__

Main aim of this chapter - to understand the meaning of an upper and lower bound, know how to find them AND be able to manipulate them in complex calculations.

__**Wednesday 27th June**__

(i) we decided that the LOWER BOUND is the smallest number that a given variable can take (given a value and how it has been rounded) and that the UPPER BOUND is the smallest number (greater than the given value!) that it CAN'T be !! (there are all sorts of issues with whether the upper bound can or cannot be actually taken by the variable - if we try to have this distinction - the lower bound is attainable but the upper bound in unattainable - we should be OK)

Generally the value given is BANG in the middle of the interval formed by the upper and lower bounds...

eg 73 (nearest whole number)

LB is 72.5, UB is 73.5

However, if we are rounding to a given number of significant figures around a power of 10 it is a little harder...

eg 100 (1sf)

LB is 95, UB is 150

(ii) we then started looking at doing CALCULATIONS WITH BOUNDS

eg a rectangle measures 8cm by 13 cm (each measurement correct to the nearest cm).

What are the lower and upper bounds for the AREA of the rectangle?

We MUST start by working out the upper and lower bounds for each measurement - then combine them appropriately...

8cm: LB = 7.5cm, UB = 8.5cm 13cm: LB = 12.5cm, UB = 13.5cm

LOWER BOUND for area = 7.5 x 12.5 = 93.75 cm 2 UPPER BOUND for area = 8.5 x 13.5 = 114.75 cm 2

NO HOMEWORK SET TONIGHT!!

__**Monday 2nd July**__

Today we started looking at which bounds to use for different sorts of calculations. They key here is to use the right bounds:

Addition: Upper Bound UB + UB, Lower Bound LB + LB Subtraction: Upper Bound UB - LB, Lower Bound LB - UB Multiplication:Upper Bound UB x UB, Lower Bound LB x LB Division:Upper Bound UB ÷ LB, Lower Bound LB ÷ UB

It is important that you understand WHY we have to use these bounds - think about what's actually going on when you do subtraction and division.....

So long as you write out the LB and UB for the values you're given (be careful!) and show your working carefully you should be absolutely fine!

Homework set today (copy available on school website: **Module 3, Chpts 1 and 2 Number and Bounds** DUE IN NEXT MONDAY PLEASE!!

We started with a few exam questions about Bounds - so long as we write down the bounds we're using and make our working clear (using WORDS and NUMBERS!!!) we should be fine.
 * __Tuesday 3rd July__**

Next topic...Percentages (started today)

Reminder - homework sheet due in next Monday!