Heelgetalle en die ordening daarvan

5. Die laaste syfer van 3 ¹⁹⁹³ is ...

6. Jy ry teen ’n konstante spoed van 105 km per uur verby telefoonpale wat ewe ver van mekaar af staan. As dit 72 sekondes neem om van die eerste tot die vyftiende paal te reis, bereken die afstand, (in meter) tussen twee opeenvolgende pale.

Assessering

Memorandum

1. “Minder as “0” nie positief nie

2.

-2 -1 0

1. Temperature; bankbalanse; ens.

4. Getalle met geen breuke of desimale daarby nie, bv. 2 nie 2½ of 2,5 nie

5. Z

KLASOPDRAG 2

2. 4 ⁰ – 8 ⁰ = –4 ⁰ C

• –13
• –5
• –27
• –8 – 5 + 7 = –6

4. Tel alle (+) getalle en (–) getalle op. Trek hulle van mekaar af.

• –9 + 6 = –3
• –18 – 13 + 7 = –14
• 20 – 75 = –55
• 10 – (–2) = 10 + 2 = 12

6. –31 – (–17) = –31 + 17 = –14

7.1 –6 + (–3) = –9

7.2 5 – (–5) = 10

HUISWERKOPDRAG 2

• 13 – 18 + 4 – 17 = –18
• –9 – (–8) + (–16)

–9 + 8 – 16 = –17

• – (–16) ² + (–3) ²

= –256 + 9

= –247

• (–13) ² – (–13)

= 169 + 13

= 179

• a – b + b = a
• a – b – a = – b
• – b – b + a = –2 b
• $y^2-x^2-x^2=y^2$

• waar
• fals
• $y+z=z+y$ waar
• $-x+y=-x+y$ waar

3.1 a = –2

3.2 a = 12

3.3 a = –3

3.4 –8 = a

4. R615 – R(46 + 480 + 199)

= R615 – R725

= R110 (–) Verlies

KLASOPDRAG 3

1. ( )

2. of

3. × of ÷ : van links na regs

4. + of – : van links na regs

• –42
• 36 + 34 = 70
• 35
• 3 x (–1) + 6 = –3 + 6 = 3
• –24 × 25 = –600
• (–2) ³ = –8
• (–64) – (+2) = –64 – 2

= –66

• (15 – 9) ² = (6) ² = 36
• (–6) ² = 36
• –2(9) = –18
• $\frac{-\text{11}}{3}$ = –3 $\frac{1}{3}$
• $\frac{\text{24}}{-\text{12}+2}$ = $\frac{\text{24}}{-\text{10}}$ = –2,4
• –6 x $\frac{5}{7}$ = $\frac{-\text{30}}{7}$ = –4 $\frac{2}{7}$
• $\frac{\text{53}}{-\text{25}}$ = –2 $\frac{3}{\text{25}}$ of –2,12

1.5 –50 ÷ 5 = –10

2. p = (–2) × (3) ÷ (–2) ²

= –6 ÷ 4

= $\frac{-6}{4}$ = –1 $\frac{1}{2}$ / –1,5

• p = 4(–2)(3) ÷ (–2)(3)

= –24 ÷ (–6)

= 4

HUISWERKOPDRAG 2

• (13) ² – (–13) ² – 13 ²

= 169 – 169 – 169 = –169

• (7 – 8) ² – (8 – 7) ² – 8 ² – 7 ²

= (–1) ² – (1) ² – 64 – 49

= +1 – 1 – 64 – 49

= –113

• (5)3 – 33 – 22

= 15 – 55

= –40

2. $\frac{-\text{147}}{-\text{21}}$ – (–55)

= 7 + 55

= 62

3. 17 x (–15) ÷ (–7)

= –255 ÷ (–7)

= 36,4

4. (–88 + 7) – (–58)

= –81 + 58

= –23

5. –7 – (–5 × 17)

= –7 + 85

= 78

• p = –60
• p = –8
• p = 7
• 2 p + 6 = –4

p = –5

7. a = 4

8. –(–3) = 3

• {–1; 0; 1; 2; 3}
• {2; 3; 4; 5}
• {–1; –2; –3}

Tutoriaal 1

1. 30; $\frac{-\text{53}}{7}$ = –7,6 √; 10; –145 √

2.1 $\eta$ = $\frac{\text{27}}{4}$ = 6 $\frac{3}{4}$

$\eta$ >6 $\frac{3}{4}$

$\eta$ $$ {7; 8; 9; . . . } √√

• {5; 4; 3; 2; 1} √
• √√
• √√

• [–(4)] ³ √ = –64 √
• –8 – 9 + 8 + 9 √ = 0 √
• 15 + (–40) √ + (–12) √ = –37 √
• $\frac{6^1}{\text{11}}$ x $\frac{1}{-24_4}$ √

= – $\frac{1}{\text{44}}$ √

• (0,09) √ x (–0,04) = –0,0036 √
• –1 √√
• 87 √√

√ √ √

4.8 –0,225 a ⁵

4.9 $\left(\frac{-12^3{a}^{ab}{b}^{4b^3}}{4a^{5}b}\right)$

√ √ √

= 9 a ² b

• [3(–1) – 3{–2)] ² √

= [–3 + 6] ²

= 9 √

• –3(–2) ³ + 3(–1) ² √

= –3(–8) + 3(1) √

= 24 + 3

= 27√

5.3 3(–2) ² √

= 3(4)

= 12 √

TOETS

• 0 √
• 1 √
• $\frac{-8^4{M}^{6^3}}{2M^3}$ - –4 M ³ √√

√ √

• –8 c ¹² d ⁹

√ √ √

• 30 p ⁵ q ⁶
• $\frac{-6^3{a}^{8^6}}{-2a^2}$ + 12 a ⁶

√ √ √

= 3 a ⁶ + 12 a ⁶ = 15 a ⁶

• –2 + 3 + 4 + 1 √ = 6 √
• –6 a ³ – 2 a ² b – 4 a ³ – 5 ab ² √

= –10 a ³ – 2 a ² b – 5 ab ² √√

√√√1.9 $\frac{k^4}{{\mathrm{3M}}^9}$

√ √ √

• –3 a ² b ² + 6 ab ² + 4 ab

√ √ √

• –3 a ⁴ + 1 $[\frac{\text{12}{a}^6}{-{\mathrm{4a}}^2}$ – $\frac{{\mathrm{4a}}^2}{-{\mathrm{4a}}^2}]$

1. –2(2 p – 3 q – 4 r ) – 3(–2 p + 3 r – 4 q ) √

= –4 p + 6 q + 8 r + 6 p – 9 r + 12 q √√

= 2 p + 18 q – r √

3. 5 a ³ b – 10 a ³ b ³ – [–6 a ² b ² (–3 a + 12 ab )] √

5 a ³ b – 10 a ³ b ³ – [18 a ³ b ² – 72 a ³ b ³ ] √

5 a ³ b – 10 a ³ b ³ – 18 a ³ b ² – 72 a ³ b ³ √

5 a ³ b – 18 a ³ b ² + 62 a ³ b ³ √

4. $\frac{-2(a+b)}{-\mathrm{3a}}$ = $\frac{-\mathrm{2a}-\mathrm{2b}}{-\mathrm{3a}}$ √

= $\frac{-2a}{-3a}$ – $\frac{\mathrm{2b}}{-\mathrm{3a}}$

= $\frac{2}{3}$ + $\frac{\mathrm{2b}}{\mathrm{3a}}$

√ √

√ √

5. x ( x + 1)( x + 2) + 1

= ( x ² + x )( x + 2) + 1

= x ³ + 2 x ² + x ² + 2 x + 1

= x ³ + 3 x + 2 x + 1

2(3)(4) + 1 = 25

4(5)(6) + 1 = 35 Onwaar

5(6)(7) + 1 = 211 Onwaar

Verrykingsoefening

1. $\frac{1}{\frac{\mathrm{3x}-1}{3}}$

= $\frac{1}{2}$

$\frac{2}{1}$ = $\frac{\mathrm{3x}-1}{3}$

6 = 3 x + 1

7 = 3 x

(2 $\frac{1}{3}$ ) $\frac{7}{3}$ = x