UNIT 12 Arithmetic: Revision Activities

Transcription

1 UNIT Arithmetic: Revision Activities Activities. Secret Sums. Number Puzzle.3 arts. Postcodes Notes and Solutions ( pages)

2 ATIVITY. Secret Sums opy these calculations and fill in the missing digits, marked by the asterisks ( )

3 ATIVITY. Number Puzzle ach of the letters A, B,,,, and G stands for one of the digits,, 3,,, and. In the grid below you are given the totals for each row and column: A A B A B 0 G 3 3. educe the value of from the th horizontal line.. What possibilities are there for and from this line? 3. Test out these possiblities for and in the other four horizontal equations.. heck your answers in the vertical equations.

4 ATIVITY.3 arts Scores in this ring are doubled Scores in this ring are trebled 0 3 The diagram shows a dartboard. Work through the questions below, which relate to the game of darts.. With just one dart it is possible to score 0 (with a 'bull's-eye' at the centre of the board) or 0 (with a treble 0). What other scores between 0 and 0 are possible with just one dart?. With only one dart, what is the smallest number (greater than 0) that it is impossible to obtain? 3. With 3 darts, and assuming that every dart scores, (a) what is the highest score possible, (b) what is the lowest score possible?. Using exactly 3 darts, what is the lowest score (greater than 0) that it is impossible to obtain?. In how many different ways is it possible to score using one, two or three darts?. There are 0 sectors on the board. Any adjacent sectors make one quarter of the board. Which quarter of the board gives the highest total when the numbers around its outside edge are added up?. With 3 darts you can score 0 ( ) and 0 ( ). There are eight other scores between 0 and 0 which you can obtain with 3 darts. ind as many as possible, saying how they are obtained.. Suppose only darts are allowed, but that the scores of each dart are multiplied together to make the total score. ind all the totals up to 0 that are not possible to obtain.

5 ATIVITY. Postcodes Since 0, when the 'Penny Post' was introduced by Rowland Hill, there have been many changes in the postal service and, particularly in recent years, many technological advances. Much of the post is now sorted automatically. Of particular importance has been the introduction of postcodes, which were started in and now cover the whole of the UK. This alpha-numeric system, made up of between and numbers and letters, was designed to divide the whole country efficiently and effectively into ARAS ISTRITS STORS UNITS and was decided upon partly because people can remember a combination of numbers and letters more easily than, for example, just numbers. o you think this is true? Here is a typical postcode: ARA X Any letters ISTRIT 3 Any digits 0 to STOR Any digit to UNIT P Any letters. (a) What is the maximum number of ARAS possible using postcodes of this form? (b) or each area, how many ISTRITS could there be? (c) or each district, how many STORS are possible? (d) or each sector, how many UNITS are possible?. (a) Using your answers to question, how many UNITS could there be in the whole country? (b) There are about million household and business addresses in the UK. ould each one have a unique postcode? In fact, the Post Office uses 0 areas 00 districts 000 sectors units 3. (a) On average, how many districts per area are used? (b) How many sectors per district are used? (c) How many units per sector are used? (d) How many households/business addresses are there per unit?. Why do you think the Post Office does not identify each address with a unique postcode? xtension Obtain your local postcodes from your nearest main Post Office. Illustrate the districts, sectors and units on a local map.

6 ATIVITIS. -.3 Notes and Solutions Notes and solutions are given only where appropriate =. ither = and = or = and = 3. A = 3, B =, =, =, =, =, G =.3.,, (a) 0 (b) We think that there are ways (we are counting, for example,,, and,, as different ways) =. You can obtain : 0,, 0 : 0,, or 0, 0, : 0,, 0 : 0,, : 0, 0, : 0,, or 0, 0, or 0,, : 0,, or 0, 0, : 0,, or 0, 0, : 0, 0,. It is not possible to score 3,, 3, 3,, 3,,

7 ATIVITY. Notes and Solutions.. (a) = or = 0 (b) (c) ( if repeating letters are excluded) to possible districts sectors are possible ( to, excluding zero) (d) = units, (or 0 if repeating letters are excluded). (a) Total possible number of units = million (b) Yes, it would certainly be possible with a postcode system of the type now used, to identify each individual household and business address. 3. (a) (b) (c) (d) districts per area (up to are available) 30. sectors per district There are about 0 units per sector = addresses per unit.. The present sorting system is not yet sophisticated enough to cope.