1.1 Prime factors, square roots and cube roots  (Page 2/2)

 good  average  not so good

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]

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

Parent signature: Date :

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

Assessment

Memorandum

Class assignment 2

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

Homework assignment 2

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(8) = 16
• :13

2.7 () ² = 54

2.8= 36

• :2(9) = 18
• :9 - 27 = -18

Class assignment 3

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

• 2³ . 3 ^7,5
• :3(3 + 4) = 21
• :81
• :16

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

• :9
• : $\frac{6}{2}$ = 3

3.3: $\sqrt{9+\text{16}}$ = $\sqrt{\text{25}}$ = 5

3.4: 4 $x^8$

• :4 ³ = 64
• :3

Enrichment exercise

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

• :23, 29
• :1, 2, 3, 6, 12
• :4, 6, 12

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

• :2 x 3 = 6
• :9
• :4 – 1 = 3

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