Acknowledgement

What I have learn from this assignment. I learn to create blog and familiarize with its features : post, edit. customize the background, edit profile, edit font and size and etc. This is my first time doing blog. I create this blog learning from Youtube and also learning from My Friends and My Lecturer.

A big thank to Miss Nadhirah, from My Friends who have been helping me to complete my assignments. With Allah guides and permission as well as helping hands and taughts from my friend, I am able to complete the blog before the  dateline

Stem and Leaf Diagrams

linear Inequalities

Introduction to Logarithms

Representation of data

Example:-

1. 21, 22, 26, 27, 18, 5, 7, 8, 35, 31, 61, 70, 44, 41, 52, 56, 57, 56, 57, 56, 58

Draw a stem and leaf diagram foe the above data

a) find the median

b) the mode

0  5 7 8

1  6 8

2  1 2 6 7

3   1 5

4  1 4

5  2 6 6 7 8

6  1                  key : 1/6

7  0                  Represent : 16

a) median

= 32 + 35 / 2

= 66/2

= 33

b) mode

= 56

2. Draw a stem and leaf diagram to represent the data below:-

23, 6, 36, 24, 21, 15, 13, 15, 3, 21, 33, 9, 17, 15, 24, 21, 35, 14, 6, 18

0  3 6 6 9

1  3 4 5 5 5

2  1 1 1 3 4 4            key: 2/1

3  3 5 6                     Represent: 21

Rules of Indices

Linear inequalities

Linear Inequalities

< Less than

> More than

≤ Less than or Equal to

≥ More than or Equal to

Open circle > < 

Close circle ≥ ≤

Example:-

1. Solve the following inequalities

a) x – 5 ≥ 2 (x + 6)

= x – 5 ≥ 2 x + 12

= x – 2x ≥ 12 + 5

= -x ≥ 17

= x ≤ 17

b) –x + 2 < 6 (x – 3)

= -x + 2< 6x – 18

= -x – 6x < -18 – 2

= -7x < -20

= x > -20/-7

= x > 2.8

2. -14 ≤ 2x

= x -14 ≤ 2

= x ≤ 2 + 14

= x ≤ 16

3. 3x – 1 ≤ 14

= 3x ≤ 14 -1

= 3x ≤ 15

= x ≤ 15/3

= x ≤ 5

    

Geometric sequences

Introduction to arithmetic sequences

Geometric Progression

Geometric progression example question:

1. write down the first five terms of the geometric progression which has first term 1 and common ratio ½

Answer:

              1^½, ½^½, ¼^½, ⅙^½, ⅛^½, 

2. find the 10th and 20th terms of the GP with first term 3 and common ratio 2.

Answer:

10th

u_n = ar ^n-1

u₁₀ = 3 x (12) ^10-1

u₁₀ = 3 x (12) ⁹

u₁₀ = 3 x 512

u₁₀ = 1536 

20th

u₂₀ = 3 x (2) ^20-1

u₂₀ = 3 x (2) ¹⁹

u₂₀ = 1572.864

3. find the 7th term of the GP 2, -6, 18

Answer:

u_n = ar ^n-1

u₇ = 2 x (-3) ^7-1

u₇ = 2 x (-3) ⁶

u₇ = 1456

Arithmetic progressions

Arithmetic progressions example question: 

1. write down the first five term of the AP with first term 8 and common difference 7 

    

   Answer:

               8th , 15th, 22nd, 29th, 36th, 

2. write down the first five terms of the AP with first term 2 and common difference -5

Answer:

            2th, -3th, -8th, -13th, -18th, 

3, find the 17th term of the AP with first term 5 and common difference 2

Answer:

a = 5

d = 2

u_n = a (n - 1) d

u₁₇ = 5 + (17 - 1) 2

u₁₇ = 5 + (16) 2

u₁₇ = 5 + 32

u₁₇ = 37

Indices

Example :-

1.   Find the values of the unknown in the following equation

a)   10k = 0.01

b)   (1/5^)h = 1

Answer:-

a) 10^k = 0.01

10^k = 1/100

10^k = 1/10^-2

10^k = 10^-2

K = -2

b) (1/5) ^h = 1

(1/5) ^{h =} (1/5) ⁰

H = 0

2.   Use the laws & properties of indices to simplify the given expressions:-

a)   2h^-2 x 4h⁵

b)   RT⁹ ÷ R^-1_T³

Answer:-

a)   2h^-2 x 4h⁵

= 8h-2+5

= 8h³

b)   RT⁹ ÷ R^-1_T³

= R^{1 - - 9} T^9-3

=R²T⁶

3.   Solve the following of indices, evaluate:-

a) 3^x = 27

b) 81 = 9^2x+3

Answer:-

a) 3^x = 27

3^x = 3³

X = 3

   

b) 81 = 9^2x+3

9² = 9^2x+3

2 = 2x + 3

2-3 = 2x

-1 = 2x

-½ = x

Logarithm

Law of Logarithm

Log_a¹ = 0

Log_a^m + log_aⁿ = log_a^{(m x n)}

Log_a^{b n} = n x log_a^b

Log_a^m – log_aⁿ = log_a(^m/n)

Example:-

1.   Write the following indices to logarithms form:-

a)   5² = 25

b)   164²

c)   125 = 5³

Answer:-

a)   Log₅²⁵ = 2

b)   Log₄¹⁶ =2

c)   Log₅¹²⁵ = 3

2.   Write is log₅⁶²⁵?

Log₅⁶²⁵ = ?

5^x = 625

5^x = 54

Log₅⁶²⁵ = 4

3.   Log₇7 + 4log₇^3-2log₇⁹

= 1 + log₇³⁴ – log₇⁹²

= 1 + log₇⁸¹ – log₇⁸¹

= 1

4.   Solve the equation:-

Log₃ (2 + x) = 4

Log₃⁴ = 2 + x

81 = 2 + x

81 – 2 + x

79 = x