Wiskunde Graad 7

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Hersiening, inoefening en vaslegging – Tweede kwartaal 2022 Memorandum

Afdeling A – Telgetalle

1.1 900 1.2 HD 1.3 2 1.4 D (4)

2. 137 654; 317 654; 713 654; 731 564; 731 654 (2)

3. 661 704; 661 074; 616 470; 616 074; 166 074 (2)

4.1 630 481 = 600 000 + 30 000 + 0 + 400 + 80 + 1

4.2 5 901 286 = 5 000 000 + 900 000 + 0 + 1 000 + 200 + 80 + 6 (2) 5.1 28; 32; 36; 40; 44; 48; 52 √ Patroon: + 4 √ (2) 5.2 4 575; 4 550; 4 525; 4 500; 4 475 √ Patroon: ̶ 25 √ (2)

6.1 2 718 = (1 359 x 2) 6.2 5 674 > 5 467

6.3 32 799 > 32 797 6.4 9 452 ÷ 2 < 4 728

6.5 53 679 750 > 53 679 705 6.6 7 + 7 ÷ 7 ̶ 7 = 1 (6)

7.1 Priemgetalle = {23; 29; 31} (1)

7.2 Saamgestelde getalle (1)

7.3 𝑭𝟐𝟒 = {1; 2; 3; 4; 6; 8; 12; 24} (1)

7.4 1 x 24 2 x 12 3 x 8 4 x 6 (1)

7.5 𝑭_𝟐𝟒 = {1; 2; 3; 4; 6; 8; 12; 24} (1)

8.

Getal Naaste 5 Naaste 10 Naaste 100 Naaste 1 000 Naaste 10 000

42 748 42 750 42 750 42 700 43 000 40 000

29 567 29 565 29 570 29 600 30 000 30 000

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9.1 19 x 37 = □ x 19 □ = 37 (1)

9.2 (9 + 12) + 34 = □ + (12 + 34) □ = 19 (1)

9.3 7 x (10 + 6) = (7 x 10) + (□ x 6) □ = 7 (1)

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(2)

9.4 11 x 9 = 99 en 99 ÷ 11 = □ □ = 9 (1) 9.5 7 x (10 + 6) = 7 x 10 + □ x □ = 70 + □ = 112 □ x □ = 7 x 6 □ = 42 (1)

10.1 48 ÷ 12 + 19 4 + 19 √ = 23 √ (2)

10.2 122 ̶ 42 ÷ 3 122 ̶ 14 √ = 8 √ (2)

10.3 (97 + 35) ÷ 4 + 6 132 ÷ 4 + 6 √ = 33 + 6 √ = 39 √ (3)

10.4 16 x (19 + 21) ÷ 8 16 x 40 ÷ 8 √ = 640 ÷ 8 √ = 80 √ (3)

10.5 9 + 9 ̶ 9 x 9 ÷ 9 9 + 9 ̶ 9 x 1 √ = 9 + 9 ̶ 9 √ = 9 √ (3)

11.1 724 832 (1) 11.2 296 684 (1)

11.3 8074 11.4 205 √

x 39 19 √𝟑𝟖𝟗𝟓

72666 √ ̶ 38 √

+ 242220 √ 09

314886 √ (3) ̶ 0 √

95

̶ 95 √ (4)

12.1 12 12.2 20 (2)

13.1 1 13.2 12 (2)

14.1 2 : 3 14.2 2 : 5 : 7 (2)

14.3 6 : 2 : 4 → 3 : 1 : 2 (1)

14.4 5 pakkies lekkers kos R45. ∴ 1 pakkie kos R45 ÷ 5 √ = R9 √

9 pakkies lekkers kos dan R9 x 9 √ = R81 √ (4)

14.5 R100 vir 500 g beteken R200 vir 1 kg wors √

∴ kos 5 kg → R200 x 5 kg √ = R1 000 √ (3)

Afdeling B – Eksponente

1.1 𝟒^𝟐 = 4 x 4 √ = 16 √ 1.2 𝟑^𝟒 = 3 x 3 x 3 x 3 √ = 81 √

1.3 𝟏𝟎^𝟑 = 10 x 10 x 10 √ = 1 000 √ 1.4 𝟎^𝟓 = 0 x 0 x 0 x 0 x 0 √ = 0 √ (8)

2.1 2 x 2 x 2 = 𝟐^𝟑 2.2 2 x 3 x 2 x 3 = 𝟐^𝟐 x 𝟑^𝟐

2.3 7 x 7 = 𝟕^𝟐 2.4 6 x 6 x 6 x 4 = 𝟔^𝟑 x 4 (4)

(3)

3.1 8 3.2 9 3.3 11 3.4 144

3.5 900 3.6 2 3.7 216 3.8 0 (8)

4.1 √𝟏𝟔 Daarom 16 = 2 x 2 x 2 x 2 = 𝟐^𝟒 √ (3)

2 16

2 8

2 4

2 2

1

√ √

4.2 √𝟖𝟏 Daarom 81 = 3 x 3 x 3 x 3 = 𝟑^𝟒 √ (3)

3 81

3 27

3 9

3 3

1

√ √

4.3 √𝟏𝟐𝟓 Daarom 125 = 5 x 5 x 5 = 𝟓^𝟑 √ (3)

5 125

5 25

5 5

1

√ √

5.1 √𝟑𝟔 + 𝟔𝟒 = √𝟏𝟎𝟎 √ = 10 √ (2)

5.2 √𝟐𝟓 + √𝟒𝟗 = 5 + 7 √ = 12 √ (2)

5.3 √𝟏𝟎𝟎 𝐱 𝟒 = √𝟒𝟎𝟎 √ = 20 √ (2)

5.4 √𝟔^𝟐 = √𝟑𝟔 √ = 6 √ (2)

5.5 ^𝟑√𝟏 + 𝟕 = √𝟖^𝟑 √ = 2 √ (2)

5.6 ^𝟑√𝟔𝟒 − ^𝟑√𝟏 = 4 ̶ 1 √ = 3 √ (2)

6.1 𝟑^𝟐 + 𝟑^𝟑 = 9 + 27 √ = 36 √ 6.2 𝟒^𝟑 − 𝟑^𝟑 = 64 ̶ 27 √ = 37 √ 6.3 𝟓^𝟑 ÷ 𝟓^𝟏 = 125 ÷ 5 √ = 25 √ 6.4 𝟔^𝟐 x 𝟐^𝟑 = 36 x 8 √ = 288 √

6.5 (𝟏𝟐 − 𝟖)^𝟐 = 𝟒^𝟐 √ = 16 √ 6.6 𝟓^𝟑 ̶ √𝟐𝟕^𝟑 ÷ √𝟗 = 125 ̶ 3 ÷ 3 √ = 124 √ (12)

(4)

Afdeling C – Gewone breuke

1.1 ^𝟐_𝟑 ; _𝟏𝟐^𝟗 ; ^𝟑_𝟖 ; ^𝟓_𝟕 (1)

1.2 ^𝟔_𝟓 ; ^𝟖_𝟑 (1)

1.3 2 ^𝟏_𝟐 ; 7 ^𝟑_𝟒 ; 4 ^𝟐_𝟑

(1)

2.1 5 ^𝟑_𝟓 = ^𝟐𝟖_𝟓 2.2 8 ^𝟓_𝟔 = ^𝟓𝟑_𝟔 2.3 6 _𝟏𝟐^𝟓 = ^𝟕𝟕_𝟏𝟐 (3) 3.1 ^𝟖_𝟑 = 2 ^𝟐_𝟑 3.2 ^𝟏𝟗_𝟕 = 2 ^𝟓_𝟕 3.3 ^𝟑𝟓_𝟗 = 3 ^𝟖_𝟗 (3)

4.1 ^𝟏_𝟐 = _𝟏𝟐^𝟔 4.2 ^𝟓_𝟖 = ^𝟏𝟓_𝟐𝟒

4.3 _𝟏𝟐^𝟖 = ^𝟐_𝟑 4.4 ^𝟑𝟓_𝟒𝟓 = ^𝟕_𝟗 (4)

5. ^𝟑_𝟒 ; ^𝟒_𝟖 ; ^𝟏_𝟔 ; _𝟏𝟐^𝟕 ; ^𝟏_𝟑 ; ^𝟏𝟑_𝟐𝟒 ^𝟏𝟖_𝟐𝟒 ; ^𝟏𝟐_𝟐𝟒 ; _𝟐𝟒^𝟒 ; ^𝟏𝟒_𝟐𝟒 ; _𝟐𝟒^𝟖 ; ^𝟏𝟑_𝟐𝟒 √

^𝟑_𝟒 ; _𝟏𝟐^𝟕 ; ^𝟏𝟑_𝟐𝟒 ; ^𝟒_𝟖 ; ^𝟏_𝟑 ; ^𝟏_𝟔 √ (2)

6.1 ^𝟒_𝟓 + _𝟏𝟎^𝟗 = _𝟏𝟎^𝟖 + _𝟏𝟎^𝟗 = ^𝟏𝟕_𝟏𝟎 √ = 1 _𝟏𝟎^𝟕 √ (2) 6.2 6 ^𝟑_𝟒 + 3 ^𝟏_𝟐 = (6 + 3) + ( ^𝟑_𝟒 + ^𝟐_𝟒 ) √ = 9 + ^𝟓_𝟒 √ = 10 ^𝟏_𝟒 √ (3) 6.3 ^𝟓_𝟔 ̶ ^𝟑_𝟓 = ( ^𝟐𝟓_𝟑𝟎 + ^𝟏𝟖_𝟑𝟎 ) √ = _𝟑𝟎^𝟕 √ (2) 6.4 5 ^𝟕_𝟖 ̶ 4 ^𝟒_𝟔 = (5 ̶ 3) + ( ^𝟐𝟏_𝟐𝟒 ̶ ^𝟏𝟔_𝟐𝟒 ) √ = 2 + _𝟐𝟒^𝟓 √ = 2 _𝟐𝟒^𝟓 √ (3)

6.5 ^𝟓_𝟖 x 16 = ^𝟓_𝟖 x ^𝟏𝟔_𝟏 √ = ^𝟖𝟎_𝟖 √ = 10 √ (3)

6.6 4 ^𝟓_𝟔 x 3 = ^𝟐𝟗_𝟔 x ^𝟑_𝟏 √ = ^𝟖𝟕_𝟔 √ = 14 ^𝟑_𝟔 = 14 ^𝟏_𝟐 √ (3)

6.7 ^𝟔_𝟕 x ^𝟓_𝟔 = ^𝟑𝟎_𝟒𝟐 √ = ^𝟏𝟓_𝟐𝟏 = ^𝟓_𝟕 √ (2)

6.8 4 ^𝟏_𝟓 x 2 ^𝟑_𝟒 = (4 x 2) + ( ^𝟏_𝟓 x ^𝟑_𝟒 ) √ = 8 + _𝟐𝟎^𝟑 √ = 8 _𝟐𝟎^𝟑 √ (3)

(5)

6.9 ^𝟒_𝟓 ÷ ^𝟐_𝟑 = ^𝟒_𝟓 x ^𝟑_𝟐 √ = ^𝟏𝟐_𝟏𝟎 = 1 _𝟏𝟎^𝟐 = 1 ^𝟏_𝟓 √ (2) 6.10 3 ^𝟑_𝟒 ÷ 1 ^𝟏_𝟑 = ^𝟏𝟓_𝟒 x ^𝟑_𝟒 √√ = ^𝟒𝟓_𝟖 √ = 5 ^𝟓_𝟖 √ (4)

6.11 9 ^𝟑_𝟓 ̶ 2 _𝟏𝟎^𝟑 x 3 ^𝟏_𝟐 = 9 ^𝟑_𝟓 ̶ (2 x 3) + (_𝟏𝟎^𝟑 x ^𝟏_𝟐) √

= 9 ^𝟑_𝟓 ̶ 6 _𝟐𝟎^𝟒 √ = 9 ^𝟏𝟐_𝟐𝟎 ̶ 6 _𝟐𝟎^𝟒 √ = 3 _𝟐𝟎^𝟖 = 3 ^𝟐_𝟓 √ (4) 6.12 5 ^𝟐_𝟔 + 6 _𝟏𝟐^𝟕 ̶ _𝟏𝟐^𝟒 van 2 ^𝟏_𝟒 = 5 ^𝟐_𝟔 + 6 _𝟏𝟐^𝟕 ̶ _𝟏𝟐^𝟒 x 2 ^𝟏_𝟒 = 5 ^𝟐_𝟔 + 6 _𝟏𝟐^𝟕 ̶ _𝟏𝟐^𝟒 x ^𝟗_𝟒 √

= 5 ^𝟐_𝟔 + 6 _𝟏𝟐^𝟕 ̶ ^𝟑𝟔_𝟒𝟖 √ = (5 + 6) + ^𝟏𝟔_𝟒𝟖 + ^𝟐𝟖_𝟒𝟖 ̶ ^𝟑𝟔_𝟒𝟖 √ = 11 _𝟒𝟖^𝟖 = 11^𝟏_𝟔 √ (4)

Afdeling D – Desimale breuke

1.1 387,6 = 300 + 80 + 7 + 0,6 1.2 2 904,64 = 2000 + 900 + 0 + 4 + 0,6 + 0,04 1.3 76 932,457 = 70000 + 6000 + 900 + 30 + 2 + 0,4 + 0,05 + 0,007 (3)

2.1 0,6 > 0,06 2.2 0,7 < 0,77

2.3 0,84 > 0,48 2.4 0,5 = 0,50

2.5 4,108 < 4,810 2.6 101,111 > 101,011 (6)

3.1 ^𝟑_𝟓 3.2 ^𝟏_𝟐

3.3 ^𝟐𝟗_𝟓𝟎 3.4 ^𝟏_𝟖 (4)

4.1 0,8 4.2 0,26

4.3 0,45 4.4 0,75

4.5 5,9 4.6 8,52

4.7 15,168 (5)

5.1 7,9; 8,3; 8,7; 9,1; 9,5; 9,9 Patroon: + 0,4 (2)

5.2 0,52; 0,59; 0,66; 0,73; 0,8; 0,87 Patroon: + 0,07 (2)

5.3 3,835; 3,843; 3,851; 3,859; 3,867; 3,875 Patroon: + 0,008 (2)

6.1 ^𝟓𝟑_𝟏𝟎 6.2 ^𝟏𝟒𝟖_𝟏𝟎𝟎

6.3 ^{𝟔𝟑𝟕𝟓}_{𝟏𝟎𝟎𝟎} (3)

(6)

7.

Getal Tiene Ene Tiendes Honderdstes

14,513 14,000 15,000 14,500 14,510

19,876 20,000 20,000 19,900 19,880

12,007 12,000 12,000 12,000 12,010

(6) 8.1 0,8 + 4,09 + 8,264 0,800

4,090 + 8,264 √

13154 √ (2)

8.2 11,02 + 0,426 + 3,8 11,020 0,426 + 3,800 √

15246 √ (2)

8.3 29,35 ̶ 18,974 29,350

̶ 18,974 √

10,376 √ (2)

8.4 531,457 ̶ 291,76 531,457

̶ 291,760 √

239,697 √ (2)

9.1 43,2 x 3,4 43,2

x 3,4 √

146,88 √ (2)

9.2 7,43 x 0,35 7,43

x 0,35 √

2,6005 √ (2)

9.3 6,018 ÷ 3 2,006 √

3 √𝟔, 𝟎𝟏𝟖 ̶ 6 √ 0 ̶ 0 √ 01 ̶ 0 √ 18

̶ 18 (4)

(7)

9.4 9,52 ÷ 8 1,19 √ 85𝟗, 𝟓𝟐 ̶ 8 √ 1 5 ̶ 8 √ 72

̶ 72 √ (4)

Afdeling E – Funksies en verwantskappe

1.1

4 →

√𝒙

→ 2

9 → → 3

16 → → 4

25 → → 5

81 → → 9

(5) 1.2

1 →

𝟑√𝒙

→ 1

8 → → 2

27 → → 3

64 → → 4

125 → → 5

(5) 1.3

0 →

x

^𝟏_𝟑

+

^𝟏_𝟔

→

^𝟏

𝟔

1 → →

^𝟑

𝟔

2 → →

^𝟓

𝟔

3 → →

^𝟕

𝟔

4 → →

^𝟗

𝟔

(5) 1.4

0,01 →

x 0,5 + 0,25

→ 0,255

0,02 → → 0,26

0,03 → → 0,265

0,5 → → 0,5

0,75 → → 0,625

(5)

(8)

2.1

𝒙 1 2 3 4 5 12 100 𝒏

𝒚 6 12 16 24 30 72 600 𝒏 𝒙 𝟔

(4) 2.2

𝒙 1 2 3 4 8 12 18

𝒚 = (𝒙 + 2) x 3 9 12 15 18 30 42 60

(3) 2.3

𝒙 1 2 3 4 7 12 25,1

𝒚 = 𝒙 x 2 ̶ 0,2 1,8 3,8 5,8 7,8 13,8 23,8 50

(3)

Afdeling F – Heelgetalle

1.1 ̶ 9; ̶ 6; ̶ 3; 0; 3; 6; 9 (1)

1.2 ̶ 12; ̶ 10; ; ̶ 8 ; ̶ 6; ; ̶ 4; ̶ 2; 0 (1)

1.3 ̶ 20; ̶ 24; ̶ 28; ̶ 32; ̶ 36; ̶ 40 (1)

2.1 ̶ 6 < 6 2.2 7 > ̶ 7

2.3 ̶ 24 > ̶ 25 2.4 ̶ 16 < ̶ 15 (4)

3. ̶ 19; ̶ 16; ̶ 14; 13; 15; 18 (1)

4.1 7 + 9 = 16 4.2 ̶ 7 + ̶ 9 = ̶ 16

4.3 ̶ 4 + ( ̶ 5) = ̶ 9 4.4 4 + ( ̶ 5) = ̶ 1

4.5 ̶ 19 + 27 = 8 4.6 9 + ( ̶ 18) = ̶ 9 (6)

5.1 9 ̶ (5) = 9 + ( ̶ 5) = 4 5.2 ̶ 9 ̶ (5) = ̶ 9 + ( ̶ 5) = ̶ 14

5.3 9 ̶ ( ̶ 5) = 9 + (5) = 14 5.4 ̶ 9 ̶ ( ̶ 5) = ̶ 9 + (5) = ̶ 4 (4)