3 NumeBer 1 q 1 identity and use natural numbers, integers, ame numbers, common factors and common a ‘multiples, rational and rational numbers 7 Use the four rule for calculations wth whole numbers and decimal fractions {8 Give approximations to specified numbers of significant figures and decimal places 40 Demonstrate an understanding of ratio, direct and inverse proportion; ide a quantity in & ‘Given ratio; use sales in practical situation; calculate average speed 14. Calculate @ given percentage of quantity; exoress one quantiy 2s a percentage of another, calculate percentage increase or decrease ee Be ea es say ane coer from ni carrency 0 arcther a 16 Salve problems involving simple interest and compound interest . 3.1 Place value ‘Whole numbers are made up from units, tens, hundred, thousands and so on. . tsi oa : In the number 3264: : In the words we write ‘three thousand, two hundred and sixty-four’, 3 Exercise 1 eee ~ 5 Le ase BE as ’ 5. GOO8 6, 26104 7. $250000 ‘8. 826111 : In Questions 9 to 16 write down the number which goes in each box Dr9043 10, 74 500 +[ +4 11, s16=s00+[_]+6 ’ 9. 2912.99 -[ J+ 9049 [+2004 1047 145065 ~ 5000 +[“]1-s © 1g, 63410 = 6000+ 3000 +[]+-10 56 75678 =] + se + 00 4 J8 #7. Write these numbers in figures {@) Seven hundred and tweaty (6) Five thousand, two hundred and six {@ Sixteen thousand, four hundred and thiny (@) alta milion {o) Thwee hundred thousand and ninety (Fight and a haf thousand, 18, Here are four number cards ®8@ & & (2) Use all the cards 19 make the largest possible number. (b) Use all the cards to make the smallest possible number 18, Write these numbers in words: (@) 4020 (6) 607 (© 25400 {) 6800000 fe) 21425 20, Here are five numbers cand BGIBED (a) Use all the cards to make the largest possible odd number (6) Use all the cards to make the smallest possible even number. 21. Write down the number that is ten more than: (a) 247 (321 (e) 604 2. Write down the number that is one thousand more then: (a) 392 (b) 25611 (@) 256900 She nll the number by 1, SOU, Fill in one other digit which you know must now be the caleuator () Prini starts again with the same 2-igit number and this time she mllplies it by 1000, Fil nal ive digits on the caleulator this time.24, Write these numbers i order, rom the smallest to the largest: @) 2142, 2290, 2088, 2136 () 5329, 5029, 5299, $330 (© 25117, 25200, 25171, 25000, 25500 25, Find a number m so that Sn+7 sor. B Find a number x so that 6x-+ 8 = 68 Find a pair of numbers @ and for which 8a + 07, 2. Find a pair of numbers p and q for which 7p + Sq = 7050. 3.2 Arithmetic without a calculator Here are examples to remind you of non-ealeulator method's @) 427 (274 (9 51 100 = 5700 +5186 ~ 535 [ad two zeros Tite @ 374 138r4 or 138 x6 ora a Exercise 2 — Work out, without a caleulator 1. 653.4 2844 2. 2106 +329 3. 64+ 2144 507 5, 387-175 6. 527-486 7.90768 27 10 10. 5 1000 M735 13, 3168 14, 9224 «7 15. M034 17. 39555 18, 26008 19, 36457 21, 28941541714 22 97OH—5135, 23, 6001 — 5994 25, 2906-1414 26, 471659 27. 25x58 29.74 1609-425 30, 289-414-7831, 7 4295-48 Speed tests “These questions can be done et fe wath books open, or fread out by the teacher with books closed. In either ease write down the answer onfy. Be as quick as posible 4. 65981 +2580 8, 1024816 wads 16, 1944+ 6Test 1 Test 2 Tet 3 Test 4 130-8 1.6416 Lise? nas 236-18 9x6 3 0329 aes 0 45607 psx? 598445 5.4952 8x4 1 600-12 16-7 650438 6 3436 @ “n9x4 14529 1.665511 Lsi-n a7 8 13100 & 105~70 83633 9.55455 9. 99-499 9.14 9.20% 5 o-18 10.6717 10. 220-30 10, 99 +55 U1, 57010 11, 100 520 11,200 145 2927 RIK3 122x242 In a8+8 43.9417 13, 55-6 Boe 13,50 100 1450-59 19418 14, 200-5 14, 199-26 15.9 100 15.0 15.162 15, $017 Fe vot inverse means ‘oposite’ © 6 Theinverse of adding is subtracting: $4419 Bs The inverse ofaubirting isang: 316 '¢ The inverse of muliplying is dividing: 7 ‘© The inverse of dividing is multiplying. 30.53 ‘Work out 14 x 6 because multiplying isthe inverse of dividing Since L4 x 6 —84, the missing digit is 8 Work out 1340+ 5 because dividing isthe inverse of mulipying Since L340 % $= 266, the missing digi is 6 Start from the right: 7.42 =9 Midele column: 8-+5=13, 387 4252 wvExercise 3 — Find the missing digit. 8, Thete is more than one correct answer foreach ofthese questions Ask a friend to check your solutions a =25 ff): O-«meach calculation the same number is missing from all the boxes. Find the missing number in each case. oL-O-O-2 Pol-O+O-9 of O+-2 10. In the cicle write +, —, x of + to make the calculation correct. 7403 I. Write the following with the correct signs @ 5433-0 (sH4Q3Q2=4 Notice that $3.62 ‘When writing decimals in order of sie its helpfil to write them with the same number of figures after the decimal point Example Write these three numbers in order: 0:08, 6107, 041 0.08—0080 - 0.107—0.107 : 010.100 Now we can sce thatthe correct order from lowest to highest i. 0-08, 0-1, 0-107.76 Number Exercise 4 Tn Questions 1 to 8 write down each statement a true (T) of false (F), nd decide whether its 1, 03 i ess than 031 2. 0-82 is more than 0825, 3. 07 is equal to 070 4. O47 is less than 071 5, 0002s more than 0.002, 6. 0.65 Fess than 0-06 7. 0-1 is equal to 8, Sis equal 10 5.00, 9. The number 43.6 can be writen 40-43 + Write the number 72 in this way. 10. Write the decimal numbers for these additions (a) 2004304544 (0) 60474 ©) 9484+ 3+} {In Questions 11 t0 18 arrange the numbers in onder of size, smallest fs 1, 041,031, 02 12, 0.75, 0538, 072 13, 043, 0432, 041 14. 0-609, 0461, 06 15, 0.04, 015,02, 038 16, 18, 018,081, 118 17, 07, 0061, 0.07, 041 18, 02, 0025, 003, 0.009 19, Here are numt swith eters Pt the numbers in order ad then srt don the letters to make B @ 20, Increase these numbers by (a) 3241 () 0755, (106 21, Increase these numbers by Ga) 5.68 05 © 129 22, Write the following amounts in dollars: (2) 350 cents () IS cents (6) Seents (@) 1-cents (6) 1260 cents (f) Scents 23, Copy each statement and say whether it is true of Falk, ) 854 = 854406 (0) 306 = 6e (© se= S005 (@) S0e is more than $0.42«scale readings To multiply. move the decimal point to the right To divide, move the decimal Point 10 the left. 45x 1000, | Beercise 6 Work out 1. 0634. 10 2. 0838 « 10 40.074 x 100 5 7.0563 10 & 142 100 10.0.3 100 11, 071 « 1000 Multiplying and dividing decimals by 10, 100, 1000 sate 10 = 384 1061 « 10= 1061 sind 100484 82x 00 = 86 15951019 624-9 + 100 = 6249 si +100 = 0563 4. 0815 « 100 0022 x i000 8. 0081 100 12,395.1013, 624510 16, 256% 100 19. 13-10 22, 218+ 10 25, 095 « 100 28, 007 x 1000, 31, 66 « 10 M062 « 10000 14. 1. sone 127+ 1000 osu 100 ML x10 57610 100+ 100, 09100 17S + 100 18. 705 + 1000, 21. 07 + 100 24, $.6-¢ 1000 2.32410 30. 999 = 100 Bao 555+ 10000 vt oe BABI What extra card could he take to ‘@ “a number en times as big es 3142 () Mel chose three cards to make 52 @) What cards could she take to make @ number ten times s big as $2? (i) What cards could she take 4o make & number 10 times ) 04x oor 2 figures after the decimal points 3 figures after the decimal points Bx 8 = 16) 187 = 28) $002 x08 =016 Sod x 007 = 0028 Beercise 8 Work out, without a caleuator 1.02%03 205%03 3.04x03 4.02003 5.06%3 07s 109%2 Bsxot 9. 04x09 10,002 07 11.21% 06 247 <05 1321304 14, 5206, 18, 42003 16.212 06 17, 08502 18327 x04 1, 126x001 20. 002 x 1 2. 005 1) m2. 2x001 23. 65 x 002 24 05 0002 Dividing by a decimal Example a) 936-504 Multiply hoth numbers by 10 so that you can divide by a whole n [Move the decimal points tothe right} So.work out 9346-24 ae A956 (0) 0.0378-+0.07 Multiply both numbers by 100 so that you can divide by a whole number: {Move the decimal poins t the rg So work out 378-57 1 0.5¢ a78 Exercise 9 __ a — Work out, without a caleulator 1084+ 04 2.093.203 3.0872 +02 408-02 5280 6 125205 7.8205 8 40202 9.7201 10.0368 04 1, 0915-003 12, 0248-004 1306254008 14. 85400 15, 1.272 +006 816.448 008 17, 012000218. 75 = 0.005 19. 0.09203 20. 077214 21, 00s5 0-11 22. 21.2857 23, 24854 aw. 3124 26.3208 woss4 29.0732406 30, 01638 + 0.001 BL 105+ 06 32. 75204 133. A cake weighing 72k is cut into several pieors cach weighing (kg. How many pices are there? © SS 34. A phone call costs S0-04, How many cals can T make if L have $352) 35, A sheet of paper is 0.01 em thick, How many sheets are there ina pile of paper Sem thick? Cross-numbers Mak of the crossnumber and a then fil in the numbers using the clues piven. Across Down 1 13x7 1 10L-7 r F 2o2isx i900 227204 F 4 265 — 248, 3441 +09 S.2x2e2x2«2x2 €2xH-CH2) ear 7.90199) oe 8 8. 65234917 F re 9. 9. 4ig-= 11 7 10, 216.4 (81 x 100) 1h 22x 2x3%3 15, 023 x 100, = Pr 16. 8x81 B c Across Down Across Down 12d x40 15586 1.26% 10 1.02% 100 2. 1600 — 27 2 64204 2. 6314 x 1000 267204 4.913 85 3. 0.071 x 1000 4. 600 ~ 563 1800 + 100 52+ 0%9) B11 44243719 §.025% 100 42106 7.045005 6 7-31) x10 73205 6. 420 «005 8 7x5-0 B 8x8 x 100-82 — $008 x 1000 8. 08863 x 10000, 9. a1s6 9, 008 x 700 9.315001 9, 0032 » 1000, ; m2 46 10, 49% 30% 4 Mbt 10, 5.706 + 0.001 4 ins 13, | 01235 499-4 108, BS 14. 201-112 14 1504 15. J million + 190000, (0.01 5 $700 16. fof 372 16, 1000 ~ 936| 3.5 Flow diagrams Find the operation Exercise 10 In the flow charts, the boxes A, B, Cand D each contain & single F nathematical operation (ike +5, x4, -15, #2) | oa F Now copy and complete each flow chart on the right, using the same operations. | .othaHte oS fn Lp ® BEC} oth Hepp E ofa ~ otk ' ot hE BEE I ot fh peep ip ro SBE ES © D B o tf HYe otf pete fp : ote @: ot hE EE EE pS otf Eee fpsO AP eatdes +, wi A Ip ste DE oS GREED » SER ER ER EE ot A fa}-{e . D otf te lep pe os A > B > cht Z o> i B fe 2 DE wo SKE ote EE] wee oSah- SE YeH (e At * > In Questions 5, 6,7 find the operations A,B,C.D.Properiescf muntes 83 Properties of numbers Factors Any numbor which divides exactly into 8 i a factor of 8 The factors of § are 24,8. ‘Muliples Any number in the 8times table is « multiple of 8, ‘The int five multiples of 8 are 8,16, 24,32, 40. Prime A prime number has just wo diferent factors: 1 and isl ‘The number 1 isnot prime, [Kt does not have two diferent factors ‘The ist five prime numbers are 2, 3, 5,7, IL “a Prine factor The factors of 8 ate I, 2,4, 8, The only prime factor of § i 2 138 the only prime number which isa fastor of 8 “The frst few multiples of 5 are 5,10, 15,20), 2 “he Least Consmon Multiple (LCM) of and Si 20 [vis the lowest number which sin both ists (@) The actor of 12are 1,2, 3,@),6,12 The factors of 20 are 1, 2.(8), 5, 10,20 The Highest Common Factor (H.CF.) of 12 and 20s 4 Itis the highest number which i in both lists. 4, Write down all the factors ofthe following numbers: oo OS OK GA | 2. Write down all the prime numbers fs than 20, 4. Write down two prime numbers which add up to another prime number, Do this in two diferent ways, 4. Use a calculator to find which of the following are prime numbers © HI | 1 ISL) 298 [Hint: Divide by the prime numbers 2,3, 5,7, Hand so on.) 5, Prime factors can be found using a “actor tre’ fe Here is a factor tee for 140, 4¢_Hore isa factor tre for 40. eee Draw a factor tree for each of these numbers: 36 69) 2G (4) 200) 1500Here isthe number 00 written asthe product ofits prime factors. 600= 242 2%3% 5x5 Use this information to write 1200 as a product ofits prime factors. Write down the ist four multiples of: 3 © Ob Wl ©» . Find the “oddone out (a) multiples of 6 : 12, 18,24, 32,48 (b) mips of 9 = 18, 27,48, $6, 72 ). Write down two numbers that are multiples of both 3 and 4 ‘Copy and complete each sentence: {@) An foddjeven} number is exactly divisible by 2 (An number leaves a remainder of I when divided by 2 AML J mumbers are multiples of 2. | Copy the table and then write the numbers Ito 9, one in each box, so that all the numbers satisfy the conditions for both the row and the column. Prime number Multiple 3 Factor of 16 Number greater than § Oas mumber Even number 18 14 Find each ofthe mystery numbers below {@) Lam an odd number and a prime aumber. Tam a factor of 14 () 1am a two-digit multiple of 50. {e) Tam one less than a prime number which is even. (4) Tam odd, greater than one and a factor ofboth 20 and 30, (a) Write down the first six multiples of 2, () Write down the frst six multiples of 5. (6) Write down the LCM. of 2 and 5 (a) Write down the first four multiples of 4 () Write down the first four multiples of 12 (6) Write down the LGM. of 4and 12. Find the LOM. of (a) 6and9 (6) 8and 12 (@) Wand 35 (@)24and6 fe) 3,5and10 (4, and 9umber Tacos common faiors| fom | 1a3a68 in aaaan | Be | EARS tats | }eeaeen nTactors of 18 and 24, common factors ‘Write down the FCF. of 18 and 24 AK. Find the H.C. of f@) I2and 18 (b)22and ss (@) 4S and 72 {@) 12, 18.and.20 (36, 60and 72 (1) 20,40 and 50 19, Don't confuse your LCM. with your H.C Fs © (a) Find the HCE. of 12 and 30, () Find the LCM. of 8 and 20, (@) Write down two numbers whose H.C. is 11 (@) Weite down two numbers whose LCM. is 10. Given that 30 =2 x 3 5 and 165 = 3. 5 11 ind the highest common factor of 30 and 165 fe. the highest number that goes into BW and 165), F315 = 33x $e Tand 273 =3 x 7% 13, find the highest ‘common Factor of 315 and 273, tional and irrational numbers A rational number a mn always be written exactly in the Form © be he form | where a and d are whole numbers, fp b=} © | Alt these are rational numbers An irrational number cannot be V2. V5, n, V2 are all irrational number In general Vis ierational unless nis a square number. itten in the form 4 * Ib this triangle the ength ofthe hypotenuse is exactly V5 Acaleulator, $= 2236068, This value of v5 i nov exact and is Sbrrect only to 6 decimal places,Exercise 12 - - 1. Which ofthe fllowing numbers ae rational? 5 v ay “i 3a z ylag? 2. (a) Write down any rational number berween 4 and 6 (6) Write down any irrational number between 4 and 6 (6) Find a rational number between v2 and v3, (@) Write down any rational number berween x and V0. 3. (a) For each triangle use Pythagoras’ theorem to calculate the length x 2 (6) For each triangle state whether the peri rational or irrational . sa (6) For each triangle state whether the area is rational : or irrational @ : (4) In which triangle is sin@ an irrational number? r 7 " “angle A Tangle B 4. The diagram shows a circle of radius Sem drawn inside a square Write down the exact value ofthe following and state whether the / x 7 cosine rational or ot | (@) the sicumterence ofthe cele j (b) the diameter ofthe circle (@) the area ofthe circle | (©) the shaded ara, '. Think of two irational numbers x and y such that * is rational a 6. plain the difeence between «rational number and an ietionat umber 7. (a) Is possible to multiply a atonal numer and an ieaional 4 umber to give an answer which i (©) Is it posible to multiply «wo irrational numbers together to give ‘a raional answer? e (©) IFeither or both are possible, give an example“The times which most people use in thee everyday lives ate times messured from midnight oF from mid-day (noon). Inthe moraing © Yotlock is 9 hours after midnight and is written 9.00a.m. In the 40pm. Using the 24-hour clock all times are measured from midnight. This means 9.00a.m. is written 09:00 and 4.00 pam, is written 1600 (a) 800a.m, = 08:00 (0) 920pm. = 21:30 | Remember am. is an abbreviation of ante merdiem and means before midday pm. i an abbreviation of post meridiem and means after rida Exercise 13 | Write down the following in the 24-hour system, 2. 9.30pm, 3. 6:00pm, 5.240 pm. 6. 10.00pm 7. 715pm, 8. 10.45pam, 9. 830am, 10. 45am, 11, 2.28am, 12. 130p.m, 1720p, 14, 650a.m, 18. 70am, 16 Two minutes before midnight, 17, Two and a half hours before midnight. 1 Five minutes before noon, 19, Three and a half sours afternoon 20, One hour ater midnight 21, One and a half hours before noon, G2. Twenty minues after midnight 23, Five hours before midnight F24. Six minutes after noon. 25, Filly minutes after midnightWrite the following in the 12-hour system, 26.0700 27,1930 2112028. ods 2. 32:15 3.001038. 8s Bt 35.2000 36, 120037, O10 4 3. 3.0707 40.133 AL IS 2. 4B is4s 44 162048, 05:16, Time intervals 4¢ Find the time interval between 15:40 and 18:05 From 1540 to 16:00: 20 minutes (count on to the next hour) From 1600 0 18:05: hours S minutes (count on from 16:0) Altogether there is 2 hours 25 minutes. a Exercise 14 = Find the number of hours and minutes between the following | 1. 20:10 and 21:20 2. 21:40 and 23:50 3. 2215 and 23:10 4, 19:30 and 20:05 5. 20:16 and 23:36 6, 1125 and 13:10 : 7. 08:40 and 12:00 8. 21:17 and 23:10 9, 2804 and 25:57 10, 1745 and 23:10 3 11, 0S:15 and 07:05 12, 11.26 and 1440 13, 9.80a.m. and 11.0Sa.m. 14, 9.30a.m. and 2.05pm, = 18, 11.l0am.and 1.30pm, 16, 7.308m. and 7.20pm, 4 17. 1004s. and 1240p.m, 18, 5am. and 1.00pm, 19, 11,55am.and 3.10pm. 20, 1.38am. and 8.400, 21, 22:30 on Monday to 03:30 on Tuesday 22, 21:00 on Thursday to 01:0 on Friday 23, 17:30 on Monday to 02:00 on Tuesday 24, 23:45 on Saturday to 02:10 on Sunday 25, 22:50 on Thursday to 07:00 on Friday ] 107.00 on Friday to 0200 on Saturday 3 27, 08:30 on Monday to 04:30 on Tuesday 28, 08:15 on Wednesday to 02:45 on Thursday 29, 22:10 on Friday to 07:35 on Saturday eee ; 30, 06:30 on Friday 10 16:30 on Saturday B‘Waterloo (London) o710 Woking 0735 Basingstoke oss Andover os:16 Salisbury 0836 OB'S4 3715.08 Yeouil 0924 10421407 15:88, Honiton 001 M43 1634 Exeter lo27 1881659 | 1, How long dors it take the 07:10 from Waterloo to travel to |) Woking (©) Basingstoke (6) Andover? 2, At how many stations does the 11:38 from Waterloo stop? 3. At what time does the 08:35 from Waterloo reach Salisbury? 4. Ifyou had to be in Exeter by 15:30 which train would you catch fiom Waterloo? f 5. You arrive at Waterloo at 08:20. How long do you have to wait for the next train to Exeter? 6, The 11:35 from Waterloo runs 10 minutes late. At what time wil it reach Andover? 7. How long does it take the 11:35 from Waterloo to travel 0 {@) Salisbury () Yeovil (©) Exeter! 8. At how many stations does the 08:16 from Andover stop before it reaches Honiton? From Basingstoke? A You arrive at Waterloo at 11:08. How long do you have to walt for the next train to Exeter? reach Exeter? | 12. The 08:25 from Waterloo runs 19 minutes late, AC what time will it3.8 Long multiplication and di “To workout 327 53 we wll se he fic that 327 x 53 = (27x 50+ (8273) Se out the working tie this Heres another ample 327 Sut. 53, Bue 16350“ This ‘ss 397xS0 T3280 Ths is Skt ¥80) 984 a this is 327% 3 QL bh -rthisis Shiv 4 17334 >This is 327% 53 LSkLb>THsis Shd «Bh Exercise 16 Work out, without a ealelator, 135423 2x 438 5.45% 61 1 MsK 8416 «73 10, 306 « 28, 624% 75 13, 69483, 14, 973 «92 With ordinary ‘short’ division, we divide and find remainders. The method fr long’ division is really the same but we set it out So that the remainders are easier t find Example Work out 736-5 32 (@) 32 into 73 goes 2 times () 2x 32—64 “6 fe 3~64=9 36 (@) “bring down’ 6 96 {6} 32 into 96 goes 3 times 0 Exercise 17 4 Work out, without #6 16424 2. 495-517 3.516532 4.207419 5, 875.425 6. 514526 7. 806 4 34 8 748 9, 666-428 10, 707+ 52 11, 951 12, 80664 13.2917 45 142 15. 56278 19,gxercise 18 Solve each problem without a caleulator. 4, A shop owner buys 56 tins of paint at B4e each, How much does he spend altogether? 2, Eggs are packed eighteen t0 a box. How many boxes are newded for 828 eggs? +3, On average a man smokes 146 cgi How many does he smoke in a yea? 4, Sally wants to buy as many 2% stamps as possible. She has $$ 10 buy them. How many can she buy and how much change islet? How many 49-seater coaches will be needed fora school trip for a party of 366? {6. An ollce building has 24 windows on each of § floors ‘A.window cleaner charges 42c for each window. How much i he pad forthe whole building? 1, A lowtery prize of 9238 million was wom by «syndicate of 17 people who shated the prize equally between them How much did each person receive? B. It costs $7905 to hire a plane fora day. A teip is organised for 93 people, How much does each person pay’? 9. The headmaster of a schoo! discovers an oil wel inthe school playground. As is the custom in such cases, he receives all the money from the oil. The oil comes out of the well a arate of $1S Tor every minute of the day and night. How much does the headmaster receive in a 24-hour day?Exercise 19 ach empty 59 rm ‘contains either a number or a mathematical symbol x, +). Copy each squate and fil in the details 24 a 15, > 1 1 1 1 (©) Work out 16% of S85. [Alternative method} Since 16% = 25 we can replace 16% by 016 io So 16% of $85 = 0.16 x 85 . = 813-60 2. 10% oF $80 3. 5% of 200 5. 4% of $60 6, 30% of $80 8. 18% of 4009, 61% oF S400 ors BB 5% of 160 kg 14, 20% of 60 ke 16, 15% of 300m of S10 2, 11% of $800 17, 2% of 2000 km 20.1 6000 v4 of $2400 Example | Work out 6:5% of $1750 correct tothe nearest cent 65,175 _ 11345 io “7 100 = $1138 ‘Answer $14 tothe nearest centExercise 21 — — Give the answers to the nearest cent where necessary. 2.1% of S684 3.15% of SHIT 5, 37% of 9.64 6. 35% of $12.90 8. 68% of $5445 9. 73% of 82524 11, 63% of $1250 12, 82% of $19.50 14, 80% of $6250 18. 12% of $2450 17, 71% of $1640 18. $% of $80 20, 19% of $1190 21. 835% of SIO Example 1 ‘A coat originally cost $24, Caleulate the new price after 1.5% reduction, Price reduction = 5% of S24 S24 Stas ion“ = 1 New price of coat = 524 —$1:20 = 52280 Example 2 |A.CD originally cost $1160, Ca 8.7% increase. ‘We could work out 7% of 11-60 asin the example above. “There is, however, a quicker way which many people prefer. IT we incase the pice by 7% the final price is 107% of the old price. slate the new price after new price = 107% of $11.60, Lor x 116 = S124 10 the nearest cent For # 5% reduetion asin Example | we would multiply by 0-98 Exercise 22 1, Increase a price of $60 by 5% 2, Rede a prise of $800 by % 4. Increase a price of $65 by 60 1. Reduce a price of 82:50 by 5. Resduce a price of $2000 by 2% 6, Increase a price of $440 by 80% 7. Increase a price of $66 by 10 8, Reduce a price of 591-50 by 30% 9, Increase a price of $88:24 by 25% 10, Resuce a prive of $63 by 312. Increase a price of $7.65 by 24% 14, Reduce a prve of $899 by 22% 16, Reduce a price of $17.62 by 4 18, Increase a price of $8.55 by St 29. Increase a price of 12.80 by 10s 1, Ina closing-down sale a shop reduces all its prices by 21 Find the sale price ofa coat which previously cost $4, 2, The price ofa car was $5400 but itis increased by 6% What isthe new price? 3, The price ofa sideboard was $245 but, because the sideboard is seratched, the price is reduced by 30%. What s the new price? 4. Abii shop offers 8 7% discount for cash. How much does a ¢ash-paying customer pay for an amplifier advertised at $95? 5, A rabbit weighs 2.8 kg. After eting How much does it weigh now? its weight is increased by 1% ‘The insurance premium for et is normally $90, With & © no-claim bonus’ the premium is reduced by 3 ‘What isthe reduced premium © 2. Myxomatosis kills 9 rabbis survive? ‘of colony of 300 rabbits. How many 4 The population of town increased by 32% between 1945 and 1985. If there were 45000 people in 1945, what was the 1985 population? 9, A restaurant adds a 12% "service charge’ onto the base pice of Is. How much do I pay’ fora meal with a basic price of $880? 10, A new-born baby weighs 3-1 kg. Her weight increases by the next fortnight, What does she weigh then? I. A argo snake normally weighs 12.2ke, After swallowing a rat, the weight ofthe snake i increased by 7¥, How much does it weigh after dinner? 1. At the beginning of the year a car is valued at $3250, During the yer its vale fll by 15% ow much is it worth at the end ofthe year?Exercise 24 In Questions 10 4 find the total bil. 2 hammers at $5:30 each 5 stews at 25 for 10 5 bulbs at 38 each 1 tape measure at $115 VAT at 175% is addod tothe total cos. 3. 12 rolls of wallpaper at $370 perro 5 packets of paste at $055 per packet 2, Sitves ofl at 8Se per ire 3 spanness at $L.2S each 2 manuals at $430 each 200 bolts at 90¢ for 10 VAT at 17:5% is added to the total cost 4. 5 golf clubs at $12.45 each 48 gol alls at 815 per dozen 2 brushes at §2-40 each Too tees at Ip eas 1 step ladder at $15:50 bag at $21:5¢ VAT at 175% is added tothe total cos, 1 umbrella at $12.99 VAT at 17-54 is added to the total cost ‘5 Ina sale a dres priced at $35 is reduced by 20%. AF the end of the ‘week the sale price i reduced by a further 25% Caloulate: {@) the price in the original sale () the final price 6. (a) In 2000 a club as 40 members who subscription ‘What isthe total income from subscriptions? (In 2001 the subscription s increased by 35% and the icmbership increases 10 65. (i) What is the 2001 subscription? Gi) What i the total ineome from subscriptions in 2001? ch pay $120 annual Simple interest When @ sum of money $P is invested for T years at RY interest per annum (each year), then the interest gained Tis given by Px Rx 100 This is known as simple interes. Example Joe invests $400 for 6 months a 5 Work out the simple interest gained. 00 400 5x05 100 s=sio 3 T=05 (Gmonths is half a year) wo T=e rercise 25 1, Caleulate: {@) the simple interest on $1200 for 3 years at 6¥% per annum (@) the simple interest on $700 at 8:25% per annum for 2 years {@) the length of time for $5000 to carn $1000 i invested at 10 {@) the length of time for $400 to extn $160 if ivested at 8% per annum 2, Khalid invests $6750 at 85% per annum, How much interest has he farmed and what i the total amount in his account after 4 years? 4, Shareon invests 10800. After 4 yeas she has earned $3240 in interest, At what annual rate of interest did she invest her money? Compound interest yin deposit ‘Suppose a bank pays fixed interest of 10% on mo accounts. A man puts S500 inthe bank has ‘of $500 = $550 ‘Alter one year $500 + 10 Alter two years he has 8550+ 10% of $550 = S60 [Check that this is 1-108 x 500), After three years he has $605 + 10% of S605 = $665.50 [Check that this 1.108 x 500), Tn general after m years the money in the bunk will be S(1-t0" > 500) Exercise 26 1. A bank pays interest of 9% on money in deposit accounts Mes Wells puts $2000 in the bank, How much has she ater () one year () two years (6) three years? 2. A bank pays interest of 11%, Mr Olsen pats $$000 in the nk How much has he after (@) one y () three years (© five year? 3. A computer operator i paid 10000 a yea. Assuming her ay'is increased by 7% each year, what will her salary be in four year's ime? 4, Mrs, Borgkamp's salary in 2001 was $3000 per year, Every your har salary is increased by 5% In 2002 her salary was 30000 1.05 31 soo Tn 2003 her salary was 30000 5 1.05 x LOS = 35 In 2004 hers S34728.75 And so on, (4) What will he salary bein 2005? (b) What will her sary bein 2007? 7 as 39000 1.05 1.05 x 1.0598 hmber '5, The price of a house was $9000 in 1998. AC the end of each year the pric is inereased by 6%. (a) Find the price ofthe house after 1 year (b) Find the priee ofthe house afte 3 Years (e) Find the pre ofthe house after 10 years, 6. Assuming an average inflation rate of cost ofthe following items in 10 years: (a) car$6500 (by TV.SMD——_(@) house $50000 17. A now car is valued at $1500, AC the end of each year is valve is reduced by 15% of ls vale atthe start of the year, What will it be worth after 3 years? ve, work out the probable 3.10 Map scales and ratio The map below is drawn fo scale of 150000, in other words Tem on the map represents 50000 enon the land GARDEN CTY Example ‘On a map of scale 1:25000 two towns appear 10 em apa. ‘What isthe actual distance berween th towns in km? ‘rem on map = 25000 em on land em on map = 250 000.em on land 0.000 em = 2500 m 25km ‘The towns are 2-5 km apart.The scale of map is 1:1000. Find the actual length in metres represented on the map by 20m, “a: The scale of a map is 1:10000, Find the actual length in metres fepresented on the map by 5 em. © the table {3 Copy and com; Map scale | Length | Actual length on ‘on and © fw ri000 [oom Tim © |v 1200 | 100m m © 12500 | sem km (@ 110000 | 6em km {63 em apart on a map whose scale is 11000. ‘On a map of scale 1:300 000 the distance between Pars and Bonnieres is § cm. What isthe actual distance in ken? 6A builder's plan is draven to a scale of | em to 10 m. How long is road which is 12 em on the plan? 4 The map on page 80 is drawn toa sale of 15000, ‘Make your own measurements to find the actual distance in km between: {@) Goldings and Tewin Wood (marked «) () Panshanger Aerodrome and Row Wood. () Gravel Pitand Queen Hoo Hal, be distance between two towns is 18 km How far apart will they be on a map of sale 150000? IGim = 1 800000 em 00000 cm on land = % 1800000 em on map ance etween tovins on map = 36.m ‘The distance between two points is 25 km. How far apart will hey be on « map ofsele 120000?100. uber 4. The length ofa reservoir is $9 km, How long wilt be on a map of seale 1000002 ‘5. Copy and complete the table Maps| Acting | Leen [Sota | gaan @ 00 | Bim Pan (b t1000 | sakm | em © r000 | zim | om (@) tao0m | sokm | om te hsao km | em 6, The scale of drawing is 1m to 10m, The length of a wall is 25 m, What length will the wall be on the drawing? Ratio Example Share $60 in the ratio Total numberof shares = 2-43 = $ One share = $60-+5 = $12 The tvo amounts are $24 and S36, Exercise 29 1, Share $30 in the ratio 1:2 2 Shave 860 in the ratio 3: Divide 880 g of food between the cat and the dog in the ratio 35 4. Divide $1080 between Isobel and Carlota in the ratio 45. 5. Share 126 litres of petrol etween Maya and Tashu in the ratio 25 6, Share $60 in the ratio 1:28 17, Anwar, Belusa and Nabila divide $560 between them in the ratio. 21:5. How much did Belusa receive? 8, A sum of $120 is divided in the ratio 3:45. What isthe largest share?102 Murder 5, Ina shop the ratio of oranges to apples is 25. 1 there are 60 apple, how many oranges are there? 6. A recipe for 5 people calls for 1-5 kg of meat, How much meat is required if the recipe is adapted to feed § people? 7. A cake for 6 people requires 4 eggs. How many eggs are needed {0 ‘make a cake big enough for 9 people? 8. A photocopier enlarges the original in the ratio 2:3 ‘The height of a troe is 12 em on the orginal How tals the tee on the enlarged cops? ad ot alien 9. A photocopier enlares copies in the ratio 4:5. The length ofthe headline ‘BRIDGE COLLAPSES’ is 18 em on the original. oow long i the headline onthe enlarged copy? 10. A photocopier reduces in the ato 53. The height ofa church spice is 12 cmon the original, Haw tl i the church spite on the reduced copy? 11, A cake weighing 550 g has three ingredients: ovr, sugar and ‘ising. There is twice ss much four as sugar and one and a half| times as much sugar a raisins, How much flour is there? 12, 18 of the children in a school are boys, what is the ratio of boys to girls! 13, A man and a woman share bingo prize of $1000 between them in the ratio I. The woman shares er part between herself, her mother land her daughter in the ratio 2:1: How much does her daughter receive? 14. The numberof pages in a newspaper is increased from 36 to 54 ‘The price is increased in the sime ratio, If the old price was 28, what will the new price be? 15, Two friends bought a house for $2200000, Sam paid $140000 and oe paid the rest. Three yeas later they sold the house for $275000. How much should Sam reovive from the sale? 16. Concrete is made from 1 part cement, parts sand and 5 parts ‘aggregate (by volume). How much cement is necded to make 2m of conercte?Proportion 103 = 3.11 Proportion Example 1 Example 2 Eff lites of petrol costs £5.72, ‘A Farmer has enough hay to feed EG the cost of 27 Tires, Shhorses for 6 days. How long would the hay last for 3 horses? ‘Te cost of petro is direct “proportional to the quantity ‘The length of time for which the horses ca be fed is inversely proportional to the numberof horses be fed S horses can be fed for 6 days I horse can be fed for 30 days jorses ca be fed for 10 days E of one litre of petrol. ‘#1 five men can paint a tower in 10 days, how long would it take one man? book cost? | brercise 31 1, 15 hammers cost $20, find the cost of 7 hammers. | 2, Magazines cost $16 for 8, Fin the cost of 3 magazines, 4. Find the cost of 2 cakes if 7 cakes cost $10°50, | 4 A machine ills 1000 otis in 5 minutes, How many botles wil clin 2 minutes? 4. A train travels 100m in 20 minutes. How long will i ake to travel SO km? | 6. Eleven dises cost $13-20, Find the cost of 4 discs 4.1 12 men can build a house in 6 days, how long will it take 6 men? "9 Six women can dig a hole in 4 hours. How long Would it take 2 women to dig the same hole?108 um 10, A farmer has enough hay to feed 20 horses for 3 days. How long ‘would the hay lst for 0 horses? 11. Twelve people can clean an fice building in 3 hours. How long would it take 4 people? 12 Usually i takes 12 hours for § men to doa job. How many men axe needed to do the sume job in 4 hours? 13, Five teachers can mark 60 exam papers in 4 hours. How long wou ittake one teacher to mark all 60 papers? 14, 10 ladybieds et 400 greets in 3 hours. Copy and complete the followin: (a) 20 ladybirds eat * greenies in 3 hours, (b) 20 ladybirds eat * greenies in 9 hours, {6) 10 ladsbirds eat 200 greenies in * hours. (@) * ladybird eat 4000 greenies in 3 hours. Exercise 32 1. IFT packets of coffee costs S854, find the cost of 3 packets Find the cost of 8 botles of wine, given that 5 bottles cost $1190 3. 1F7 cartons of mill hold 14 ites, find how mach mil there is in 6 cartons 4. On an army exercise, 5 soldiers took 6 hours to dig trench. How long would i have taken 3 soldiers co dig an identical tench’ A party of 10 people exploring a desert took enough water to last 5 days, How long would the water have lasted if there had been ‘only 5 people inthe party? 6. A worker takes 8 minutes to make 2 creit boards. How long would it take to make 7 etcut boards? 7. On a rose bush there are enough greenfies to las 9 ladybird 44 hours, How long would the greenies last if there were only 6 ladybieds? {8 The total weight of & tiles is 1720, How much do 17 tes woigh? 9. A-machine can ill 3000 bottles in 15 minutes. How many botls vil fil in 2 minutes? 10, A train travels km in 120 minutes. How long wil it take to travel Skm at the sume speed? 1H, 1f4 grapefruit can be bough for $2.96, how many can be bought for 8-19? 12, £15 can be exchanged for 126 francs. How many francs can be exchanged for £3750?42. Usually it takes 10 hours for 4 men to build wall, How many men tare noeded to build the same wall n 8 hours? eeded for a journey of 440 km? 15. Ten bags of corn wil food 60 hens for 3 days. Copy and complete the following: © (a) 30 bags of corm will feed * hens for 3 days = {b) 10 bags of comm will Fed 20 hens for * days, ©) 10 bags of corm wil feed * hens for 18 days, {@) 30 bags of corn wil feed 90 hens for * days © 16, Four machines produce $000 hatteries in 10 hours. How many S tetteres would 6 machines produce in 10 hours? | 17, Newtonian spiders can spin webs in traght ns. 1 1S spiders can | spine web of length I metre in 30 mints, how long will take 6 spiders to spin a web of the same length? 16 In the army all holes are dug 4 fet deep. 1 takes 8 soldiers 36 minvtes to dig a hole 18 fees long by Il fet wide, How long will i take 5 soldiers to dig a hoe 36 fect by 10 fest? 19, I takes b beavers n hours to build a dam, How long will i ta the beavers to build the same size dam? Money is changed from one currency into another wsing the method of| E proportion GE Exchange rate for US dollars (8): | County ‘Rate of exchange © Argentina (pesos) [Ol pesos = St © Kuwait (dinars) S Arabia (rials) UK (pounds) © Euro (euros) o93e=51 | Example Convert (4) $2.80 todinare —__(b) 300€ to dollars. -©) $1=030 dinars (KD) (0) 093€ = St Ss $2250=0.30x 2250KD so 1e=_ 095 5 61sKD : q so 3006 = $30 - SME Sas x =sm2ssExercise 33 Give your answers correct to two decimal pages, Use the exchange sates given on page 105 1. Change the amount of dollars into the foreign currency stated. {@) $20 feuros} () $70 [pounds] (©) $200 [pesos} () $1.50 feuros} (@) $2.0 frias} (9, 90e [inats} 2. Change the amount of foreign currency into dollars. a) s00€ by £2300 wre (@) 90 dinars (@) 12824 pesos (9 1508R 3. ACD costs £90 in Britain and $9-70 inthe United States. How ‘much cheaper, in British money isthe CD when bought in the USA? 4. A bottle of Cointeeau costs 20-46 € in Spain and £12.60 in the UK. Which is the eheaper in dollars, and by how much? '5, The BEC “Butter Mountain’ was estimated in 2004 to be costing 218000 € per day to maintain the storage facilities, How much is this in US dollars? 6. A Jaguar XIS is sold in several cou ries at the prices given below. Britain £15000 France 29490 € USA s2sss2 ‘Write out in order a list of the prices converted into pounds, 17. An Irish gentleman on holiday in Germany finds that his wallet contains $700, If he changes the money ata unk how many euros will he 3.12 Speed, distance and time Calculations involving these three quantities are simpler when 0 constant. The formulae connecting the quantities are as follows: (@) distance ~ speed «ime () speed nee distance (©) time = S808Ep elf way of remembering these forse is to write the eters DS to find D, cover D and we have ST > Co find S, cover Sand we have 2 nd, cover § 2 > to find 7, cover Tand we have 2 5 'A mais running a a speed of 8km/h for a distance of $200 metres, Find the ime taken in minutes, 5208 metres = S:2km = 0.65 hours © tie taken in minutes = 0.68 x 60 : = 39 minutes “Example 2 54000 $000 ox 00 ond =15mis 1 Find the time taken forthe following journeys: EG) 100km ata sped of 40min (6) 250 miles ata speed of 80 miles per hour © (©) 13 metres ata speed of 20em/s (answer in seconds) res ata speed of 2-5kmjh 2 Change the units ofthe following speeds as indicated (a) 72kaw/h into mys (6) 108k into mis [© W0km/ into mis {) 30m into km | (@) 22mis into kmjh U) 0.12mi ita ems 2) 9000em into mis (6) 600 miley into miles per hour (©) 2592 miles/day into miles per second Spd, Sites and tire 1074. Find the speods ofthe bodies which move as follows (a) a distance of 600 km in § hours () a distance of 3.64 km in 7 hours (6) a distance of 1368m in 18 seconds (@) a distance of 4x 10" m in 10" seconds (@) a distance of 5 « 10" em in 2% 10" seconds (€) a distance of 10 mm in 30 minutes (inka) {) 8 distance of 500m in 10 minutes Gin km/h) 4. Find the distance travelled (in motes) in the Following (a) at speed of $5 km/h for 2 hours (b) at spoed of 40 km/h for E hour (6) at speed of 338-bkm/h for 10 minutes (@) at a speed of 15m for $ minutes (6) ata speed of 14's for I hour (f) ata speed of 4x 16! ms for 2 x 10° seconds () a. speed of 8 10° ems for 2 minutes 5. Acar tavels 60k at 30 khan then a further 180 km at 160 km/h, Find (a) the total time taken (b) the average speed forthe whole journey. 6. A eyelst travels 28 kilometres at 20km/b and then a further S80 kilometres at 25kinjh, Find: (@) the toca time taken (b) the average speed forthe whole journey 7. A swallow fies ata speed of SOkm/h for 3 hours and then ata speed of 40 kn fora further 2 hours. Find the average speed for the whole journey 3.13 Approximations A car travels a distance of 158km in 34 hours ‘What is the average speed? Distance _ 158 Time (On a caeulator the answer is 45:142857 14 kmhAopronensions 109 Hgis1n0t sensible to give all these figures nthe answer. We have used a cand atime which may not be all that accurate. I¢ would be ronable to give the answer as "45 km/h fe can approximate in two ways: SF a) we an give slemican figures (8) Db) weecan sive decimal places (dp.) A type of approximation is described below ite the following numbers correct to thee signficant figures (3s. 26592 = 2.66 (103 sf) () 05142 = 0514 003 sf) aa 1 19 $4660 = 84 700 t0 35.) (@) 0.04031 1 1 ach case we look atthe number marked with an arrow to see if tis “Tv oF mor’ 0.0403 (0 3 1) 512602 2. 081438 3.26241 4, 3555 S174 6 21082 7. ons 8. 0031 162 10, 1.232 11, 05456 12, 07163 141331 15, 2483, 16.3137 the numbers correct to Four significant figures 1486.72 18, 500.36 19, 2.8888 20. 3.1125 I 071 542 22, 3.0405, 23, 24635 24. 488852 An Questions 28 to 36 write the mumbers tothe degree of accuraey indicate. 0516356) 26, SRL ESL) 27. 6589258) 28. 58755 (4 5.1) 98.0581 (Is) M.OOTI(Isf) SSRI (SSE) 3. STSHO'SI) 2492256) BM. S2666350) 3S 00OSH (LSE) 36. GS6BT ST) 4p) 003 (002 dp) |) 783 es 836(002dp) tb) 00328, 7436 (to 2.d.p.) eich case we look atthe number masked with an arrow ta sei isis ve oF more’ ‘We count figures after the decimal pointExercise 36 Tn Questions Ito 8 write the numbers correct to two decimal places (2 4p.) 1. 5381 2. 11.0882 3.0414 4. 03666 5.8015 6, S704 7. 9.0062 8. 00724 Tn Questions 9 to 16 write the numbers corret to ane de a pace. 9.8404 10, 07413 mo. 12, 0.095 13, 6083 M1955 15.8111 16, 7071 Jn Questions 17 to 28 write the numbers to the degree of accuracy indicated ISIC dp) — IRON dp) —WLOSHSEGAps 20, 0.00555 4d p) BLOT 2dp) —«-GHTIAdp) «LORS Epi 24. 1964p) 2S,00135(4dp) — 26. 600SI(Ldp) 7 -TO(1dp) 28. S424 dp) 28, Use a ruler to measure the dimensions of the rectangles below , hand wideh in cm correct to one dp. () Work out the area of each rectangle and give the answer in em® correct to one &p. Write down the legs ® w Exercise 37 ‘Write the answers tothe degre of acuracy indicate. 1.0153 «3742 dp) 2. 1809-55240 66) 3 1842382 G sf) 4.172 -089(1dp) 5, 58+ 261 20) 6. 888x444 (dp) 7. (84-152) x75 @ 86) 8, (121 4.3758) +211 6 sf) 9, (124 1148) 0618 dp) 10, 140935 (1 dp) 11, 753528 G50) 12, (1825 ~ 6941) @ dp) 13, 9.245" — 652 (1 dp) 14, (20-666) + 0028 0 5.6) S43" (dp) 0928 0838 @ dp)_ 3.14 Metric units Length Mass Volume 10mm = tem 1000 g = 1 ke 1000 mi = 1 tee E c0cm=1m 1000 ke = 1 1000F = ty ee (for tonne) Also ml = Tem! 1 Exercise 38 - i Copy and compete 1.85cm= m 224km= m —-.063m= om &7mm= cm 62em= mm 7.12km= m © 5.0S8km= m 0.815 m= m 11, 650m= km sk= 2 14 42 bg = I6dke= 12 08ke= & 18. 400 ¢ 19.2t= ke L05t= kg m2 0462 2.7ke= 1 24. 1500 g S00 m= 7 27. 000m= 1 84S 2 61= ml en’ BL2m= I 32. 5S mi! 09/= em! P3815 mt 240 mt 2em= m3 om. = 40.0046 ks lomi= 1 42.208mm= mm — 4.28mm= cm #4. 27am .788m= km ke 47.13 kg= 48.90 29t= ke 7 |. Write down the most appropriate metric unit for measuring: | 6a) the distance between Madrid and Barovlona (b) the capacity ofa wine botle F (the mass of rusins nevded for a cake (4) the diameter of smal dill {o) the mass ofa ear (0) the area ofa football pte "Exercise 39 | Wonderfol new computercontrold machine Elks fed with waste plastic and ean be | programmed to produce any fri small objec. EAs demonstration, Mr Evans shows his cass | how to make die, He programs the machine to | reduce centimetre cubes.1. The million cubes could be stuck together wvith super elue to make @ tower Would the tower be as tal as: {@) Nelson's Colum? () The Empire State Building? (6) Mount Everest? 2 IFthe cubes were placed in a single layer, would there be enough to cover (@) the floor of your classroom? () a football pitch? 3. If the cubes wore ina solid mass, would there be enough: (@) 10 fill your clasroos () to fill large fidge-freezer? 44. Mrs Evans soon realises the potential of the cubes, which by this time ae rather Famous, and she sets out to make not a milion bout «lon ofthe eabes (1,000,000, 000), {@) Would that be enough to fill your elassroom? (6) Placed side by side, roughly how many times would the around the London ring road (184k 3.15 Problems 1 Making a profit Example AA shopkeeper buys potatoes at a wholesale price of $180 per tonne and sells them ata retail price of 2c per kg, How much profit does fe make on one kilogram of potatoes? He pays $180 for 1000kg of potatoes the pays S[I80 + 1007] for [kgf potatoes, Lhe pays 18e for 1k He sells at 22e per profit ~ de per kgProtems 1 119 | peercise 40 __ Find the proft in each ease, ‘Commodity Retail pres Wholesale prise 1, cans of drink 15e each ‘SUT per 100 profit per ean? 2, rulers 24e each 130 pee 1000 profit per euler? 43. birthday cards 22e per ean S13 per 100 profit per eard? 4, soup © each 38550 for $0 cans Profit per ex? 3 5. newspapers 2e each 36 for 200 Profit per paper? 6 box of matches Me each $15.20 for 80 profit per box? 7. potatoes 220 per kg 160 per tonne profi per kg? & carrots 38e per ke | $230 per toane profit per kg? 9, T-shins 8495 each 3840 per dozen profit per Tshirt? | 10, exes 96e per dozen 50 per 1000, profit per dozen? 1. oranges S for 30e S14 For 400 | profit per orange? 12, car tyres 519.50 each 2480 for 200 profit per 140? 1B wine SSe for 100 mi 40 for 10 litres profit per 100 mt? 14. sand 16 per ke S110 per tonne profit per ke? 18. wi 23e perm | s700 for 10 kam profit perm? 16, cheese S264 per kg 387.50 for $0 ke profit per ke? 17. copper tube 466 per m S160 for $00 m profit per m? © | 18, apples 9 each 51008 per gross profit per apple? carpet 86:80 per m 1600 for 500m? profit per m?? {in of soup Be per tin 72 for 40 sins Profit per tin? | Brercise 41 = 1, There are 1128 pupils in a school and there are 36 more girls than boys, How many girs attend the school? 2. A generous, but not very bright, teacher decides to award tothe Person coming 10th in atest, 2c to the person coming 9th, 4 tothe person coming 8th and so on, doubling the amount cach time. How ‘uch does the teacher award to the person who came top? 1920, aged 75. How old was the tee in 1975? 4. Washing-up liquid is sold in 200 ml containers. Each container ‘costs 57e. How much will it cost to buy 10 litres of the liquid? 8. A train is supposed to eave Rome at 11:24 and ative in Milan at 12:40. The train was delayed and arived 2] hours late Atta time di the tein arive?6, Big Ben was stopped for repairs a TAS on Tuesday and restarted at 0820 on Wednesday For how long had it been stopped? How moch would I pay for nine lites of paint i to litres cost $2307 8, A television set was advertised at $282.50 for cash, or by 12 equal instalments of $25.30. How much would be saved by paying cash? 9, ges are packed twelve toa box. A farmer has enough exgs to fll 316 boxes with unbroken eggs and he has 62 cracked eggs leftover How many eggs had he to start with? 10, A car travels 9km on alte of petrol and petro costs 80-68 pe ie (Over a period of one year the car travels & distance of 9600 km. How mich does the petrol cost for the whole year? Exercise 42 1. Copy and complet the following bil (65 kg of potatoes at S0e per kg = $ 44g of beef at per kg = $720 jars of coffe at 95e per jar = 86-65 Total = § 2. A hotel manager was abe to buy loaves of bread at $4-44 per dozen, whereas the shop price was 43e per loa. How much di he sve on each oat? ‘3. John Lowe made darts history in 1984 with the frst ever perfect ‘zame played in a tournament, $l scored in just nine darts. He won 4 special prize of £100 000 from the sponsors of the tournament. His frat eight darts were six treble 0s, eble 17 and teble 18. (2) What did he score withthe ninth dart? (b) How much did he win per dart thrown, to the nearest pound?© 4. How many’ 50 ml bottles can be filled from a jar containing 7 ites 4H of liquid? y together to give 60 and which ft wo monk wih en x3 DO =» : “6 Two mumbers m and = are such that Js greater than 10 and mis tes than 8 Arrange the numbers 9, = and min orde of size, starting with th smallest T 4, One dey a thied ofthe class is absont and 16 children are present | How many children are in the class when no one is away? A. Atri leaves Manchestcr at 09:00 and travels towards London at 150 km/h, Another train leaves London for Manchester, also at © 09:00, and travels at 120 km/h. Which tran is nearer to London. Eien they moet | E 9. Aman is35 cm tr than hs daughter, who s 5 om shone than Shermer. The man was born in 1989 andi 180 al How tll is his wife? Eo na simple code A = 1, B= 2,C=3,...7=26. | Decode the following messages © wnsi20 5 9s pois S 6,9, 14,9, 19,8 F019, x7, 18, 90-7) 4 NOMA Ey . 18, (0 H5),2, 5 $),3% 19,2 [63,0022 © hexsxaese) . 21, 10085), (100+ 25). 5,284.2) Lx, 00), 1.279), 099),Exercise 43 1. Twelve caleulators cost $102, How many calculators could be bought for $7680? 2. A-car travels 38 m in 0-7 scoonds, How far does it tavel in wore wie () 2 minstes? 3. The outline ofa coin is shown below ( vy gatas NA CCaleulate the sizeof the angle, a, to the nearest 45 of a degree The diagram below shows the map of «farm which grows four ferent crops inthe regions shown, ach square represents one hectare. {@) What isthe total area of the farm? (©) What area is used forerop A? (©) What percentage of the farm is used for @ crop C i) crop D (i) crop A (iv) crop B? ', An examination is matked out ofa total of 120 marks, How many marks did Imran get i he seored 65% of the marks? 6. A man worked 7 hours per day from Monday to Friday and 4 hours overtime on Saturday, The rate of pay from Monday to Friday is $450 per hour and the overtime rat is time and half, How much did he earn during the week? 7. A man smokes 40 cigarettes a day and each packet of 20 cigarettes costs $3.48. How much does he spend on cigarettes in a whole year (of 365 days? 8. A shopkeeper buys coffee at $3.65 perky and sll it at 9Se per 100 g. How much profit does he make per kg?D9, Five 2's can make 25: 3 © (a) Use fours's to make 100 () Use three 6's 10 make 7 | (0) Use thive sto make 0 (d) Use ie S's to make 61 {@) Use four 7s to make 1 (F} Use three 8 to make 11 0, Find the missing digits op] Tp op -EE Ce Tp cr oy 78 F °nte)] °m op e +l 1s - ia Al 3 tele 3]2 A | krercise 44 $1. A special now chou on ofera $48 pr kilogram, Mrs Mann buys bl aKilopam How mach change dos se eciv i she ays witha ssno1” 2. Acup and a saucer together cost $280. The cup costs 6e more | than the saucer, How much does the cup cost? 4A garden 9m by 12 m is tobe rated with fertilizer. One cup of FFerlizcr covers an area of? and one bag of ertlzer i sulcent for 18 cups © (a) Fi tho area ofthe garden, (©) Find the number of bags of erttizer needed “4 Copy and complete the pattern below. : \ANDLNF 4 VINA VAS 7 FS Six lamp posts leat equal distances from each other along a siraght oad. If he distance between each pair of lamp posts is 20 m, how Tar it Irom the fst lamp post tothe sixth?6, An engincering firm offers all ofits workers a choice of two pay rises. Workers can choose either an 8% increase on their sles ot they’ ean accept arse of $3200, (a) A fiter earns $20800 a year. Which pay rise should he choose? () The personnel manager earns 846000 a year. Which pay rise should he choose? 1. A ship's voyage stated at 20:30 on “Tuesday and finshed at 07:00 on the nextday. How long Was the journey in hours and minutes? 8, Work out, without using calelatr: (a) 06-006 (b) 0.04 1000 (o) 04 t00 (72-5 {e) 10% of 90 we: £160. '9, In 1984 the population ofthe United States was 232 million, The population Was expected to geow by 12% by the end of the century Find the expected population atthe end ofthe century, corret to the nearest milion 10, Find to numbers which: (a) multiply to give 12 and add up 0 7 () multiply to give 42 and add up to 13. (6) multiply to give 32 and add up to 12 (4) multiply to give 48 and add up to 26 Exercise 45 1. Ina simple code A = 1, B= 2, C= 3 and so on, When the wo BAT is writen in code its total score is (2-+ 1+ 20) = 23, (a) Find the score forthe word "ZOOM (b) Find th score forthe word “ALPHABET" (6) Find a word witha seore of 4. 2. How many cubes, each of edge I em, a internal dimensions 5 em by 8 em by 3 em? aired 40 fill box with 3. A swimming pool 20-m by 12 m contains water to a uniform depth fof Lf mand I'm of water weighs 1000 kg. What isthe weight of the water inthe pool?sour 3s in any row (>) F 4 Place the following numbers in order of size, smallest Ss 0.12, 0012, 021, 0021, 043 B 5 The houses in a street are numbered from | to 6. How many times does the number 2° appear? 6, Draw a large copy ofthe square below. EERE ‘Your task isto fil up all 16 squares vsing four Is, four | and four 4's. Bach number may appear only onc | or column (1), The fist row has been dravmn already © 7. Between the times 11:57 and 12:27 the odometer of car changes from 23793 km 10 23825 ken BF —_Atwhat average speed isthe ear travelling? {Which of the shapes below can be drawn without going over any line twice and without taking the pencil from the paper? Write yes" for no! foreach shape, ‘LD ® o pc P& & [Revision exercise 3A 2: (a Cate he pend a mae er e raspberry jam in two sizes. of 30cm in 1 minute. peer (b) Calculate the time taken for a bullet to <> € teva hme pcd os — (c) Calculate the distance flown, in a time of $5 Which jar represent the beter value for © money? You are given that lke = 2201,3. The pump shows the price of petrol ina earage, ‘frotal s{o15) (218) Lives [20),010) Eerie (516) 10) One day’ I buy $20 worth of petrol: How many lttes do I buy? 4, (@) On a map, the distance between two points is 16cm, Calculate the scale of the map ifthe actual distance between the points is Bkm. (©) On another map, two points appear 1-Sem apart and ae in fact 60m apart Calculate the sale of the map, 5. In December 1999, a fatory employed 220. people, each person being paid $650 per week. (@) Catoulae the total weekly wage bill for the factory: () In January 2000, the work forve of 220 vas reduced by 10 per cent Find the number of people employed at the factory after the reduction, Also in January 2000, the weekly wage ‘of $650 was increased by 10 per ent Find the new weekly wage © (4) Cafeulate the total weekly wage bill for the factory in January 2000, (@) Calealate the ditference between the total weekly wage bills in December 1999 and January 2000, 6. The following are the fist six numbers, ‘written in onder of siz, of a patter, 4,13, 28, 48, 76,109. {@) Which of these numbers are (odd numbers, Gi) square numbers, Gi) prime numbers? (6) The difference between the frst and second sumbers, that is 13 ~ 4, i 9 between the second and the third its Derween the thitd and the fourth iti 2 Work out the diference between 8. A train traves between Milan and Pina, a 9. A school decdes o have a disco fom 8 pam 6) the foueth and the Ath, (i) the fifth and the sixth a (6) By consiering your answers in (b) the seventh and eighth numbers of the pattern [Explain tow you reached this decision (4) Use the method you have described to 4 Write down the next two terms in the 4 Following patter. 14,12, 25,43, 66, 7. The sketch 0°a clock tower is shown, soc A mode! of te tower is ma of 11020. (@) The minute hand on the tower clock is 40 cm long. What isthe length of the ‘minute hind on the model? (©) The height ofthe model i 40 om. What Js the height, in metres, of the clock sing a scale stance of 108 kn, in 45 minutes, a a steady speed. It passes through Resta 40 minutes after leaving Milan, How fas, in km, is it from Rosta to Pina? to midnight. The price ofthe tickets willbe Ne. The costs at as follows Disco ard DL. $2 Hire of hall, $5 an hour 200 cans of sot drinks at 15e each 200 packets of rips at 10e each Printing of tickets, $5 (8) What is te total cost of putting on the iso?(0) How many tickets must be sold to cover the cost? (@) 100 tickets are sol, alte dens are [sold at 206 cach and all the packets of trisps at 12eeach,ealelate the probit or Toss the school finally makes. 0. A man buys 500 pencils at 24 cents | cach. What change does he receive rom on 41, Every day at school Stephen buys rol for | 2c, evisps for 2c and a drink for 42. How © nach does he spendin dollars inthe whole schoo! year of 200 days? 12, An athlete runs 25 laps ofa track in BW minutes 10 seconds, {) How many seconds does he take to un 2S haps? (b) Hoow long does he take to run one lap, ithe runs the 25 laps ata constant speeat? IB A pile of 250 tiles is 2 m thick, What isthe thickness of one tile im em? Examination exercise 38 | 1. Copy and complete these statements Copy the flloving bill and complete it by filling inthe four Blank spaces, § rolls of wallpaper at $3.20 ach s 3 tins of paint at $ brushes at $240 cach Total Work out th dlifernce between | ! tonne = 1000 kg foe fon and one ton = 2240 Ib tonne 1b = 4548 Give your ansver tothe nearest kg [A motorist trvelled 200 km in five hours Her average speed for the fist 00k was S¢km/h, What was her average speed for the second 100 km? Work out (a) 20% of $65 (6) 37% of $400 Bz x [al= iss se] p (aj-s-4 p «-C-» worn 2: Cony and complete thes statements Be 1th number inthe answer space prime, write PRIME net to it EWcitismot prime, wit asthe product ofits pine factors. f The frst io have boon done or Jou Answer 39.2313 a7 Remi : 41. PRIME Ws 28. 196 3.15000 people attended pop concert al ofthe pid 930 cach, a thd of them paid $40 cach and the rest pd $30 each, 98 Calculate the total amount paid4. The woman is standing next to a Aood-level masker, {@) In what units must the numbers be? tees {b) Estimate the height of the woman, in the same units, = 15 $1750) (©) Write your answer to part (bin metres. 98 5, 16500 Europeans were interviewed in a survey on heart disease 3 The results show that one in five has high blood pressure, seven out of ton have high cholesterol levels, ‘one in four ia regular smoker, fone in five takes no exercise x16500 #3 (a) What percentage of the group has high blood pressure? 5 (8) How many people in the group have high cholesterol levels? “75 (6) The population of Europe is 492 milion Use the survey results (0 estimate how many people in Europe are regular smokers. (a What isthe ratio BET oF people who take no execs y wal ‘number of people Who take exercise 6. (a) Nine dots ean be aranged in a square, : 5, so 9 isa square number. “The fist three square numbers are 1, 4 and 9 Write down the next three square numbers. \5,21/28 4 (6) Six dots can be arranged ina trangle, £7, 0 6 is a triangle number ‘The fist four triangle numbers are 1,2, 6 and 10. Write down the next swo triangle numbers. = 12, (©) i Study the sums of odd numbers. Copy and film the two spaces 1 1324 Leads 1s34547 oe Gi) What do you notice about these answers.“ (i) Work owt the som of the frst 10 odd numbers. ‘Work out the sum ofthe fist 210 odd numbers (Stuy the sums of these triangle numbers, (@) Copy and fil in the two spaces ly a4 34 6=4 64m (i) Write down the next two lines ofthis pattern, 25,96 (i) What do you notice about these answers? 2.500 suelo IN 964, Mahesh and Jayraj share $72 inthe ratio 75. How much does Mahesh receive? £0 03a 8. Aroes goes 10 « bank to change $100 into ral ‘The hank takes $240 and then changes the rest of the money ata rate of $1 = 3.75 vals, [How much does Arceg receive in rials? wospage 65 Exercise 15 1. G@) 36/37 and 16/17 (6) 24-04 © -13 2a) 24-04) 0.2 2G@)03 38,08 © @) 1636) 24-04 5 (@) 65,05. 1b) No intersction page 57. Revision exercise 2 1. (a) 30,37 20 7,10 wes (©) 26.38 Zao wT 3 @7 @7 4 4 sao 9 @ixu-6=7-1 Sad oe CG 142434445044 Od pees eno TAy=6By=4s-3Cy= 10-5, Dy=3e : # sq, units 9.10.7. 2,144,210. (2) e+ 15< 200 page 68 Examination exercise 28 1 (a) 44-4 744-28 = 16 =F ()55-5x6=5 (@ 1-nx0=1F 6 6x5=6 @B Tate4 22 a} 42 a 51a) @ 14,916 Gi) square numbers ii) (14 12 4 15 417 419) 5 325 0) () 36,49, 64,81 (i). 9 Gi) PHF HE = 6. (9) 45,125, 8 fo) 32,12 (@ dort 3 Tea) 2, 11,2 (© 430-23 (29, 39) and (39, 29) 8 (a) 120, 24,20 © 1610 18 (8) 120,....0 (9 (12-14, 92-96), 46-48, 24-26) Number 1 page 70 Exercise 1 20 2. 400 3.80 46 5, 6000 6, 20000, . S0on000 —&. 8HED0 8, 200 10. 70 110 12. 00 ‘00 14. 60 15, 400 16, 700,70, (a) 720. () 5206.) 16430 (€) 500000 (e) 300090. (F) 8500 (a) 8753 (6) 3578 (@) four thousand, six hundred and twenty (b) sx hundred ane (6) twenty-five thousand, four hundred (@) six milion, eight hundred thousand (@) ewenty-one thousand, four hundred and wwentyfive 20. (a) 75423) 23574 @3T (9 104 22 (a) 13 () 26611 (©) 25790028. (a) 5.0 &) 52000 24, (a) 2058, 2136, 2142, 2290 (b) $029, $299, $329, $330. (c) 25000, 25117, 251171, 25200, 28 26. 10 2a =10,b=7 2% p= 1000, 9= 10 LS ORS 8.2 641 7.39 64 368 15000 HL 36S BSG 13, 252815.85 2, 4369 Bo. 164 page 73 Test 1 16, 324 23.7 30, 365 697k, 24, 108028, Bost Test 2 ge 74 1G) 2885 +514 2) 82 3) is 41a) 150 5.(a) 448 ro Exercise 3 6, 357 = 285 Ta? 9. (a) 4xd—a 10.(@) ~ wo page 76 Exercise 4 637 wis ery od 0) () 108 (82848 @s@+ aT 0 4T (6723 492 2120 roves 347 19,52 82 26, 30477. 5800 24, 2018 28188 (50 ws © 889 (@ 335 us as (2) 950 fo) 8x 848 W@ + O-=- O+ sT 6F o7%T &T (© 982 (a 316711, 02,031, 041 12. 0.58, 0.702, 0.75 1B. 041, 0-43, 0432 14, 06, 0.608, 061 15. 0.08, 015,02, 035, 16, O18, O81, 118, LS 17, 0061, 007,01, 07 1, 0.009, 0.025, 0.03, 02 18. CARWASH, 20a) 251) ORS — fe) 116 21. (a) 568 (HOSS) 130 22. (@) S350 (b)S015—(e) S003 (SHIN) SIZED SOO 2.) T OF @T @T page 77 Exercise 5 1.43 2.02 3.94 412 6.107 Tita 8 1s 9. 315 12.52. 13. 0.06 18176 15 36 16. 108 18, 125 page 77 Exercise 6 16 2.838 3.815 404 5. 74s 62 163, a2 41 10.30 11. 710 12.395 13 064 14, 0897 18. 0175 16, 0.236 17,0127 18 0-705, B13 20. 008 21. 0007 22218 23, 0035 24, 00086 25.95 26.1114 27032 28. 70 29. 576 30. 9.99 31, 660 321 33. 0.022 34. «200 35, 0.009 36. 00555; 37. (a) 0 () @ 5,2 Gi) $2.0 ii) 0,5, 2and page 78 Exercise 7 1108 2. 2098 3.2671 4, 21695 5.96 6231 9.18 airs 9. 0.082 wo. bt 11.436 2241 1B 136 14. 623 15 2.46 6. 84 1728 18.103 1.018 20. 401 21. 666 224i B36 24. 644 poge 79 Exercise 8 1.005, 2.015 3012 4. 0.006 6.35 Tis & 08 9. 036 1, 0.014 12.235 1382 M32 15.0126 16, 1272 18.0327 1910126 20.038 21.0088 20. 24 0.001 page 79 Exercise 9 Lad 23 3.436 44 4 625 Tis 9.70 10. 092 11305 12.62 11s 15.212 nw 18. 1500 19.03) 210s 22. 304 256 24. 078 28.014 27.0075 28.015 2s. 1.22 30. 1638 3195 B12 M88 38, 580page 80. Cross-numbers ‘PT EPDEP)® PREM EEpP* “Me bhpT Asoo © A f° z 2: misfit 7 > . Pope CEP > ba of « 7 fg [« page 81 Exercise 10 4. (a) 11,22, 11,38 (0) 12,24, 13,38 (9 7,14, 28,17, 51 (2) 9, 16, 32, 21, 63 (e) 11, 18, 36,25, 75 (©) 13,20, 40,29, 87 2. (a) 6 12,27, 20,5 (0) 3,821, 14, (©) 816,31, 4,6 (10, 20, 38,28, 7 1.2 © 12,24, 9, 32,8 3. (a) 1,22, 44, 22,54 (0) 10,25, 30, 28,7 16, 31, 62, 40,10, (a) 4,154, 31, 9,2) (e) 100, 115, 230, 208, 52 (f) 24, 39,78, $6, 4. (@) 4,16, 48,38, 19 (0) 5,25, 75,65, 24 (2) 6 36, 108, 98,49 (2) 8, 64,48, 38, 19 (9,10, 100, 300,290, 145 5. x4, squire root, 10, x26 reciprocal, +1, square, $37. +3, cube, +=2, +100, page 83 Exercise 17 1.) 142,36 @ L322 6 1200=2 x2 7.04) 3.6.9, 12 Ba) 2) 56 22ST INIT D 4 101, 151, 293 are prime 5 (a) W=22x3%3 (6) 200=2%2%2«5%5 9 1,2,3,6,9,18 2 = 2x22 IxdKS Dx3e5x5 (©) 4,812.16 (©) 10,20, 30,40 (@) 11,22, 33,44 (@) 20, 40, 60, 80 9. 12,24, Ta (@) even (b) odd (@) even Prime number | Multiple of 3 | Factor of 16 Number > 5 7 9 s ‘Oa number sp Even number (6) 50 1 @s nw? 13. (8) 2.4,6,8,10, 12 (0) 5,10, 15, 20,28, 30, @ 10 14. (4) 48, 1, 16 (6) 12,24, 36, 48 2 15a) 18 om (70 (@) 2 30 0 232 16. 12 1.6 18. (a) 6 ot ws 6 © 10 19.) 6 ©) 40 (©) 11,22 or others) (@) 2,5 (or others) 20.15 21. 21380 Aromas page 86 Exercise 12 1. Rational (v1 3.@) A4 BVT 4 (@) 6xem, rational {@) Seem, rational 71a) No page 87 Exercise 13, yaad Bah +3 (by A rational, Birational B VIB (@ Both rational (@) B (0) Gem, rational (6) 36cm, rational {@) 36 — Seem" ieratonal (0) Yeos. vSxv2=4 1. 08:00 2, 2130 3. 18:00 4, 0530 5 1940 6. 2200 7195 9083010415 M0225 A. 1830 ih jos 0650 AS OTAO.—— 16.2558, 2130 TB. HESS eee 20,000 «21. 1030 22,6020. 19K0 A. 1206 SF ons) 26. 700am, 27. 7.30pm, 28 12am, B. 445m, 3. 8.30pm. oispm, a2910am 38 114Sam. 34. 1110pm, 38 800pm. 36, noon Wi luoem, 38 400am, 38. 7.07am, 40. 113pam, a, 1215pm 42, 1230p. Bldspm 4. 420pm 45. S16am page 88 Exercise 14 Th idmins 22h 10mins 3, $Smins 4 38mins_—§ 3h 20mins 6 1h 45:ming Ade doming 8 1hsSmins 9, SSmine 10. Sh25mins UL, 1h SOmins 12 3h L4mins 13. 1h1Smins 14. 4h 3$mins 1S. 2620mins 16. 12h im Mh 18. 7h 20min 19, 3h [Sinins 20, ThOSmins 21 3h 22, 4h40mins 28 Sh 30mins 24. 2h 25mins 25. $h lOmins 26. 19h 29h 28 17h 3Omnins 29. 9h 25mins 3M. 340, page 89 Exercise 15 1. (@) 25mins (6) 4Smins—(@)_1h 6mins at 3. 0954 4.1138 5. 15mins 612 7. (a) 1ha2 mins () 2h 32mins (©) 3h 43 mins 82 9, 1407 10, (921 11, 27mins 12. 1201 page 00 Exercise 16 805 2439 4.1383 5, 2745 6 188 7.4322 9, 28224 10, 8558 11, 46300 12, 66281 14, 29515 15, 97525 page 9 Exercise 17 1 225 318 4 535 6 2202 Tam & isr10 9.r18 10. 13131 113516 23 13 3 1 siri7 1S. 2961 r 1S page 91 Exercise 18 1. 4708 2.46 4.21, 1echange 5.8 6. $80.64 7. $i4 milion 9. 521600 et iapage 92 Exercise 19 “Geyeele] *h PT stele pe ‘Se fae ‘ee “l= [e]-[= =l-]l-le] © =]-[= : ‘fe ae "CET le] EEE ER] &fele[=T mr a] 2a] =f ee fe fee 8 eem) “EE PE Ee] & fh ==)page 93 Exercise 20 Ls. 2.88 3510 4.583 55240 69S 10. $960 1S ASS ARSkE A kg 16.45m 17. 40km IK. S710. 19, 494g 20. 6g —21. S204 page 94 Exercise 21 1.8028 2,$h16 431 4529 8.8576 7. 5093 859703 981697 1.8038 11.8079 DSL 14,550 15.3294 16, $1106 17.31.23 19, 51125 20 21, $9.19 page 94 Exercise 22 1.96 2.8736 S77SS 4. S104 $1960 6572. S132 8.54575 91 $1030 10,842 TL S1203, 1 $949 S7AS 4. STOL 1S. $1234 16, $1692 17. S317 18, $902 19, S888 20. SAI page 95 Exercise 23 1.53520 -2,S5724 RL SITLSD 4, $8838. 2NIBKG $5850 7 59400 «9.5952 AMBRE IL L30SHKE 12. $276250 page 95 Exercise 24 1, S171 2. S406 3. $7796 4. siss34 5 (@) S28 () S216 (@) $480 (6) () $1620 Gi) $1053, page 97 Exercise 25 1. (@) $216) SISO (6) 2yeaes (@) S years 2, $2205 intrest; S045 3.75% annual rate page 97 Exercise 26 1. (a) S2180(b) $237620 (6) $2590.06 2 (a) $5550 (b) $6BBELG_(e) $8425.29 3. 513107.96 4 (a) $36465.19 (6) $40202-87 5. (a) $9400 () S107191.(@) SIBLIT6 6. (a) $1403 (b) S734) $107946 7. Sm211-88 page 99 Exercise 27 1. 200m 2. 500m 3.(b) 200m (©) 1km (4) 06km 465m 5. 24km 6 120m 7. ta) 28km_(b) 325km(@) 27m page 99 Exercise 28 1. 150em 2 3.28em 4. 59cm (a) Gem (b) S4em (@) S6em (4) 14em (@) 100em 6 25em page 100 Exercise 29 1. $10, $20 2, $45,815 3.3308, 550 4. $480, 86005. 26,90 6. $10, 520,530 7. S10 8 ss0 8. eis sipoge 101 Exercise 30 Ls as a9 4. 305 in, 40g in s4 2ke 16 & ikem 9. 250m 10, 32cm 1030p 253 13. S200 M4 ae 15 si75000 16, [om rage 103. Exercise 31 1528 2.6 as 4.400 S 10min 6 $480 7.8840 days 8 Dhow day TL Sours 12. Mme 13, 20hours 14 (a) $00 2400 (@) FE hours (a) 100 page 104 Exercise 32 1. $3.6 2 siv04 2 lites 4 10nows 5, 10days 628 nin 7 Ghowes £26558 9. 400 botles 10.165 in UL Ue grapefruit 12.315 francs 13. Sen 1455 es 15. (@)18b hens (O) 9days. () IWhens (d) 6 days 16. 7500 batteries 17. 18 15min 18, 1152min_ 19. 2n hours age 106 Exercise 33 1. (@) 60 (£4410 (©) BWDpeIos A) L39SE__(e) $625 ils) 027 dinars 2 (a) E3763 (O) $3968.25 (6) SOF) S3NOO fe) STIG S200 3339 4. Cheaperin UK. byS2 8.54408 6 Briain £15000, USA £16305, France £19977 7. 651 pace 107 Exercise 34 1. (0) 24hours —() 3h 7fmin_(@) TSseconds (4) hours Za) 20mis—(}30ms ADEs (G) UURKMA——_@) 79:2KM/R ( 12em)s—(@) 90m hy 25mmph_—_—(Y OF es per second 3. (a) 75k )43rkm/h (6) T's) ADDIS fe) 25x 10"ms (© 200k fg) Skin 4) 110000m —) 10000m ——(@ $6400 (@) 400m) 80M 0m ) 96000 S.(@) 3h TLmin (6) 768km/h 6 (@) 4houss27 minutes () 236kmm 7, Ahm ge 109. Exercise 35 1235 Rose 4.262 4.356 51 om woes 008 3.59 wi moss 07 ons 15.25 16.31 17.4867 18, Soo 1.2889 231182 ogTIS# 30H Dae 2 488900 2.0513 36.58 7. 63 ms de 08 wow Mise 2 ge B25 LSM AS OO 36, 7000 page 110. Exercise 36 1538 2105 S0d1 4.037 S802 87047, 901 S007 984 W007 os mol keL kas IS 81 GTI IT SIG BOLO 0.0056 1.07 )r22.683 2208 1965 -25,00714 26, 601-73 OR, 542 29, (a) 59m by 33em Lem by 29m () 195em", 18cm" Exercise 37 Los 2,345 343i 4.193 5.022 6.30127 13 & isa 9.0099 Wb mi 6140 12, 12789 ery 14.476 15,5991 16, 0:16 page 111 Exercise 38 1. 085m 2, 2400 263m 4, 025m 5. 07em 6. 20mm 7 1200m & Tonem 9. s80m 10, 015m 11, 065km 12. 250m 15, s000g 14, 220g 15, 64008 16, 3008 17, 00g 18, O4kg 19. 2000ks 20. 025 21, 500k 2 23. 0.0078 24, Ske 25.081 26. 200011 a. 28. 45001 29, 600ml 30, 3000em" 31, 204 2. 33. 91cm" 4. 06: 38. 150007 36, 0241 a7 38. Sem BOSE 40. 46m 41 00167 2. 0208'm 43. 28cm 44. 027m 45. 0788km 46.14000k¢ 47. 13008 48. 009m 49, 2900ke 50, 00197 S51. (For discussion) poge 111 Exercise 39 For discussion) 1. (@) Nelson's Column S6m (6) Mount Everest 8700m 2. (a) No ©) 3 (a) No (b) No 41a) No & 5 a) Yes () about 4 times page 113 Exercise 40 La zie 4% 4d 84 6 le 1.6 Bide 9878 He A DSe FSR Ise Se 1516 16.S089 Te, 19.5360 20,15 page 113 Exercise 41 2.85. 3. 130 years 5 7. $1035 & s2i10 10.5 page 114 Exercise 42 1, $3.25, £1480, 7, $1740 26 3. (@) double 18 (6) £11111 440 41S maz 18 8. Both same () 9.150m, 10. (a) WHAT TIME DO WE FINISH (@) SPURS ARE RUBBISH () WE ARE UNDER ATTACK page 116 Exercise 43 Lo 2. (a) Sm_(b) Sm (©) 6km a 4, (@) 40 hectares () 15 hectares 37.5%, 225% 58 6. siss.s0 7. $2518.50, 8 sss 2) +E OHS SEES G)SSHSHE oO8 10, Fromlettoright (@) 7.3 (4.3 7.86 A720 C36 680 a a apage 117 Exercise 44 1. $3.26 2.170 3.(a) 108m? (b) 3 5. 100m 6 (a) $3200. (6) 8% 7. ch 30min 8 (a) 054 (0) 40. (©) 0.004 Gd) 22 Ke) £9) LAO 9. 240 milion 10.) 4.3 (0) 7.6 (RA (a) 282 page 118 Exercise 45 1. @) © (65 2120 3. 000% 4 0012, 0021, 003,042,021 5.16 7 than 8 (a) Yes (6) No. (@) Yes (@) Yes (€) Yes tf) Yes. (g) Yes (h) No age 119. Revision exercise 3A 1, 95e for 1b 2.(@) D60Sms. (6) 165. (©) 173km 245.1 hes fa) 1:50000_{b) 1:4000000 Ea) si8000 (18 ( snis (@ SUIS ©) SUAR0 ess © fa) ) 1349,10 Gi) 4.49 Gi 13,109 ) 27 G33 (6) 148,193 (94,12 2.49) 2em (6) Sm &12km 9.) $100 (6) 500. (6) $44 prot ss un Sist 12. (@) 18105) 7245 13. bem 14, $25.60, $670, tot $5530 157k 16. 33hkmh 17.@) SI () SHB (9 S170 nage 121, Examination exercise 38 1. 13,7, 9,23 2. 43 Prime, 45 = 3° x 5, 47 Prime, 49 = 7? 3. $550000 4(@) mm (186mm (Lom Sta) to 1380 ©) 12min ——@) Us 40rd 6 ta) 16,35,36 (8) 15,21 ©) () 143459, 143+527=16 Gi) square aumbers i) 16100 Gv) 210% = 44100 (ty as629 610-16 (iy ov 15=35 Is 21=36 2.32 26 ris Handling data 1 pore 124 Exercise 1 1. @ $425 (by S150 © 9290 @ {@) 81333330 (b)Sis000 —_@) $665670 (4) $1000 (e) SI2000 3. (a) $21.600000 (4) SSo00000 —_(e) $1000000 4. (@) Smin, 34min, 10min (b) 18