Mathematics Grade 9 ANA Exemplars 2012 Memo (Afrikaans)

Downloaded from hlayiso.com JAARLIKSE NASIONALE ASSESSERING GRAAD 9 WISKUNDE MEMORANDUM STEL 1: 2012 VOORBEELD

Downloaded from hlayiso.com JAARLIKSE NASIONALE ASSESSERING 2012 GRAAD 9 WISKUNDE MEMORANDUM REËLE GETALLESTELSEL 1.1.1 4 - rasionaal (1) 1.1.2 √2 - irrasionaal (1) 1.1.3 0,2- rasionaal (1) 1.2 GETAL RËEL NIE - ONGEDEFI REËEL NIEERD 0 √ 7 7 √ 0 √7 √ √−7 √ (4) 1.3 1.3.1 (1) 0,7 = 1.3.2 (1) 0,13 = 1.3.3 (1) 2,01 = =2 1.4.1 2,5 × 10 × 7 = 1,75 × 10 (1) 2

Downloaded from hlayiso.com 1.4.2 0,007 (2) 1.4.3 1,12 × 10 × 3 × 10 = 3,36 × 10 (2) 1.5.1 1,6 (1) 1.5.2 −√5 (1) 1.6 1.6.1 0,152, 0,153, 0,154 enige een van die drie (1) 1.6.2 0,71; 0,72; 0,73; 0,74; 0,75; 0,76; 0,77 enige een van die sewe (1) 1.7.1 2 en 3 (2) 1.7.2 4 en 5 (2) 1.7.3 1 en 2 (2) 1.7.4 4 en 5 (2) NATUURLI TELGETAL HEELGE RASIONA IRRASIO REËLE KE GETAL TAL LE GETAL NALE GETAL GETAL 7 √ √ 15 √ √ 1 2 8 0,081 √ √ 2 √ √ −√16 √ √ √ 0,528 √ √ 2,6 √ √ 6 √ √ √ √ √ 2 3

Downloaded from hlayiso.com 1.9.1 0,6 < 0,625 < 0,75 < 0,8 (1) 1.9.2 0,2 < 0, 2̇ 0̇ < 0, 2̇ < 0,24 (1) 1.9.3 √0,36 < √0,366 < 0, 6̇ < 0,69 (1) 1.9.4 < − <− < (1) 1.9.5 −0, 12 < −0,11 < ̇−0,1 < −0,01̇ (1) 4

Downloaded from hlayiso.com FINANSIëLE WISKUNDE 1.1. Verkoopsprys = 22 × 1,50 = 33 (3) Wins = Verkoopsprys - kosprys = 33 − 20 = 13 1.2.1 a) 18% 75 000 = 13 500 (2) b) Belasting = 12 000 + 20% ( 97 500 − 80 000) = 12 000 + 2 100 = 14 100 (2) c) Belasting = 20 000 + 25% 30 000 = 27 500 (2) d) Belasting = 42 000 + 35% 80 000 (2) = 70 000 1.2.2 Belasbare R140 000 R100 000 R230 000 inkomste Belasting R25 000 R16 000 R45 500 1.3 Vermeerdering : 1 740 − 1500 = 240 (2) % vermeerdering = × 100 = 16 1.4 = (1 + ) = 1500(1 + 2(0,11)) = 1 830 of 5

Downloaded from hlayiso.com × × ER = = = 330 (2) Totale bedrag = 1500 + 330 = 1 830 1.5.1 Belegging = (1 + ) , = 2 750 1 + = 5 891,92 (3) 1.5.2 Rente verdien = 5 891,92 − 2 750 = 3 141,92 (1) 1.6 1.6.1 = (1 + ) × = 9500 1 + × = 24 463,29 Rente = 24 463,29 − 9 500 (4) = 14 963,29 1.6.2 = (1 + ) × = 9500 1 + × = 17 793,32 Rente = 17 793,32 − 9 500 (4) = 8293,32 1.6.3 = (1 + ) , × = 9500 1 + × = 15 956,86 Rente = 15 956,86 − 9 500 = 6456,86 (4) 1.6.4 = (1 + ) , = 9500 1 + = 16630,37 6

Downloaded from hlayiso.com Rente = 16630,37 − 9 500 = 7130,37 (4) VERHOUDING EN KOERS 1.1 Spoed = = 300 /ℎ (3) 1.2 (3) Minute 2 4 6 8 20 Koste R1,60 R3,20 4,80 6,40 R16,00 1.3 Aantal mans Tyd 5 45 9 × = = 25ℎ of Tyd geneem deur 5 mans = 45ℎ Tyd geneem deur 1 man = (45 × 5)ℎ × Tyd geneem deur 9 mans = = 25ℎ (3) 1.4 (3) Tyd Aantal ure 8 3 2 2 =8×3 = 12 of In 8 ure aantal werkers = 3 In 1 uur aantal werkers = 3 × 8 In 2 ure aantal werkers = 3 × 8 ÷ 2 = 12 7

Downloaded from hlayiso.com 1.5 (2) AANTAL kg KOSTE in R 3 24 7 = × = Koste = 56 of Koste van 3 = 24 Koste van 1 = 24 ÷ 3 Koste van 7 = 8×7 = 56 1.6.1 Direk eweredig. (1) 1.6.2 =5 (1) 1.6.3 = 5(25) = 125 (1) 1.7 KOSTE in R AANTAL APPELKOSE 5,60 15 10,08 , = , , × = (3) , = 27 1.8 , (3) Koste per = = 8,65 1.9 AANTAL kg KOSTE in R 0,35 25,10 1 = , , = = 71,714 … (3) Koste ~ 71,71 8

Downloaded from hlayiso.com 1.10 Aantal kg Koste in R 12,5 90 17,2 , = , , × = , Koste= R51,84 (3) 1.11 Afstand in Aantal 130 6,5 80 = , × , = =4 Aantal =4 (3) 1.12 AANTAL AANTAL 5 40 1 = × = (3) =8 9

Downloaded from hlayiso.com SPOED/TYD/AFSTAND 1.1 × = 120 × = 600 = ℎ =5ℎ (2) ∴ tyd is 5 ure. 1.2 × = × 8 = 600 = km/h. = 75 km/h. (2) ∴ Spoed is 75 km/h. 2. S (km/h) T (h) A (km) Kar 100 x 100x Vliegtuig 300 6-x 300(6-x) 100 + 300(6 − ) = 1200 100 + 1800 − 300 = 1200 −200 = −600 =3 Tyd geneem deur vliegtuig = (6 − 3)ℎ = 3ℎ (3) 3. = (120 × 1,5) km = 180 km , = km/h = 125 km/h , = ℎ = 3ℎ (3) 10

Downloaded from hlayiso.com 4. S (km/h) T (h) A (km) Stap 5 0,5 2,5 Fiets 0,25 0,25 = × = (5 × 0,5) km = 2,5 km × 0,25 = 2,5 , = , (3) = 10 km/h 5.1 Gemiddelde spoed = km/h (3) = 7,5 km/h 5.2 Afstand = × = (7,5 × 6) km = 45 km (1) 6 × = (3) ( + 20) = t= ℎ 11

Downloaded from hlayiso.com EKSPONENTE 1 1.1 99 × 1001 = 99 × 1 = 99 (1) 1.2 × = = (1) 1.3 (2) = = 1.4 = ( ) (3) = −8 1.5 = = =2 (3) 1.6 . . . . . . = . = =3 (4) = 1.7 (2 )× = (2 )× = = 10 10 = (3) 1.8 ( )( ) = = = (1) 1.9 ( . . )÷ = ÷ = (2) 1.10 × (3) ( ) = = 27 = 27 12

Downloaded from hlayiso.com PATRONE, FUNKSIES EN ALGEBRA 1. 1.1 90 en 69 (2) 1.2 36; 72; 108 ; 144; 180 ; 216 (2) 1.3 39; 48 (2) 1.2 2.1 Tel 6 by. (1) 2.2 =6 −3 (1) 2.3 6 − 3 = 45 (1) 6 = 48 =8 = 45 3.1 (2) Aantal 1 2 3 4 5 6 7 panele Aantal 2 3 4 5 6 7 8 pale Aantal 6 12 18 24 30 36 42 plate 3.2 = +1 (2) 3.3 =6 (2) 3.4 ( ) = 10 + 1 = 11 (2) ( ) = 6 × 10 = 60 4. INVOER REËL UITVOER 1 −2 + 3 1 2 −1 (3) 3 −3 13

Downloaded from hlayiso.com 5. INPUT REËL UITVOER −2 7 −1 1 0 2 −1 −1 1 1 2 7 (5) 6.1 = −2(0) + 6(0) − 8 = −8 (1) 6.2 = −2(−1) + 6(−1) − 8 = −2 − 6 − 8 = −16 (1) 6.3 = −2 +6 −8 (1) 6.4 = −2( + 2) + 6( + 2) − 8 = −2( + 4 + 4) + 6 + 12 − 8 = −2 −8 −8+6 +4 = −2 −2 −4 (4) 7. 7.1 =3 =1 (1) 7.2 = 3 = 27 (1) 7.3 =3 = (1) 14

Downloaded from hlayiso.com PRODUKTE 1. 1.1 6 −3−5=6 −8 (2) 1.2 5 −6 +3= − +3 (3) 1.3 5 −6 + 3 = −6 +8 (3) 1.4 −9 (2) 1.5 9 −4 (2) 1.6 3( + 2 − 3) = 3 +6 −9 (3) 1.7 −5(2 + − ) = −10 −5 +5 (3) 1.8 − 8 + 16 (3) 1.9 4 − 12 + 9 (3) 1.10 3(16 − 24 + 9) = 48 − 72 + 27 (3) 1.11 −5 +6−( + 4 + 4) (5) = −9 + 2 1.12 3 − 6 − 12 + 12 − 5 + 10 (6) = −14 + 6 + 10 1.13 (9 − 1) − ( − 1) =3 − − + (6) = + 1.14 4( − )−( + + ) =4 − − − − =3 − − (6) 1.15 − − ( − + ) = − − +2 − =2 − (6) 15

Downloaded from hlayiso.com FAKTORE 1. 1.1 4(2 + 3 ) (2) 1.2 −5(2 + 3 ) (2) 1.3 + (1) 1.4 4(6 − 3 + 4) (2) 1.5 ( − 1) (2) 1.6 −2 (1 + ) (2) 1.7 2 (4 − 5) (2) 1.8 6 ( −2 + 3) (2) 1.9 4 (2 −3 − 5) = 4 (2 − 5)( + 1) (2) 1.10 ( − ) − ( − ) = ( − )( − ) (3) 1.11 ( − )( + ) (3) 1.12 − )( + ) (2) 1.13 ( − ) = ( − )( + ) (3) 1.14 ( + )( − )=( + )( + )( − ) (3) 1.15 (4 + )(4 − ) (2) 1.16 3( −9 ) = 3( + 3 )( − 3 ) (3) 1.17 ( − 4) = ( − 2)( + 2) (3) 1.18 (4 − ) = (2 − )(2 + ) (3) of ( )( ) = 2. 2.1 (97 − 3)(97 + 3) = (94)(100) = 9400 (2) 2.2 (101 − 100)(101 + 100) = 1(201) = 201 (2) 2.3 (55 − 25)(55 + 25) = (30)(80) = 2400 (2) 2.4 (20,5 − 15,5)(20,5 + 15,5) = (5)(36) = 180 (2) 16

Downloaded from hlayiso.com VERGELYKINGS 1. 1.1 6 = 24 (2) =4 1.2 ( − 3) = 0 (3) = 0 of =3 1.3 22 + 4 = 9 − 12 7 = 16 of 16 = 7 (2) = = 1.4 × 36: 9( − 5) − 4(3 − 4 ) = 468 9 − 45 − 12 + 16 = 468 25 = 525 (3) = 21 1.5 × 15: 45 + 3 + 195 = 5(2 + 1) 48 + 195 = 10 + 5 38 = −190 = −5 (4) 1.6 5 =5 ∴ =4 (4) 1.7 2 =2 ∴− =5 (2) = −5 1. 8 3 =3 ∴ +1 =4 (2) =3 2.1 + +1+ + 2 = 78 (2) 3 + 3 = 78 3 = 75 = 25 17

Downloaded from hlayiso.com Die getalle is 25; 26; 27 2.2 OUDERDOM OUDERDOM OOR 4 JAAR Ben +4 Patrick 5 5 +4 (4) 5 + 4 = 3( + 4) 5 + 4 = 3 + 12 2 =8 =4 Ben is 4 jaar oud en Patrick is 20 jaar oud. 2.3 Oppervlakte = × −12 +6 = −6 × = ( ) = = (2 − 1) (4) 2.4 Oppervlakte = × 2 − 8 = × ( + 2) = ( ) = ( )( ) = (3) = 2( − 2) 2.5 =2 Oppervlakte = × = 32 2 × = 32 18

Downloaded from hlayiso.com 2 = 32 = 16 = ±4 =4 (want > 0) ∴ =4 en = 2(4) = 8 (5) ONGELYKHEDE 1. 1.1 (2) 1.2 • (2) 1.3 (2) • • • 1.4 (2) 19

Downloaded from hlayiso.com 1.5 • • • (2) 2. (2) 2.1 < 2 en ∈ (2) 2.2 3≤ ≤ 7 en ∈ (2) 2.3 √3 ≤ < 2,1 en ∈ (2) 2.4 −3 ≤ ≤ 0 en ∈ of −4 < < 1 en ∈ (2) 2.5 < −2 of ≥0 ∈ (2) ALGEBRA ̈ ESE BREUKE 1. 1.1 2 (2) 1.2 − (2) 1.3 × × = (5) 1.4 ( ) ( ) (5) × × ( ) ( )( ) = ( ) 1.5 + = = (1) 20

Downloaded from hlayiso.com 1.6 ( ) ( ) (3) = = 1.7 ( ) ( ) (4) = = ( ) = ( ) = 1.8 ( ) ( )( ) (4) = ( )( ) ( )( ) =( )( ) 21

Downloaded from hlayiso.com GRAFIEKE 1. 1.1 2 3 (4) 22

Downloaded from hlayiso.com 1.2 y   23 x  1 3 2 (4) 2. 2.1 = −2 − 2 (2) 2.2 = −2 + 3 (2) 2.3 = +1 (2) 23

Downloaded from hlayiso.com 3. (3) Y 8 7 x  3 6 5 y  x 1 4 3 3y  x  3 2 B 1 A  -5 -4 -3 -2 -1 0 1 2 3 4 X  C 4. =2 +2 (3) 24

Downloaded from hlayiso.com RUIMTE EN VORM 1.1 A. Trapesium B. Oktogoon/agthoek C. Driehoek D. Reghoek E. Parallellogram (5) 1.2 A. Silinder B. Reghoekige-basis piramide C. Kubus D. Driehoekige piramide (4) 2.1 (1) 2.2 70° Oos van Noord of 20° Noord van Oos of 70° Noord (2) 3. In ∆ en ∆ = = 90° ( gegee) is gemeenskaplik = (gegee) ∴∆ ≡∆ ( 90°, , ) (5) 4. + = (Pyth) + (3) = (5) = 25 − 9 ℎ = 16 ℎ =4e ℎ (5) = − = 4 − √7 = + (Pyth) =7+9 ℎ = 16 ℎ =4 ℎ 25

Downloaded from hlayiso.com 5. + = 180° (ko-binne < , KL||NM) + 120° = 180° = 60° + + = 180° (som van< van ∆) Maar = (< teenoor gelyke sye van ∆) +2 = 180° 60° + 2 = 180° 2 = 120° ∴ = 60° + + = 180° (som van< van ∆) maar = (< teenoor gelyke sye van ∆) +2 = 180° 120° + 2 = 180° 2 = 60° ∴ = 30° + + = 180° (Suppl.< <) 60° + + 30° = 180° = 180° − 90° = 90° (4) 6. = (< teenoor gelyke sye) 40° + + = 180° (som van< van ∆) 2 = 180° − 40° 2 = 140° = 70° = = 70° (verw < , || ) + = 180° (Suppl.< <) = 180° − 70° (6) = 110° 26

Downloaded from hlayiso.com 7.1 In ∆ en ∆ (4) = (gemeenskaplike sy) = (verw. < , || ) = (verw. < , || ) ∴∆ ≡∆ (<, <, ) ∴ = = (ooreenk sye van kongruente ∆ ) 7.2 In ∆ en ∆ (4) = (bewys) = (verw < , || ) = (verw. < , || ) ∴∆ ≡∆ (<, <, ) ∴ = = (ooreenk sye van kongruente ∆ ) 7.3 Die hoeklyne van ‘n parallelogram halveer mekaar (1) 8. = = = (ewer. sye van gelykvormige (6) vierhoeke) = × = = 2,25 = × = = 24 (6) 9. In ∆ en ∆ = (verw < || ) = (verw < , || ) 27

Downloaded from hlayiso.com = ( regoorstaande < ) ∆ ||| ∆ (<, <, <) (5) ∴ = = ∆ (ewer. sye van gelykvormige ∆ ) ∴ = =9 , = = 7,5 = + = 2,5 + 7,5 = 10 TRANSFORMASIES 1. (1) 1.1 (−1; −4) (1) 1.2 (3; −6) (1) 1.3 (−3; −4) (1) 1.4 (−4; 3) (4) 2. Refleksie in die Y-as Vertikale translasie (2) 3.1 Refleksie in die Y-as. (4) 3.2 Refleksie in die Y-as en dan refleksie in die X-as of (3) refleksie in die X-as en dan refleksie in die Y-as . 4. ′(−6; 9) ; ′(3; 15) ; ′(15; −6) (1) 5.1 28

Downloaded from hlayiso.com (1) 5.2 (1) METING 1. 1.1 Oppervlakte van ∆ = ℎ = × 3 × 4 cm = 6 cm (2) 1.2 Oppervlakte van ∆ = ℎ = × 6 × 4 cm = 12 cm (3) 1.3 Oppervlakte van ABEG = ( + ) (3) 29

Downloaded from hlayiso.com = (9 + 6)4 cm = 30 cm 1.4 Oppervlakte van BDEG= × ℎ = 6 × 4 = 24 cm (3) 1.5 = + (Pyth.) = 3 + 4 cm = 9 + 16 cm = 25 cm ∴ = 5 cm 1.6.1 Omtrek van ∆ = (5 + 5 + 6) cm = 16 cm (2) 1.6.2 Omtrek van ADEG = (9 + 5 + 6 + 4) cm = 24 cm (4) 2. = + (Pyth) = 49 + 120 ℎ = 169 ℎ = 13 ℎ Area = =( × × ) ℎ = 66,36 ℎ (3) 3.1 Totale buite-oppervlakte = 2(8 × 12) + 2(12 × 18) + 2(8 × 18) cm = 912 cm (6) 3.2 Volume= × ×ℎ = (8 × 12 × 18) cm = 1728 cm (3) 4. Volume van silinder = ℎ 550 = × (5) × ℎ × ℎ= cm ×( ) ℎ = 7cm (4) 5. Volume= × ×ℎ 50 × 30 × ℎ = 24000 cm 30

Downloaded from hlayiso.com ℎ= cm × ℎ = 16 cm (3) DATAHANTERING 1. 1.1 20 30 30 40 50 50 60 70 70 70 70 80 80 90 100 (1) 1.2 1.2.1 Mediaan = 70 (1) 1.2.2 Modus = 70 (1) 1.2.3 Omvang = 100 − 20 = 80 (1) 1.2.4 Gemiddeld = = 60,67 tot 2 desimale plekke (2) 2. 2.1 24 passasiers (1) 2.2 Omvang= 70 − 1 = 69 (1) 2.3 Gemiddeld = = 26,7 = 27 (3) 2.4 OUDERDOM TELMERKIES FREKWENSIE IN JARE 1 - 13 |||| || 7 14 - 26 ||| 3 27 - 39 |||| ||| 8 40 - 70 |||| | 6 (4) 2.4.1 27-39 (1) 31

Downloaded from hlayiso.com 2.4.2 18 passasiers (1) 3. 3.1 22 (1) 3.2 Omvang= 15 − 2 = 13 (1) 3.3 SKOENGROOTTES TELMERKIES FREKWENSIE 1-5 |||| 4 6 - 10 |||| |||| || 12 11 - 15 |||| | 6 (4) 4. 4.1 18 babas (2) 4.2 15 babas (1) 4.3 11-15 maande (1) 5. (2) 5.1 DOBBLESTEEN MUNTSTUK UITKOMSTE 1 K 1K S 1S 2 K 2K S 2S 3 K 3K S 3S 4 K 4K S 4S 5 K 5K S 5S 6 K 6K S 6S (6) 32

Downloaded from hlayiso.com 5.2 1 K S 2 K S 3 K S 4 K S 5 K S 6 K S (2) 5.3.1 (1) 5.3.2 = (1) 6 (1) 6.1 (1) 6.2 (1) 6.3 = 7. (1) 7.1 = (1) 7.2 = 8. (1) 8.1 3 (1) 8.2.1 (1) 33

Downloaded from hlayiso.com 8.2.2 = (1) 8.2.3 (1) (1) 9. K K S K K S S K K S S K S S (4) 34