1.5 Division in algebra

3.2 Write down the coefficient of p. ......................... [1]

3.3 Write down the exponent of p . ......................... [1]

3.4 What is the reciprocal of -5? ......................... [1]

[4]

4.

4.1 Determine by how much 7 a + 5 b + 9 c is bigger than 2 c + 3 a - 7 c . [3]

4.2 Determine by how much n + 3 m + 3 k is smaller than -3 k - 7 m + 2 n [3]

4.3 Subtract $x$ ² - 2 $x$ + 4 from 5 c ² + 6 $x$ - 9 [3]

[9]

5. Write down an algebraic expression for each of the following.

5.1: 23 m reduced by the square of n ........................... [2]

5.2 Subtract the product of m and n from the difference between m and n . [2]

5.3 You have twenty coins. y of them are fifty-cent coins and the rest are ten-cent coins.

5.3.1 how many ten-cent coins do you have (in terms of y ) [1]

5.3.2 What is the total value of your money? [2]

[7]

6. Complete the following tables and give a formula for each in the form y = ......

6.1 y = .................................................. [3]

6.2 y = .................................................. [4]

[7]

7. Bonus question

Study the following pattern:

1 = 1 x 1

1 + 3 = 2 x 2

1 + 3 + 5 = 3 x 3

1 + 3 + 5 + 7 = 4 x 4

Now determine:

1 + 3 + 5 + 7 + 9 + ..... + 21 + 23 + 25 + 27 + 29

2]

Enrichment exercise for the quick learner

1. If p  q means 3 p + q ² , (3  4)  5 will be equal to...

a) 60 b) 100 c) 87 d) 72 e) 91

2. In the multiplication shown, S and T are different digits between 1 and 9. The value of S + T is ...

S 6

x 2 T

2 1 5 0

a) 13 b) 14 c) 15 d) 16 e) 17

3. How many digits are there in 5 ⁸ ?

a) 2 b) 5 c) 6 d) 8 e) 40

4. The average of the numbers 0,1 ; 0,11 and 0,111 is ...

a) 0,041 b) 0,107 c) 0,11 d) 0,1111 e) 0,17

5. In a certain class ¹ / ₃ of the pupils are girls. If 6 boys represent one quarter of the number of boys in the class, how many pupils are there in the class?

a) 18 b) 24 c) 27 d) 32 e) 36

6. If ½ - x = x - ¹ / ₃ , x will be equal to...

a) ¹ / ₁₂ b) ¹ / ₆ c) ⁵ / ₁₂ d) ⁵ / ₆ e) ³ / ₁₂

7. Calculate the value of x if .....

a) 4 b) 2

Memorandum

Classwork assignment 1

• 2 m ³
• $\frac{{\mathrm{5y}}^4}{p^3}$
• $\frac{8}{m^2}$
• $\frac{4\left(\text{32}{m}^{\text{10}}\right)}{{\mathrm{2m}}^4}$ = 64 m ⁶

1.5 a ⁴

1.6 $\frac{\text{20}{b}^{2}c}{3}$

2. $\frac{\mathrm{4a}}{3}$ – 2 b

2.1.1 $\frac{\mathrm{1a}}{5}$

2.1.2 $\frac{{\mathrm{2a}}^2}{5}$ – 3

• a – 4 b + 6 c
• $\frac{2}{b^2}$ – 5 a ² b ² c ⁴ + $\frac{{\mathrm{9b}}^5{c}^7}{a^2}$
• $\frac{-{\text{mpq}}^5}{n^3}$ + $\frac{{\mathrm{7m}}^5{n}^4}{q^4}$ + $\frac{{\mathrm{5p}}^6{q}^8}{{\text{mn}}^3}$

HOMEWORK ASSIGNMENT 1

1.1 $\frac{{\mathrm{7p}}^7{q}^3}{{\text{mn}}^3}$

1.2 $\frac{-{\text{ac}}^2}{b}$ + $\frac{\text{12}{a}^3{b}^5}{c^2}$ – $\frac{{\mathrm{8a}}^2}{c^2}$

1.3 $\frac{{\mathrm{5a}}^2}{2}$ – $\frac{\text{25}b}{2}$

= $\left(\frac{{\mathrm{5a}}^2-\text{25}b}{2}\right)$

1.4 $\frac{a^6{b}^6\text{.}{a}^4{b}^8}{a^2{b}^3}$

= $a^8{b}^{\text{11}}$

1.5 $\frac{3\left(\text{16}{k}^2{p}^8\right)}{{\mathrm{2k}}^3{p}^2}$

= $\frac{\text{24}{p}^6}{k}$

• 6 ab ² + 12 a ² – (6 ab )
• $\frac{\mathrm{3b}}{2}$ + $\frac{\mathrm{3a}}{b}$
• $\frac{3{\text{ab}}^2+{\mathrm{6a}}^2+2\text{ab}}{4\text{ab}}$

= $\frac{\mathrm{3b}}{4}$ + $\frac{\mathrm{3a}}{\mathrm{2b}}$ + $\frac{1}{2}$

3. $\frac{-5\text{ab}+\text{15}{a}^4{b}^7}{{\mathrm{5a}}^3{b}^2}$ = – $\frac{1}{a^{2}b}$ + 3 ab ⁵

TUTORIAL

QUESTION 1

A.1. False: x

1. True
2. True
3. True
4. False: 2
5. True
6. False: 5 base
7. False
8. False
9. False: 4 y ²
10. False: 7 x – 14 y
11. False: 5 x ²
12. True
13. True

B.1. 3 b

2. a + b

QUESTION 2

1. 7; 10; 16; 28

1. (150 x 3) + 1 = 451
2. (1 000 – 1) ÷ 3 = 333

QUESTION 3

A.1. 2(3)[3(–2) + 5(6)]

= 6[–6 + 30]

= 6[+24] = 144

2. $\frac{3-(-2)-(6)}{(-2)-(6)}$ or $\frac{3+2-6}{-2-6}$

= $\frac{-1}{-8}$ = $\frac{1}{8}$

B.1. 6 a – 5 b

2. 2 x – 4 y – 1

QUESTION 4

1. 4 a ² b c – ab ² c
2. 15 a ⁵ – 6 a ⁵ = 9 a ⁵
3. 12 a ⁴ b ⁶ (– a ³ b ³ )

= –12 a ⁷ b ⁹

1. –15 a ³ b ² + 20 ab ³
2. 14 a ² + 8 a – 3 a – 9 a ² + 4 a ² + a

= 9 a ² + 6 a

6. $\frac{{\mathrm{9a}}^2{b}^2\text{.}{\mathrm{8a}}^3}{{\mathrm{4a}}^2{b}^2}$ = 18 a ³

7. $\frac{14^2{a}^{a4}{b}^{b3}}{b{c}_1}$ x $\frac{12^2{c}^{4\mathrm{c2}}}{-7a^3{b}^2}$

= -4 abc ²

QUESTION 5

5.1 $\frac{a^{2}b+5{\text{ab}}^2-6\text{ab}}{\text{ab}}$

= a + 5 b – 6

5.2 $\frac{{\mathrm{3a}}^{2}b+\text{15}{\text{ab}}^2-\text{18}\text{ab}}{\text{ab}}$

= 3 a + 15 b – 18

5.3 $\frac{a^{2}b+5{\text{ab}}^2-5\text{ab}}{\text{ab}}$

= a + 5 b – 5

TEST

• 4 a ² b c – 17 ab ² c
• 15 a ⁵ – 15 a ⁵ = 0
• 7 ab + 4 ab = 11 ab
• 3(8 a ⁶ b ⁹ ) (– a ⁶ b ⁶ )

= –24 a ¹² b ¹⁵

• –7 a ³ b ² + 35 ab ³
• 15 a ² + 25 a – 4 a –8 a ² + 6 a ²

=13 a ² + 21 a

• 3(3)[2(–2) + 4(6)]

= 9 [–4 + 24]

= 180

2.2 $\frac{3-(-2)-(6)}{(-2)+(6)}$

= $\frac{3+2-6}{-2+6}$

= $\frac{0}{4}$ = 0

2.3 $\frac{3(6)}{(3)(-2)(6)}$

= $\frac{\text{18}}{-\text{36}}$

= – $\frac{1}{2}$

2.4 $\frac{9(3{)}^{5^{{}^{3^2}}}}{-3(3{)}^3}$

= $\frac{9(\stackrel{3}{9)}}{-3}$

= –27

• 3
• –5
• 1
• $-\frac{1}{5}$

• 7 a + 5 b + 9 c – (2 c + 3 a – 7 c )

= 7 a + 5 b + 9 c – 2 c + 3 a – 7 c

= 4 a + 5 b + 14 c

• –3 k – 7 m + 2 n – ( n + 3 m 3 k )

= –3 k – 7 m + 2 n – n + 3 m 3 k

= –6 k – 10 m + n

• 5 x ² + 6 x – 9 – ( x ² – 2 x + 4)

= 5 x ² + 6 x – 9 – x ² – 2 x + 4

= 4 c ² + 8 x – 13

• 23 m – n ²
• ( m – n ) – mn

• 20 – y
• 50 y – 10(20 – y )

= 50 y – 200 + 10 y

= 60 y – 200

• y = x ²

49; 81; 100; 225

• y = 3 x + 2

17; 29; 18

7. 15 ² = 225

Enrichment exercise

1. b
2. a
3. c
4. b
5. e
6. c
7. d