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Tutorial 1: (Number Systems)
Total: 30
1. Simplify:
1.1 $\sqrt{\text{100}-\text{36}}$ [1]
1.2 $\sqrt{\frac{\text{25}}{\text{49}}}$ [1]
1.3 $\sqrt{{2}^{6}{3}^{\text{15}}}$ [2]
1.4 $\sqrt{9}(\sqrt{9}+\sqrt{\text{16}})$ [3]
1.5 9² [1]
1.6 $\sqrt{a}=\text{4,}a=$ [1]
1.7 $\sqrt[3]{a}=\text{5,}a=$ [1] [10]
2. Use the 324, and answer the following questions:
2.1 Is 324 divisible by 3? Give a reason for your answer. [2]
2.2 Write 324 as the product of its prime factors [3]
324 | ||
2.3 Now determine $\sqrt{\text{324}}$ [2]
2.4 Is 324 a perfect square? Give a reason for your answer. [2] [9]
3. Determine each of the following without using your calculator.
3.1 $\sqrt{\text{81}}$ [1]
3.2 $\sqrt{\frac{\text{36}}{4}}$ [2]
3.3 $\sqrt{{3}^{2}+{4}^{2}}$ [2]
3.4 $\sqrt{\text{16}{x}^{\text{16}}}$ [2]
4. If x = 3, determine:
4.1 ${4}^{x}$ [2]
4.2 $\sqrt[x]{\text{27}}$ [2] [11]
Tutorial
I demonstrate knowledge and understanding of: | Learning outcomes | 0000 | 000 | 00 | 0 | ||
1. | natural numbers ( N ) and whole numbers ( N 0 ) | 1.1 | |||||
2. | the identification of the different types of numbers; | 1.1 | |||||
3. | compound numbers; | 1.2.6 | |||||
4. | divisibility rules; | 1.2.6 | |||||
5. | the multiples of a number; | 1.2.6 | |||||
6. | the factors of a number; | 1.2.6 | |||||
7. | prime numbers; | 1.1 | |||||
8. | prime factors; | 1.2.6 | |||||
9. | expressing a number as the product of its prime factors; | 1.2.6; 1.2.3 | |||||
10. | expressing prime factors in exponent notation; | 1.2.3 | |||||
11. | even and odd numbers; | 1.1 | |||||
12. | square roots of a number; | 1.2.7 | |||||
13. | cube roots of a number; | 1.2.7 | |||||
14. | the smallest common factor (LCM); | 1.2.6 | |||||
15. | the biggest common divider (BCD). | 1.2.6 | |||||
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Test 1: (Number Systems)
Total: 30
1. Tabulate the following:
1.1 All the prime numbers between 20 and 30. [2]
1.2 All the factors of 12. [2]
1.3 All factors of 12 which are compound numbers [2] [6]
2. Determine the smallest natural number for * so that the following number is divisible by 3. (Give a reason for your answer)
1213156*3 [2]
3. Determine the following without using your calculator.
3.1 $\sqrt{\text{36}+\text{64}}$ [2]
3.2 $\sqrt[3]{{2}^{9}}$ [2]
3.3 $\sqrt{2\frac{7}{9}}$ [3]
3.4 $\sqrt{\text{0,04}}$ [2]
3.5 $\sqrt{\text{100}-\text{36}}$ [2]
3.6 $\sqrt[3]{8\times \text{27}}$ [2]
3.7 $(\sqrt{9}{)}^{2}$ [2]
3.8 $\sqrt[3]{\text{64}-1}$ [2] [17]
4. Determine $\sqrt[3]{\text{1 728}}$ using prime factors, without using a calculator.
[5]
5. Bonus question
If (n) means n ^{n} what is the value of ((2)) ? [2]
Enrichment Exercise for the quick learner
(Learning unit 1)
Each question has five possible answers. Only one answer is correct. Place a cross (X) over the letter that indicates the correct answer.
1. If n and p are both odd, which of the following will be even?
a) np b) n ² p + 2 c) n + p +1 d) 2 n +3 p +5 e) 2 n + p
2. R 120 is divided amongst three men in the ratio 3 : 4: 9. The one with the smallest share will receive ...
a) R16 b) R20 c) R22,50 d) R24,50 e) R40
3. How many triangles are there in the figure?
a) 8 b) 12 c) 14 d) 16 e) 20
4. A decagon has 2 interior angles of 120° each. If all the remaining angles are of the same size, each angle will be equal to ...
a) 15° b) 30° c) 120° d) 150° e) 165°
5. The last digit of the number 3 ^{1993} is ....
a) 1 b) 3 c) 6 d) 7 e) 9
6. The figure below has 5 squares. If AB = 6, the area of the figure is...
a) 12 b) 20 c) 24 d) 36 e) impossible
Learning outcomes(LOs) |
LO 1 |
Numbers, Operations and RelationshipsThe learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems. |
Assessment standards(ASs) |
We know this when the learner : |
1.1 describes and illustrates the historical and cultural development of numbers; |
1.2 recognises, classifies and represents the following numbers in order to describe and compare them:1.2.3 numbers written in exponent form; including squares and cubes of natural numbers and their square roots and cube roots;1.2.6 multiples and factors;1.2.7 irrational numbers in the context of measurement (e.g. square and cube roots on non-perfect squares and cubes); |
1.6 estimates and calculates by selecting suitable steps for solving problems that involve the following:1.6.2 multiple steps with rational numbers (including division with fractions and decimals);1.6.3 exponents. |
1.1 48 = 2 ^{4} × 3; 60 = 2² × 3 × 5; 450 = 2 x 3² x 5²;
P 48 = {2, 3}; P 60 = {2, 3, 5}; P 450 = {2, 3, 5};
2.1 i)== (2 ^{10} )
= 2 ^{5}
= 32
ii)== (2³ x 5³)
= 2 x 5
= 10
2.2 a) 36
b) 192
c) 1
d) 1
e) 2
f) 17
g) 63
h) 9
i) 10
j) 4
k) 27
l) 8 x ^{6}
1.1= (2 ^{12} )
= 2 ^{4}
= 16
1.2= (2 ^{4} x 3 ^{4} )
= 2 x 3
= 6
2.1= 3² = 9
2.2 5a²b ^{5}
2.3=x 3 =
= 1,2
2.4: 4 + 64 = 68
2.7 () ^{2} = 54
2.8= 36
21. LCM : Lowest common multiple
LCM of 2, 6, 12 :
24 HCF : Highest common factor
HCF of 24 and 48 :
2. 38 = 2 x 19
57 = 3 x 19
95 = 5 x 19
HCF = 19
LCM = 19 x 2 x 3 x 5
= 570
TUTORIAL 1
1.1= 8
1.2
1.7 :125
2.1 :3 + 2 + 4 = 9
9 ÷ 3 = 3 Yes!
2.2: 324 = 2² x 3 ^{4}
2.3:= (2² x 3 ^{4} )
= 2 x 3²
= 18
2.4: Yes! 18 x 18 = 324 /18² = 324
3.3: $\sqrt{9+\text{16}}$ = $\sqrt{\text{25}}$ = 5
3.4: 4 ${x}^{8}$
1. d
2. c
3. d
4. $\frac{\text{180}(\text{10}-2)}{\text{10}}$ = 144º (one angle) (1 440 – 240) ÷ 8 = 150 ( d )
5. b 3 ^{1992} ends on 1
6. d AB = 6
(2 x ) ^{2} + x ^{2} = 36
4 x ^{2} + x ^{2} = 36
5 x ^{2} = 36
TEST 1
2. :* 2 1 + 2 + 1 + 3 + 1 + 5 + 6 + 3 = 22
3.1 $\sqrt{\text{100}}$ = 10
3.2 2 ^{3} = 8
3.3 $\sqrt{\frac{\text{25}}{9}}$ = $\frac{5}{3}$ = 1 $\frac{2}{3}$
3.4 $\sqrt{\frac{4}{\text{100}}}$ = $\frac{2}{\text{10}}$ = 0,2 / $\frac{1}{5}$
3.5 $\sqrt{\text{64}}$ = 8
4. $\sqrt[3]{{2}^{6}{\mathrm{x3}}^{3}}$ = 2 ^{2} x 3
= 4 x 3
= 12
5. (2) = 2 ^{2} = 4
(4) = 4 ^{4} = 256
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