Week 1 – SS3 First Term Mathematics Notes

SCHEME OF WORK FOR SS3 MATHEMATICS
FIRST TERM

1. Revision: Indices and Logarithm
2. Surds
3. Surds in relation to Trigonometry
4. Matrices and Determinants
5. Linear and Quadratic Equations
6. Surface Area and Volume of Sphere and Hemispherical shapes
7. Mid-term Test
8. Longitude and Latitude
9. Longitude and Latitude
10. Arithmetic of Finance
11. Revision
12. Examination
13. Vacation

 
 
 WEEK ONE        
TOPIC: BASIC CONCEPT & APPLICATION OF LAWS OF INDICES
CONTENT:

• Basic Concept of Laws of Indices
• Application of Laws of Indices

Basic Concept of Laws of Indices
A number of the form a^m where a is a real number, a is multiplied by itself m times
The number a is called the base and the super script m is called the index (plural indices) or exponent.
1.    A ^m x A ⁿ = A^{m + n} ——————–Multiplication law
Example: X³ xX² =( X x Xx X) x (X x X) = X ⁵
Or X³ x X² = X^{3 + 2} = X⁵
2.    A^m ÷ Aⁿ=A^m-n ———————Division law
Example: X⁶ ÷ X⁴ = X^6-4 = X²
3.    (a ^m )ⁿ = a^mn —————-Power law
Example: (x³)² = X³ x X³ = X³⁺³ =X⁶
Or X^3X2 = X⁶
4.    a^m ÷ a^m = a^m-m = a⁰ =1
a^m ÷a^m = a^m/a^m = a^o = 1
a⁰………………………………….Zero Index
:. Any number raised to power zero is 1
Example: 3^o = 1, c^o = 1, y^o = 1
5.    (ab)^m =a^mb^m ————-Product power law
e.g. (2xy)²= 4x²y²
6.    Negative index        
a ^–m = 1/a^m ————- Negative Index
Example: 2 ^-1 = ½, and 3 ^-2 = 1/3 ² = 1/9
7.    a^1/n =ⁿ√a ————–Root power law
Example : 9 ^½ =√9=3

 27 ^1/3 =³√27 = 3 ie (3)³ = 3
8.    a ^m/n = (a ^1/n) ^m = (ⁿ√a)^m ———–Fraction Index
or a ^m/n = (a^m) ^1/n = (ⁿ√a)^m
Example : 27^2/3 = 3√27=3²=9.
EVALUATION
1. 27^5/3 2. 1000000000⁰
Application of Laws of Indices
Solve the following
(i)    32 ^3/5         (ii)    343 ^2/3    (iii) 64 ^2/3(iv) 0.001    (v) 14 ⁰
Solution:
i)    32 ^3/5 = (32 ^1/5) ³ = (⁵√32) ³
= 2 ³ = 8
ii)    343 ^2/3 = (343 ^1/3 )² = (³√343)²
= (7 ³)^1/3)²
    = 7² = 49
iii)    64 ^2/3 = (64 ^1/3)² = (4 ³)^1/3)² = 4 ²
iv)    (0.001)³ = (1/100)³ = (1/10)³)³ = (10 ^-3)³
= 10 ^-9 = 1/10 ⁹
v)    14 ⁰ = 1
EVALUATION
1)    Simplify the following
a)    216 ^4/3    b) 25 ^1.5    c) (0.00001)²
d)    d 32 ^2/5 e) 81 ^¾
Reading Assignment: F/Maths project book 1(New third edition).Chapter 2 pg.4 – 6
WEEKEND ASSIGNMENT
1)    Evaluate 3 ^x = 1/8 1 (a) 4 (b) -4 (c) -2 (d) 2
2)    Simplify    2r⁵ X 9r³    (a) P²    (b) 2p⁴ (c) P³ d)18r⁸
3)    Solve 3^-y = 243        (a) -5     (b) 5        (c) 3         (d) -3
4)    Solve 25^-5n = 625    (a) 1/5     (b) 2/5    (c) 1 1/5     (d) – 2/5
5)    Simplify (0.0001)²=     (a) 10^-5    (b) 10 ^-3    (c) 10^-8    (d) 10^-10
Theory
1. 16^3/2 x 8^2/32. 3X² x 4X³
32^1/56X⁷