Week 6, 7 and 8 – SS1 First Term General Mathematics Notes

WEEK 6
INDICES
INDICES: are numbers expressed in powers on ten i.e. . The analysis and simplification of indices depends on the basic interpretation and rules of indices as enumerated below.
LAWS OF INDICES

3. = 1
4. = (
5. ( =
6. =

EXAMPLES:
Write down the values of the following in index form:

1. x x 4x 2 (iii) 16 (iv) ()

SOLUTION

2. x 4x 2 = (5 x 4 x 2) = 40 =
3. = (16 = 4
4. =
5. = = = 1÷ = 1 x = or 2.25 or 2

Simplify the following:

1. x ( (b) 3÷ 6

SOLUTION

1. x = x =
2. (3÷6) = () = .

ASSESSMENT
Simplify the following questions:
(1(2)(3). x ÷ (4) -10÷ (-5) (5) x x (6)
ASSIGNMENT: MAN Mathematics for senior secondary school 1

1. Page 11 Exercise B1 numbers 8, 10, 17,20 and 30.
2. Page 12, exercise B3 e,f,I,k,r,t ,v and z
3. Page 13 exercise B4 a, b, c, d, e, g, h and i.

 
 WEEK 7 Review of first half and periodic test
Week 8
LOGARITHMS OF WHOLE NUMBERS
The logarithms of any number N to any base M is the index or power to which the base must be raised, to equal the number N.
The logarithms of any given number consist of two parts called the characteristics and the mantissa.The characteristics is a whole number which can either be positive, zero or negative integers, While the Mantissa is the decimal (fractional) part of the integers always from the table values.
EXAMOLE
399 = 2.6010. 2 Is the characteristics of the number and 6010 from table is the Mantissa or 3.99 x
Find the Logarithms of the following numbers:

1. 8615 (b) 690460 (c) 1.607

SOLUTION

1. 8615 = 8.615 x : in mathematics table, check logarithm of 86 under 1 difference 5 = 9350+3
2. 690460 = 6.90460 x
3. 1.607 = 1.607 x

ANTILOGARITHM: Is the opposite of logarithm.
Find the original number of the following logarithms numbers:

1. (b) (c) 6.3892

SOLUTION

1. = 1.862, from antilogarithm table check 27 under zero since there is no third value and the zero before the point (characteristics) determines where the point occupies in the number. Add onto every positive characteristics to determine your value
2. = 3698.0 or 3698
3. 2450000.0

MULTIPLICATION OF NUMBERS
When multiplying numbers in logarithms, their table values are been added before checking antilogarithms for its solutions.
EXAMPLE
Evaluate the following using table:

1. 143.8 x 23.46 (b) 8234 x 70000

SOLUTION
(a)143.8 x 23.46 = NUMBER LOGARITHM
143.8
23.46 +

Antilogarithm of 5280 = 3374
143.8 x 23.46 = 3374.0

 
 (b) 8234 x70000 = NO LOG
8234
70000 +
=
Antilog of 7609 = 5766 characteristics is 8+1 =9 numbers before point
8234 x70000 = 576600000
DIVISION OF NUMBERS IN LOGARITHMS: When dividing numbers in logarithms we subtract their values
EXAMPLE
Evaluate the following numbers using table:

1. 912.4 ÷ 30.42 (b) 36.75 x 284.7 ÷ 26.45

SOLUTION

1. 912.4 ÷ 30.42 = NO LOG

   912.4
   30.42 –
   =

Antilog of 4770 = 2999
912.4 ÷ 30.42 = 29.99.
(b) 36.75 x284.7 ÷26.45 = NO LOG
36.75
284.7 +

26.45 –

Antilog of 5973 =3957
36.75 x 284.7 ÷ 26.45 = 395.7
ASSESSMENT: Using table evaluate the following numbers:

1. (a)497.2 x 8.789 (b) 89 x34.56 x2.094 (c) 8050 ÷ 20.15 (d) 45.08 ÷ 5.462
2. (a) 98.45 x 56 ÷ 30.8 (b) (c)

    

3. Find the antilogarithms of the following numbers:

1. (b) (c) 0.5971 (d) 7.8903 (e) 2.0079