NQF Level: 2 US No: 7480
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1 NQF Level: 2 US No: 7480 Assessment Guide Primry Agriculture Rtionl nd irrtionl numers nd numer systems Assessor: Workplce / Compny: Commodity: Dte: The vilility of this product is due to the finncil support of the Ntionl Deprtment of Agriculture nd the AgriSETA.
2 2 Before we strt T his ssessment guide contins ll necessry ctivities nd instructions tht will enle the ssessor nd lerner to gther evidence of the lerner s competence s required y the unit stndrd. This guide ws designed to e used y trined nd ccredited ssessor whom is registered to ssess this specific unit stndrd s per the requirements of the AgriSETA ETQA. Prior to the delivery of the progrm the fcilittor nd ssessor must fmilirise themselves with content of this guide, s well s the content of the relevnt Lerner Workook. Plese Note: This Unit Stndrd 7480 Assessment Guide must e red in conjunction with the generic Assessor Guide s prescried nd pulished y the AgriSETA. The ssessor, fcilittor nd lerner must pln the ssessment process together, in order to offer the lerner the mximum support, nd the opportunity to reflect competence. The policies nd procedures tht re required during the ppliction of this ssessment re ville on the wesite of the AgriSETA nd should e strictly dhered to. The ssessor must fmilirise him/herself with this document efore proceeding. This guide provides step-y-step instructions for the ssessment process of: Title: Demonstrte understnding of rtionl nd irrtionl numers nd numer systems US No: 7480 NQF Level: 2 Credits: 3 This unit stndrd is one of the uilding locks in the qulifiction listed elow. Plese mrk the qulifiction you re currently ssessing, ecuse tht will e determined y the context of ppliction: Title ID Numer NQF Level Credits Mrk Ntionl Certificte in Animl Production Ntionl Certificte in Mixed Frming Systems Ntionl Certificte in Plnt Production Plese mrk the lerning progrm you re enrolled in: Are you enrolled in : Y N Lernership? Skills Progrm? Short Course? Note to Assessor: If you re ssessing this module s prt of full qulifiction or lernership, plese ensure tht you hve fmilirized yourself with the content of the qulifiction.
3 3 1 SO 1 Instructions to lerner: Clculte nd estimte Lerner Guide: Pge 19 Fcilittor Guide: Pge Clculte rtionl nd irrtionl numers with nd without the use of technology x {( ) 7} ( ) 8. (9 74) x ( ) x (9800 0) x ( ) ( ) x (432 3) + (24 74) = = = 249, x 84 = {( ) 7} = 649, = ( ) = (9 74) + 63 = x 56 = = 1, ( ) x 2 = 224, = 7, (9800 0) x ( ) = undefined
4 = 4, ( ) x (432 3) + (24 74) = x = Estimte the following nswers nd round off to the nerest round figure , x 4, % of R39, % of R399, x ,83 of x % of = = , x 4,5 = % of R39,99 = 25 x 39,99 = R % of R399,99 = 33,333 x 399,99 = x 54 = ,83 of 500 = 83 x 500 = x 500 = % of =3675
5 5 2 SO 2 Instructions to lerner: Clculte nd convert Lerner Guide: Pge 32 Fcilittor Guide: Pge = Simplify the frctions: = = = = = = = = = = = = = Convert the following into percentge: , , x 100 = 25% x 100 = 33,33% ,534 = 1534 x 100 = 153,4% x 100 = 24% ,675 = 675 x 100 = 67,5% 1000
6 6 3. Convert the following frctions to deciml frctions: = 2 = 0,2 2 6 = 0, = 6 = 750 = 0, = 0, Clculte the following: c d e f g h i j k 3 / / 2 1 / / 4 7 / 8 3 / 5 11 / 2 1 / 3 15 / / 3 1 / 4 x 1 / 2 1 / 4 x 3 / 4 1 / 2 7 / 8 10 / 15 1 / 3 14 / / 5 If field is divided into 8 equl sections, nd 5 sections re plnted with cotton, wht frction of the field hs cotton growing on it? l Wht is 5 / 6 of R120? m n How fr is 2 / 3 of 42 km? 1 / 5 of 965 workers re sent ecuse of txi strikes. How mny workers re sent? How mny workers re t work? o 3 / 5 of sum of money is R 80. How much is 1 / 5 of the sum of money? Wht is the totl sum of money?
7 7 p q A frmer uys ull weighing 360 kg. A month lter the ulls weight hs incresed y 1 / 12. How much does the ull weigh now? At cttle sle ull worth R 5400 is sold t 2 / 3 of its vlue. Wht ws the sle price of the ull? 1. 3 / / 2 = 3 / / 4 = 5 / / / 4 = 2 / / 4 = 3 / / 8 3 / 5 = 35 / / 40 = 59 / / 2 1 / 3 = 33 / / 6 = 35 / / / 3 = 45 / / 12 = 89 / / 4 x 1 / 2 = 1 / / 4 x 3 / 4 = 3 / / 2 7 / 8 = 1 / 2 x 8 / 7 = 4 / / 15 1 / 3 = 10 / 15 x 3 / 1 = 2 / / / 5 = 14 / 32 x 5 / 19 = 35 / If field is divided into 8 equl sections, nd 5 sections re plnted with cotton, wht frction of the field hs cotton growing on it? 5 / Wht is 5 / 6 of R120? 5 / 6 x R120 = R How fr is 2 / 3 of 42 km? 2 / 3 x 42 km = 28 km / 5 of 965 workers re sent ecuse of txi strikes.. How mny workers re sent? 1 / 5 ox 965 = 193. How mny workers re t work? 4 / 5 x 965 = / 5 of sum of money is R 80.. How much is 1 / 5 of the sum of money? R80 x 1 / 3 = R26,67. Wht is the totl sum of money? R26,67 x 5 = R133, A frmer uys ull weighing 360 kg. A month lter the ulls weight hs incresed y 1 / 12. How much does the ull weigh now? (360 x 1 / 12 ) = 390 kg 17. At cttle sle ull worth R 5400 is sold t 2 / 3 of its vlue. Wht ws the sle price of the ull? 5400 x 2 / 3 = R3600
8 8 3 SO 2 Instructions to lerner: Clculte nd simplify Lerner Guide: Pge 36 Fcilittor Guide: Pge Work out the nswers without using clcultor ( 5 / / 3 ) x ( 1 / 3 x 1 / 2 ) 3 / / 4 x ( 1 / 2 of 2) c / 8 ( 1 / 8 x 0,5) d 1 / / 4 of (9 x ) e (72 6) 8 x f Wht 1 / 3 of 36 dded to (36 12) nd divided y ( 5 / / 3 ) x ( 1 / 3 x 1 / 2 ) = ( 15 / / 24 ) x 1 / 6 = 31 / 24 x 1 / 6 = 31 / / / 4 x ( 1 / 2 of 2) = 3 / / 4 x 1 / 2 x 2 = 3 / / 4 = 4 / 4 = 1 c / 8 ( 1 / 8 x 0,5) = 3 / / 8 ( 1 / 8 x 1 / 2 ) = 3 / / 8 1 / 16 = 48 / / 16 1 / 16 = 61 / 16 d. 1 / / 4 of (9 x ) = 1 / / 4 x 8 / 1 = 1 / / 1 = 1 / / 4 = 9 / 4 e. (72 6) 8 x = 18,5 f. 1 / 3 x 36 / 1 + (36 12) ( ) = = = Simplify the following: x 3 5 x ( ) 2 + (3 4 3) Which is the lrger frction? ) 0,379 or 3 / 8. 0,856 or 4 / 7
9 x 3 5 x = ( ) 2 + (3 4 3) 4 = = Which is the lrger frction? ) 0,379 or 3 / 8 ) 0,856 or 4 / 7 3 / 8 = 0,375, thus 0,379 is lrger 4 / 7 = 0,5714 thus 0,856 is lrger 3. Simplify the following: c c 2. 4y -2x - 4x -2y 3. 14m + 7n 2mn + n 4. (3 + 6) (- 3 6) 5. ( d 10) c + 6c (2-3 + c) 8. 16p p 9. 24k rs 4r + 5rs + 10r 11. (55c +22) (4m 4n) (-5m + 6n) c c = c 2. 4y -2x - 4x -2y = 2y -6x 3. 14m + 7n 2mn + n = 14m + 7n 2mn 4. (3 + 6) (- 3 6) = = ( d 10) 2 = d c + 6c 6 = 12c 7. 3(2-3 + c) = c 8. 16p p = 15p 9. 24k + 4 = 24k + 4
10 rs 4r + 5rs + 10r = 9rs + 6r 11. (55c +22) 11 = 5c (4m 4n) (-5m + 6n) = 4m 4n + 5m 6n = 9m 10n My Notes
11 11 4 SO 3 Instructions to lerner: Rewrite nd simplify Lerner Guide: Pge 42 Fcilittor Guide: Pge Rewrite these in scientific nottion c d e 0,009 f 147, g 0, h 0, i 456,456 j = 3, x = 2,34984 x 10 5 c = 9, x 10 8 d = 7,56 x 10 8 e. 0,009 = 9 x 10-3 f. 147, = 1, x 10 2 g. 0, = 5,648 x 10-3 h. 0, = 6,002 x 10-6 i. 456,456 = 4,56456 x 10 2 j = 8,31563 x Rewrite these in Ordinry Numers 7,413 x ,524 x 10-3 c 6,14 x 10-9 d 0,7 x 10 7
12 12 e 3,027 x 10 2 f 0,324 x 10 3 g 8,791 x 10-2 h 5,212 x ,413 x 10 4 = ,524 x 10-3 = 0, c. 6,14 x 10-9 = 0, d. 0,7 x 10 7 = e. 3,027 x 10 2 = 302,7 f. 0,324 x 10 3 = 324 g. 8,791 x 10-2 = 0,08791 h. 5,212 x 10 4 = Simplify the following without using clcultor 3,6 x 10 4 x 3 x ,25 x 10-8 x 5 x 10 7 c 1,98 x 10 8 x 6 x 10 9 d 1,05 x 10-2 x 6,4 x 10-4 e 7,34 x 10 6 x 5,24 x ,6 x 10 4 x 3 x 10 2 = 3,6 x 3 x 10 4 x 10 2 = 10,8 x 10 6 = 1,08 x ,25 x 10-8 x 5 x 10 7 = 4,25 x 5 x 10-8 x 10 7 = 21,25 x 10-1 = 2,125 c. 1,98 x 10 8 x 6 x 10 9 = 1.98 x 6 x 10 8 x 10 9 = 11,88 x = 1,188 x d. 1,05 x 10-2 x 6,4 x 10-4 = 1,05 x 6,4 x 10-2 x 10-4 = 6,27 x 10-6 e. 7,34 x 10 6 x 5,24 x 10-1 = 7,34 x 5,24 x 10 6 x 10-1 = 38,4616 x 10 5 = 3,64616 x 10 6 My Notes
13 13 5 SO 3 Instructions to lerner: Clcultions Lerner Guide: Pge 45 Fcilittor Guide: Pge In Jnury Zondi s frm mkes profit of R3 600 in the Stte Lottery. He decides to shre his profits with his rothers nd sisters. He keeps one third for himself, gives one fifth to ech of his two rothers nd the reminder to his two sisters, eqully shred. Wht frction does ech of his sisters receive? How much does ech memer of the fmily receive? Wht frction does ech of his sisters receive? Totl to sisters 1 1 / 5 1 / 3 = 15 / 15 3 / 15 5 / 15 = 7 / 15 Ech sister 7 / 15 x 1 / 2 = 7 / 30 How much does ech memer of the fmily receive? Zondi: 3600 x 1 / 3 = R1200 Ech rother: 3600 x 1 / 5 x 1 / 2 = R360 Ech sister: 3600 x 7 / 30 = R Clculte the following: c 45-9 d The temperture one morning in Dorpfontein is -5 o C. The temperture t middy rises y 10 o C nd y 7pm tht evening it hs dropped y further 12 o C. Wht ws the temperture t : ii iii middy? At 7 pm in the evening? = = -20 c = 5 d. The temperture one morning in Dorpfontein is -5 o C. The temperture t middy rises y 10 o C nd y 7pm tht evening it hs dropped y further 12 o C. Wht ws the temperture t : i. middy? 5 o C ii. At 7 pm in the evening? -17 o C
14 14 3. Pul uys the following t the locl Co-op. 2.5 l cttle R per litre 2l weed R per litre 4 gs R per g 2 m wire R per m One pcket of R Wht is the estimted totl mount of money he needs? Round off to the nerest R1. c Wht is the estimted totl mount of money he needs? Round off to the nerest R10. Wht is the estimted totl mount of money he needs? Round off to the nerest R100.. Wht is the estimted totl mount of money he needs? Round off to the nerest R1. R309. Wht is the estimted totl mount of money he needs? Round off to the nerest R10. R310 c. Wht is the estimted totl mount of money he needs? Round off to the nerest R100. R Clculte the following: x 542 c 99,97 7 d ( ) x (5 10) e ( ) x = 18324, x 542 = c. 99,97 7 = 14, d. ( ) x (5 10) = 377, x 0,5 = 188, e. ( ) x -2 = -7486,5 5. Clculte the following:. 37% of R 750. One fifth of R 927 c of R d. One qurter of R 648 e. 29,5% of R 212
15 15 f. 10 x g x % of R 750 = 37 / 100 x 750 = R262,5. One fifth of R 927 = 1 / 5 x 927 = 185,4 c of R = x R = 29486,325 d. One qurter of R 648 = 1 / 4 x 648 = R162 e. 29,5% of R 212 = 29,5 / 100 x R212 = R62,54 f. 10 x 362 = 517, g x 3 37 = 427 / 100 x 337 / 100 = / = 14, Simplify the following: c + 7 7x + 3y 4x 2y c ( c c) 4 d x 10 y c + 7 = c. 7x + 3y 4x 2y = 3x + y c. ( c c) 4 = ( c) 4 = c d. x 10 y = x 10 - y 7. Simplify the following exponents ½ c 9-2 d ( 3 2 c 4 )( 4 6 c 2 ) = = 27 x 16 = ½ = 12 c. 9-2 = 1 / 3. ( 3 2 c 4 )( 4 6 c 2 ) = 7 8 c 6
16 16 8. Clculte the following: 1 of of % of of 1 = 1 / 2 x 1 / 3 = 1 / of 1 = sme s ) ove 3 2 c. 79% of 2 = 79 / 100 x 2 / 3 = 79 / Write the following in scientific nottion: ,670 c c)0,4567 d 0, = 4,567 x ,670 = 4,567 x 10 c. 0,4567 = 4,567 x 10-1 d. 0, = 4,567 x Convert to ordinry numers 3 x ,5 x 10 9 c 3,27 x d 519,24 x 10 4 e x 10 7
17 17. x 10 4 = ,5 x 10 9 = c. 3,27 x = d. 519,24 x 10 4 = e. 67,01 x 10 7 = Simplify the following without using clcultor 5,25 x 10 4 x 2,25 x ,13 x 10-5 x 1,21 x 10 4 c 171 x 10 5 x 1,4 x 10-2 d 0,309 x 10 8 x 32,14 x 10-4 e 1,52 x 10 x 3,4 x ,25 x 10 4 x 2,25 x 10 2 = 11,8125 x 10 6 = 1,18125 x ,13 x 10-5 x 1,21 x 10 4 = 2,5773 x 10-1 c. 171 x 10 5 x 1,4 x 10-2 = 239,4 x 10 3 = 2,394 x 10 5 d. 0,309 x 10 8 x 32,14 x 10-4 = 9,93126 x 10 4 e. 1,52 x 10 x 3,4 x 10-2 = 5,168 x 10-1 My Notes
18 18 Summtive Test nd Attitude & Attriute Evlution B efore the knowledge test is undertken, the lerner must e reminded of wht is expected from him / her in terms of summtive nd reflexive competence. Red nd explin to the lerner, the Preprtion for Your Finl Assessment section in the lerner workook. Lerners nd ssessor should sign off this section to cknowledge tht this step ws completed. Plese set up knowledge test from the questions given s guideline to lerners nd supply ech lerner with test sheet. Supply ech report with the following heding: Unit Stndrd: 7480 NQF Level: 2 Lerner Nme: Questions Model Answers 1. Clculte the following with the use of clcultor. Give nswers correct to two deciml plces. 72 x 4,05 (0,576 0,532) x 67 c {( ) 5} d (9800 0) x ( ) e x 2 2. Estimte the following to the nerest whole numer 1 / 4 of 25,55 0,57 of 425 c 25% of 786 d 0,2 x 399 e x 4,05 = 291,6 (0,576 0,532) x 67 = 2,948 c {( ) 5} = - 190,4 d (9170 x 0) x (3 + 3,2) = 0 e x 2 = 4230 (5 x 1 = 5). 1 / 4 of 25,55 = 6. 0,57 of 425 = 242 c. 25% of 786 = 197 d. 0,2 x 399 = 79,8 e = 2044 (5 x 1 = 5) 3. Express the frctions in their simplest form 24 / / 35 c 2 60 / / 36 = 2 / / 35 = 17 / 35 c / 120 = 2 1 / 2 (3 x 1 = 3)
19 19 4. Convert the following decimls to percentge 15 / 40 7 / 28 c 120 / 60.. c. 15 / 40 x 100 = 37,5% 7 / 28 x 100 = 25% 120 / 60 x 100 = 200% (3 x 1 = 3) 5. Clculte the following: ¼ X ¾ ¼ of 596 c 1 / / 4 c 34 / / 10 d e) 15 / 35 9 / 5 ¼ X ¾ = 3 / 16 ¼ of 596 = 149 c 1 / / 4 = 3 / 4 d 34 / / 10 = 34 / / 20 = - 34 / 20 = -1 7 / 10 e 15 / 35 9 / 5 = 15 / 35 x 5 / 9 = 5 / 21 (5 x 1 = 5) 6. Clculte the following: 62,5% 0f km 2 / 5 of R120 c If 2 / 3 of sum of money is R90, wht ws the originl sum of money? c 62,5% 0f km 2 / 5 of R120 If 2 / 3 of sum of money is R90, wht ws the originl sum of money? 7. Use scientific nottion to clculte the following: x ,3 x 10 6 x 4 x x = 9,6 x 10 5 x 5,6 x = 53,76 x = 5,376 x ,3 x 10 6 x 4 x 10-3 = 9,2 x 10 3 (2x1)(2) 8. Simplify the following c c (2 14c) (3 + 7c) c (24m + 15n 21) 3 d 17m m e 31p Write s ordinry numers 4,567 x ,56 x 10 3 c 482 x 10-4 d 0,007 x 10 5 e x c c = c. (2 14c) (3 + 7c) = - -21c c. (24m + 15n 21) 3 = 8m + 5n - 7 d. 17m m = 16m e. 31p + 5 = 31p + 5 (5x1)(5) 4,567 x 10 5 = ,56 x 10 3 = 560 c 482 x 10-4 = 0,0482 d 0,007 x 10 5 = 700 e x 10-2 = 5600,23 f (5x1)(5)
20 Give n exmple of when it is convenient to use scientific nottion Explin why you would use scientific nottion in the exmple you hve given. When working with very lrge numers or very smll ones e.g. when quoting the numer of micro-orgnisms per cuic meter of soil. Numers re too lrge or to smll to e clculted y norml clcultor (2x2)(4) Totl: 40 mrks
21 21 Assessment Feedck Form Comments / Remrks Feedck to lerner on ssessment nd / or overll recommendtions nd ction pln for competence: Feedck from lerner to ssessor: Assessment Judgement You hve een found: Competent Not yet competent in this unit stndrd Lerner s Signture: Actions to follow: Dte: Assessor report to ETQA Lerner results nd ttendnce certifiction issued Assessor s Signture: Dte: Modertor s Signture: Dte:
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