1 Mathematical Diagrams MEP Y8 Practice Book A

1 MEP Y8 Practice book A. 1 mathematical diagrams Mileage Charts In this section we look at mileage charts. Example 1. Distances in the table below are given in miles. E. PL. A. ST. RN. BA. L. TO. IS. 100. BR. ER. ET. CE. 55 84. EX. N. ZA. N. TH. PE. 108 194 110 U. O. M. N. Y. 67 125 44 77. PL. TO. N. U. TA. 50 51 34 144 75. Using the table, answer the following questions: (a) How far is it from Taunton to Exeter? (b) Jerry travels from Barnstaple to Exeter, then from Exeter to Plymouth, and finally from Plymouth back to Barnstaple. How far does he travel altogether? Solution (a) 34 miles (see table and diagram opposite).

2 ER. ET. EX. (b) Barnstaple to Exeter: 55 miles Exeter to Plymouth: 44 miles Plymouth to Barnstaple: 67 miles N. TO. N. Total distance = 55 + 44 + 67. U. TA. 34. = 166 miles 1. MEP Y8 Practice book A. Example 2 10. Devizes The network diagram opposite shows Upavon the distances, in miles, between some towns. 9. 14. Copy and complete the following 6. Shrewton Amesbury mileage chart to show the shortest distances between these 11 8. towns: RY Salisbury BU. ES. M. ES. A. IZ. RY. EV. U. D. SB. N. LI. TO. SA. W. RE. SH. N. O. V. PA. U. Solution RY. The direct distances can be completed first: BU.

3 ES. M. the shortest route from Amesbury to Devizes ES. A. IZ. is via Upavon, a total of 19 miles;. RY. EV. U. D. the shortest route from Devizes to Salisbury SB. N. LI. is via Shrewton, a total of 25 miles; 8. TO. SA. W. RE. the shortest route from Salisbury to Upavon SH. 6 14 11. is via Amesbury, a total of 17 miles;. N. O. V. PA. the shortest route from Shrewton to Upavon 9 10. U. is via Amesbury, a total of 15 miles. RY. BU. ES. M. ES. A. IZ. With this information, the table can now be RY. EV. 19. completed, as shown opposite. U. D. SB. N. LI. 8 25. TO. SA. W. RE.

4 SH. 6 14 11. N. O. V. PA. 9 10 17 15. U. 2. MEP Y8 Practice book A. Exercises 1. Use the table opposite, where the LL. U. distances are given in miles, to H. S. find out how far it is from: ED. 60. LE. LN. R. (a) Leeds to Lincoln, CO. TE. ES. N. 47 72. LI. (b) Hull to York, CH. N. A. (c) Leeds to Manchester, LD. 97 44 85. M. E. FI. (d) Sheffield to Leeds, EF. 66 36 47 39. SH. (e) Manchester to York. RK. O. Y. 38 24 80 71 57. 2. Ross travels from Leeds to Manchester, then from Manchester to Sheffield and finally from Sheffield back to Leeds. Use the table in question 1 to calculate the total distance he travels.

5 3. Hannah drives from Bristol to Exeter, continues to Plymouth, on to Barnstaple and from there back to Bristol. Use the table in Example 1 to calculate the total distance she drives. N. O. N. LE. A. 4. The table opposite gives the IS. LA. distances in kilometres 365. CA. S. N. between some towns in A. M. northern France. 49 419. S. LE. N. EA. What is the distance between: RL. 167 433 138. O. (a) Alen on and Paris, S. RI. PA. (b) Reims and Orleans, 220 293 204 135. S. IM. (c) Rouen and Calais, 355 278 340 270 146. RE. EN. (d) Paris and Reims, U. RO. 146 215 199 210 140 284.

6 (e) Le Mans and Rouen? 5. Debbie drives from Calais to Paris and back while she is on holiday. Use the table in question 4 to calculate how far she travels altogether on this journey. 6. Laura travels from Calais to Paris, on to Alen on and then to Rouen before returning to Paris. Use the table in question 4 to calculate how far she travels altogether. 3. MEP Y8 Practice book A. 7. The diagram below shows the distances, in miles, between some junctions on the M2 motorway: 1 4 4 4 10 2. Jn 1 Jn 2 Jn 3 Jn 4 Jn 5 Jn 6 Jn 7. Copy and complete the chart below to show the shortest distances between junctions: 1.

7 N. IO. CT. 2. N. JU. N. IO. CT. 3. N. N. JU. IO. CT. 4. N. N. JU. O. I. CT. 5. N. N. JU. IO. CT. N. 6. JU. N. IO. CT. 7. N. N. IO. JU. CT. N. JU. 8. The following network diagram shows the distances, in miles, between some towns in Wales: Lampeter 16. 23. Llandovery 4. 7. 15 Llanwrda Carmarthen Llandeilo Use the information in the diagram to complete a copy of the table on the next page, giving the shortest distances between the towns. 4. MEP Y8 Practice book A. EN. H. RT. A. RM. R. CA. TE. PE. LO. M. LA. EI. Y. D. ER. N. A. V. LL. O. D. N. A. A. RD. LL. W. N. A. LL.

8 9. The network diagram below shows the distances, in miles, by road between some towns close to the Scottish border: Longtown 4. Gretna 9. 9. Carlisle 8. Brampton 19. 19. Alston 20. Penrith N. TO. LS. N. O. A. PT. M. A. LE. BR. IS. Use information from the diagram RL. CA. to complete a copy of the table A. TN. opposite, giving the shortest N. RE. W. TO. distances between the towns. G. G. N. LO. TH. RI. N. PE. 5. MEP Y8 Practice book A. 10. The diagram below shows stations on the GNER railway: LONDON STEVENAGE PETERBOROUGH DONCASTER YORK. N. O. D. Some distances, in miles, are shown E.

9 N. G. H. LO. A. in the table opposite. G. EN. U. RO. V. 21. E. (a) Copy the table and fill in ST. BO. ER. the missing distances. ER. T. 68 47. ST. PE. (b) What distance is travelled CA. N. in a return journey between O. 188 167 120. D. London and York? RK. 45. O. Y. Using Flow Charts to Plan Practical Tasks A flow chart can be used to organise the instructions for carrying out a task. Boxes of different shapes are used for particular operations: START or END POINTS START END. INSTRUCTION BOXES. NO. DECISION BOXES. YES. Each box contains only one instruction. 6. MEP Y8 Practice book A.

10 Example 1. Draw a flow chart to give the instructions for making a mug of tea. Solution START. FILL. KETTLE. BOIL The flow chart gives the instructions for making KETTLE a mug of tea without sugar. PUT TEA BAG A mug of tea with sugar, needs this IN MUG extra instruction box: ADD SUGAR. POUR BOILING. WATER INTO. MUG. PUT TEA BAG. Note that the instruction box IN MUG can go TAKE OUT. TEA BAG. earlier in the flow chart, for example, immediately after the START box. The extra box ADD MILK. ADD SUGAR can also go in various positions: for PUT TEA BAG. example, before or after the IN MUG box, or STIR TEA.