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SS1 Online Class & Lesson notes
SS1 First Term Mathematics Senior Secondary School
SS1 First Term Mathematics Senior Secondary School
Curriculum
10 Sections
21 Lessons
10 Weeks
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WEEK 1 - REVISION AND BASIC OPERATIONS OF INTEGER
3
2.1
Rules of divisibility test
40 Minutes
2.2
Integers simplification
40 Minutes
2.3
Assessment of Integers
WEEK 2 - NUMBER BASES /BASE NUMBER
3
3.1
Number Systems Introduction – Decimal, Binary, Octal, Hexadecimal & BCD Conversions
30 Minutes
3.2
Expression/Conversion of numbers in Base 10
45 Minutes
3.3
Conversion from one base to another
45 Minutes
WEEK 3 - 1. [A] ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION OF NUMBER BASES . [B] APPLICATION OF NUMBER BASES TO COMPUTER PROGRAMMING.
1
4.1
Application Of Base Number To Computer Programming
45 Minutes
week 4 - 1. CONCEPT OF MODULAR ARITHMETIC; ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION OF OPERATIONS OF MODULAR ARITHMETIC
3
5.1
Modular Arithmetic
40 Minutes
5.2
Addition, Subtraction and Multiplication of Modulo Arithemetic
45 Minutes
5.3
Assessment -Modular Arithmetic
WEEK 5 - STANDARD FORM AND APPROXIMATION
2
6.1
Standard Form And Approximation
45 Minutes
6.2
Approximation (Significant Figure, Decimal Places And Rounding Off)
45 Minutes
WEEK 6 - INDICES
[a]Application of laws of indices. [b] Negative, zero and fractional indices.
2
7.1
Basic Laws of Indices
45 Minutes
7.2
Assessment – Indices
WEEK 7 - REVIEW OF FIRST HALF
Review what you have leaernt so far!
0
WEEK 8 - LOGARITHMS OF NUMBERS GREATER THAN 1 [WHOLE NUMBER]→
use of logarithm table for multiplication and division of numbers.
3
9.1
Logarithms Of Whole Numbers
45 Minutes
9.2
Antilogarithm
35 Minutes
9.3
Multiplication and Division of numbers in Logarithm
45 Minutes
WEEK 9 - LOGARITHMS CTD; [A] CALCULATIONS INVOLVING POWERS AND ROOTS. [B] RELATIONSHIP BETWEEN INDICES AND LOGARITHMS.
2
10.1
Squares Or Powers Of Numbers In Logarithms
45 Minutes
10.2
Relationship between Indices and Logarithms
45 Minutes
WEEK 10 - [A] SIMPLE EQUATION AND VARIATION. [B] CHANGE OF SUBJECT OF FORMULAE. [C] TYPE OF VARIATION; DIRECT, INVERSE, JOINT AND PARTIAL VARIATION. [D] APPLICATIONOF VARIATION TO PRACTICAL PROBLEMS.
2
11.1
Simple Equation And Subject of formula
11.2
Variation and Types of Variation
50 Minutes
Addition, Subtraction and Multiplication of Modulo Arithemetic
Addition of and Subtraction of Modulo Arithmetic:
Modular Multiplication by
Khan Academy
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Let’s explore the multiplication property of modular arithmetic:
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(A * B) mod C = (A mod C * B mod C) mod C
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Example for Multiplication:
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Let
A=4, B=7, C=6
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Let’s verify:
(A * B)
mod C = (
A mod C
*
B
mod C
) mod C
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LHS
= Left Hand Side of the Equation
data-perseus-paragraph-index=”0″>
RHS
= Right Hand Side of the Equation
data-perseus-paragraph-index=”0″>
LHS =
(A * B)
mod C
data-perseus-paragraph-index=”0″>
LHS =
(4 * 7)
mod 6
data-perseus-paragraph-index=”0″>
LHS =
28
mod 6
data-perseus-paragraph-index=”0″>
LHS =
4
data-perseus-paragraph-index=”0″>
RHS = (
A
mod C
*
B
mod C
) mod C
data-perseus-paragraph-index=”0″>
RHS = (
4 mod 6
*
7 mod 6
) mod 6
data-perseus-paragraph-index=”0″>
RHS = (
4 * 1
) mod 6
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RHS =
4 mod 6
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RHS =
4
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LHS = RHS = 4
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Proof for Modular Multiplication
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We will prove that
(A * B) mod C = (A mod C * B mod C) mod C
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We must show that
LHS = RHS
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From the quotient remainder theorem we can write
A
and
B
as:
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A = C * Q1 + R1
where 0 ≤ R1 < C and Q1 is some integer.
A mod C = R1
data-perseus-paragraph-index=”0″>
B = C * Q2 + R2
where 0 ≤ R2 < C and Q2 is some integer.
B mod C = R2
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LHS = (A * B) mod C
data-perseus-paragraph-index=”0″>
LHS = ((C * Q1 + R1 ) * (C * Q2 + R2) ) mod C
data-perseus-paragraph-index=”0″>
LHS = (C * C * Q1 * Q2 + C * Q1 * R2 + C * Q2 * R1 + R1 * R 2 ) mod C
data-perseus-paragraph-index=”0″>
LHS = (C * (C * Q1 * Q2 + Q1 * R2 + Q2 * R1) + R1 * R 2 ) mod C
data-perseus-paragraph-index=”0″>
We can eliminate the multiples of C when we take the mod C
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LHS = (R1 * R2) mod C
data-perseus-paragraph-index=”1″>
Next let’s do the
RHS
data-perseus-paragraph-index=”0″>
RHS =
(A mod C * B mod C) mod C
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RHS = (R1 * R2 ) mod C
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Therefore RHS = LHS
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LHS = RHS = (R1 * R2 ) mod C
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