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CLASS ASSIGNMENT 1
1. Indicate what the following will be equal to...
1.1: 2 x 2 x 2 = ....................... (and what the exponent form will be .....................)
1.2: 2² x 2² x 2 ^{3} x 3² x 3 ^{3} = .........................
(and what the exponent form will be ......................... )
1.4: a ² x a ² x a ^{3} = .........................
Now write out a general rule for the multiplication of exponents:
1.5: 2( a - b ) = .........................
distributive law: (2 x a ) - (2 x b )
1.6: 3 ^{0} = .........................
1.7: a ( a + b ) ^{0} = .........................
Therefore: (anything) to the power of 0 = .........................
1.8: 3 ^{1} = .........................
1.9: 1 ^{200} = .........................
2. What does each of the following mean? Also provide the simplified answer for each one
2.1: a ² =
2.2: 2 a b =
2.3: -3( a + b ) =
2.4: 4( a )² =
2.5: ( a ^{3} )² =
2.6: (3 a ²) ^{3} =
2.7: 2 p x 3 p =
2.8: a b² x a ² b ^{3} x a b ^{6} =
2.9: ( $\frac{1}{2}$ a ^{3} ) ^{4} =
2.10: 2( a ^{3} )² =
2.11: 6(2 a - 3 b ) =
2.12: -7 a ( a ² - 2 b ² ) =
3. Can you recall the order of operations for the following? Write it down.
3.1 Now make use of everything you have learnt up till now to calculate the following:
3.1.1: a x a x aaa + a ^{4}
3.1.2: 2( a + b ) - 3( a - b )
3.1.3: 3 a x 2 a ² b + 5 a ² x (-3 a b )
3.1.4: -5 a ( a - b ^{3} ) + 7 a b ^{3} - 2 a ^{5}
3.1.5: -3( a ² b ^{4} )² - 5 a ^{3} (-2 a ^{4} b ²) ^{3}
4. What is the meaning of the word substitution?
Provide an example as explanation:
5. Supposing that a = 5 ; b = -1 and c = 3 , calculate the value of each of the following:
5.1: 5 a ² - 3 b
5.2: $\frac{2{\text{ab}}^{2}}{\mathrm{3a}}$
5.3: $\frac{a\text{}+\text{}\mathrm{b\xb2}}{a-b}$
5.4: (2 a b ² c )²
5.5: -3 a b ^{3} - 2 a b ^{3} c
HOMEWORK ASSIGNMENT 1
1. Simplify each of the following:
1. ( a ^{5} ) ^{6}
1.2: 5(3 a - 7 a )²
1.3: -5(3 a - 2 b )
1.4: (3 a )² . [ (2 a )² ] ^{3}
1.5: p x 2 x m x q
1.6: w ² x 3 b x ^{1} / _{3} b x w
1.7: -5 a ( 3 a - 5 a b)
1.8: (3 a )² (2 a ) + (4 a ²) (-2 a )
1.9: (5 a b ²) ^{4} - (- 6 b ^{6} a ^{4} )
1.10: -6 a ² b ( 2 a ² - 3 a b ^{3} + 5)
2. Supposing that $x$ = -2 and y = -1 , determine the value of ...
2.1: (2 y )(2 $x$ )²
2.2: -3 $x$ ^{3} - 2 y ^{5}
2.3: (2 y + 2 $x$ )²
3. Supposing m = 2 ; n = -3 en q = 5, determine the value of each of the following expressions:
3.1: m + n + q
3.2: 4 m - 2 n - 3 q
3.3: 2( m ² + q ²) - n ²
3.4: ^{m} / _{3} + ^{n} / _{4} - q
3.5: 3m( n + q ) - 2( m + n ²)
4. A challenge: See if the knowledge that you have acquired is able to help you solve the problems that follow.
4.1 The average speed of an Intercape Mainliner is 5 a ^{4} kilometres per hour.What is the distance that the bus can complete in (5 a ^{3} + 5 a - 6) hours?
4.2 Miss South Africa buys ( a - b + 2 c ) litres of milk at 4 ab rands per litre and 5 ab litres of fruit juice at (2 a + 5 b - 3 c ) rands per litre.
What will these purchases cost in total?
Assessment
Assessment of myself: | by myself: | Assessment by Teacher: | |||||||||||||
I can… | | | | 1 | 2 | 3 | 4 | Critical Outcomes | 1 | 2 | 3 | 4 | |||
write expressions in exponent form; (Lo 2.2; 1.6.3) | Critical and creative thinking | ||||||||||||||
successfully add exponents together; (Lo 2.2; 1.6.3) | Collaborating | ||||||||||||||
successfully subtract exponents from each other; (Lo 2.2; 1.6.3) | Organising en managing | ||||||||||||||
successfully multiply exponents with each other; (Lo 2.2; 2.8.3&.4) | Processing of information | ||||||||||||||
solve expressions with brackets; (Lo 2.2; 2.8.5) | Communication | ||||||||||||||
apply the correct order of calculations; (Lo 2.2; 2.8.5) | Problem solving | ||||||||||||||
determine values of expressions with substitution. (Lo 2.2; 2.8.5; 1.6.2; 1.6.3) |
Independence | ||||||||||||||
good average not so good
Comments by the learner: | My plan of action: | My marks: | ||||||
I am very satisfied with the standard of my work. | < | Date : | ||||||
I am satisfied with the steady progress I have made. | Out of: | |||||||
I have worked hard, but my achievement is not satisfactory. | Learner : | |||||||
I did not give my best. | > |
Comments by parents: | Comments by teacher: | |
Signature: Date : | Signature: Date : |
Multiply and bases are the same: you add the exponents.
1.7 :a
3.1 :1: ( )
:2: of
3: x or ÷ from left to right
4: + or – from left to right
:=-5 a ^{2} + 12 ab ^{3} + 7 ab ^{3} – 2 a ^{5}
4. put another value in unknown place
= 125 + 3 = 128
= $\frac{\text{10}}{\text{15}}$ = $\frac{2}{3}$
= $\frac{6}{6}$ = 1
= [30] ^{2} = 900
= 15 + 30 = 45
=(–2)(16) = –32
= 24 + 2 = 26
= [–2–4]
= (–6) ^{2}
= 36
= 8 + 6 – 15 = –1
= 2[4 + 25] – (–3) ^{2}
= 58 – 9 = 49
3.4 : $\frac{2}{3}$ + $\frac{-3}{4}$ – 5
= $\frac{-1}{4}$ – 5 = 5 $\frac{1}{4}$
3.5 :3(2)[–3 + 5] – 2 [2 + (–3) ^{2} ]
= 6[2] – 2[11]
= 12 – 2
= –10
= 25 a ^{7} + 25 a ^{5} – 30 a ^{4}
= 4 a ^{2} b – 4 ab ^{2} + 8 ab c + 10 a ^{2} b + 25 ab ^{2} – 15 ab c
= 14 a ^{2} b + 21 ab ^{2} – 7 ab c
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