MATHEMATICS

Mathematics for First year Students Studying Natural Sciences or A-levels.

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Set Theory

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Set Theory Intro: Basics, Notations, Venn Diagrams etc

More Laws on Sets Theory

Disjoint Sets

Simplifying Sets to their Simplest Form-Practice Questions

Advanced Questions Involving Venn Diagram 1

Advanced Question Involving Venn Diagram 2

Shading & Describing Regions

Describing Shaded Region on a Venn Diagram

Presending the set on a venn diagram

Set Builder Notation intro

Set Builder Notation Practice

Set Interval Notation (Sets on a Number Line) 1

Set Interval Notation (Sets on a Number Line) 2

Recurring Decimals to Rational (e.g 2.34343434..... to a/b)

Proving a Number is Irrational -Root of 3

Proving a Number is Irrational -Root of 2

Proving 1 + square root of 2 is irrational

Set Theory Continued.....

Further Complex Numbers

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Complex Numbers Basics (Very Important)

Complex Numbers Practice (Basics)

Quadratic equations of complex numbers

Polar form Full

Polar form to rectangular form

Multiplication and division of complex number

Demovier's Theorem full

Q1 Part 1 Tutorial sheet

Q1 Part 2 Tutorial sheet

Functions -Polynomials, Radicals, Absolute Value, Rational etc (All)

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Relations & Functions Explained

Domain & Range of functions (several functions)

Domain of Radical Functions

Graphing Radical Functions & their domain & Range

Domain of Rational Functions

Range of Rational Functions

How to find the X & Y intercepts?

Graphing Rational Functions

Piecewise Functions

Even & Odd Functions

Completing the Square Method

Completing the Square Method - Absolute Value (Modulus functions)

Long Division of Polynomials

Synthetic Division

Synthetic Division Continued

How to find the remainder - Remainder & Factor Theorem

Solving & Graphing Polynomials

Factorization of Polynomials

Nature Of Roots

Finding Missing Values in Polynomials

System of Equations

Alpha & Beta Complete Lesson

Application of Quadratic Functions

Equations involving Absolute Values

Equations involving Radicals (square roots)

QUESTION 10 & 11 TS 4

QUESTION 9 TS 4

Exponentials & Logarithmic Functions

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Exponentials Introduction

Graphing Exponential Functions

Exponentials Equations part 1

Logarithm Introduction

Converting Logs to Exponentials

Graphing Logarithm Functions

Simultaneous Equations of Logs & Exponentials

Tutorial Sheet Full

Q1 to Q6 Tutorial Sheet

Q7 to Q10 Tutorial Sheet

Binomial Expansions - Pascals Triangle, Binomial Theorem

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Binomial Theorem Introduction

Binomial Coefficient and Factorial Notations

Binomial Coefficient and Factorial Notations Practice Question

Proving of Binomial Coefficients

Binomial Theorem Detailed

N-th term Explained

N-th term Practice Question

Independent of X

Binomial Series

Negative and Fraction Exponents on Binomial Series

Finding Square Roots using Binomial Theorem

Advanced Practice Question on Binomial Expansions

Binomial More Practice Questions

Trigonometry

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Trigonometry Introduction

Reference Angles & Trig Ratios

Pythagoras Theorem

Exam Questions

Tan Identity

Cosec,Sec & Cot Explained

Derived Identity From Basics

Verifying Trig Identities

Solving Trig Identities

Negative Angle Identities

Addition Formula Sin & Cos (A+B)

Addition Formula Tan(A+B) derived

Addition Formulae Practice Question

Doubles Angle Formulae

Doubles Angle Formulae Practice Question

Sin3x Identity Explained

Solving Trig Equations part 1

Solving Trig Equations part 2

Graphing Sine,Cosine & Tan and also Finding Phase shift,period & vertical shiift

Half Angle Formulae

Trig Function as Algebra Expressions

Tutorial sheet Question 1

trig Exam past papers recorded class

MATH EXAM PREPARATIONS WITH ADVISE

Ineaqualities

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inequalities introduction

Quadratic & Polynomial Inequalities

Fraction Inequalities

Modulus Inequalities

Compound Inequalities

Partial Fractions

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Partial Fractions full video

Partial Fractions Part 2 includes Improper Fractions

LIMITS - Calculus

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Basics Of Limits

Limits involving Surds

Limits involving Zero & Infinity

Trig Limits involving Sin

Trig Limits involving Cosine & Tan

Continuity of a Function

Limits on a Graph

More Advanced Limits - Piecewise Functions

Extra Practice

Exponentials & Natural Logarithms

L'Hopitals Rule

Sandwich Theorem

Precise Definition Of a Limit

Differential Calculus

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First Principle

Formula For Derivatives

Product Rule

Quotient Rule

Chain Rule

Sum & Difference Rule

Derivatives of Exponentials

Derivatives of Logarithms

Proof of Trig Derivatives

Implicity Differentiation

Implicity Differentiation With Exponentials

Tangents & Normal Lines to a Curve

Increasing & Decreasing Functions

Stationary Points & Critical Points

Nature of Staionary Points

Relative Maximum & Minimum

Related Rates

Integral Calculus

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Basics of Integration

Definite Integrals

Indefinite Integrals

Integration by U-Substitution

Integration by Parts

Integration by Partial Fractions

Integration by Trig-Substitution

Integration of exponentials & Logarithms

Application of Integration 1 (Area)

Application of Integration 2 (Volumes)

Matrices Full and MSM112 Tutorial Sheet 2

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MATRICES INTRODUCTION

MATRICES LESSON PART 1- Determinant and Adjoint

MATRICES LESSON 2 PART 2- Inverse,Transpose and Systems

MATRICES CRAMERS RULE

MATRICES TUTORIAL SHEET PART 1

MATRICES TUTORIAL SHEETPART 2

MATRICES TUTORIAL SHEETPART 3

MATRICES TUTORIAL SHEETPART 4

Conic Sections - Analytic Geometry

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Math1120 Tutorial Sheet 2025

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Math1120 Tutorial Sheet 1

Math1120 Tutorial sheet 2 full solutions

Math1120 Tutorial sheet 3 full solutions

Math1120 TS 4 ALL remaing questions video

Math1100 Tutorial Sheet 2025

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MATH1100 TUTORIAL SHEET 1 FULL SOUTIONS

Math1100 Tutorial Sheet 2 full solutions

Math1100 Tutorial Sheet 3 full solutions

Math1100 Tutorial Sheet 4

M112 Tutorial Sheet 1 - Trigonometry & Complex Numbers

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Question 12 - Advanced Trig Equations

Calculus Tutorial Sheet - M112 TUT 2

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Calculus Tutorial Sheet - M112 TUT 3

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MATH1120 TUTORIAL SHEETS 2024

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Q1 MATH1120 TS4 2024 PART 1

Q1 MATH1120 TS4 2024 PART 2

Q2 MATH1120 TS4 2024

Q3 MATH1120 TS4 2024

Q4 MATH1120 TS4 2024

Q6 TS4 MATH 1120 2024

Q5 MATH1120 TS4 2024

Q7 MATH1120 TS4 2024

Q8 TS4 MATH 1120 2024

MATH1120 TS7 Q11 PART 2

MATH1120 TS7 Q15

math1120 TS7 Q7

MATH1120 TS7 Q14

MATH1120 TS7 Q16 & Q17

MATH1120 TS7 Q8 SAME CONCEPT

Math1100/1120 Tutorial Sheet 2024

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Math1120 Tutorial Sheet 1

Rational function part 1

Rational function part 2

Logarithms & Exponentials part 1

Basic rule of logs class 2

sketching logs & exponentials class 3.

Equations of logs & exponentials class 4

logs and exponentials advanced equations class 5

math1100 TS 4 Rational Function recorded class

Polynomials part 1

polynomials part 1 continuation

math1100 2023 quiz 2 paper part 1

math1100 2023 quiz 2 paper part 2

math1100 sheet 6 part 4

math1100 sheet 6 part 5

math1100 test 2 2023 part 1

math1100 test 2 2023 part 2

Math1100 Tutorial Sheet 7,8 and 9 2024

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Math1100 Tutorial Sheet 9 Q3

Math1100 Tutorial Sheet 9 Q4 & Q5

Math1100 Tutorial Sheet 9 Q6 & Q8

Math1100 Tutorial Sheet 9 Q9

Math1100 Tutorial Sheet 9 Q11

Math1100 Tutorial Sheet 9 Q17 Q18 & Q19

Math1100 Tutorial Sheet 9 Q20 & Q21

Math1100 Tutorial Sheet 9 Q23

Math1100 Tutorial Sheet 9 Q22

Math1100 Tutorial Sheet 9 Q1 & Q2

Math1100 TS 8 Q13 to Q15

TS8 Q12 (MUST WATCH)

Math 1100 Tutorial Sheet-2024

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Assignment 1: 1-2

Assignment 1: 3 - 6a Guidelines

Assignment 1: 6b -8 Guidelines

Assignment 1: 9-11b

Assignment Q11c to 12 b

Math1100 Tutorial Sheet 3-2024

Phy102 Tutorial sheet 2025

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MAT 2110 _ Tutorial Sheet 1

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Math1100/1120 2023

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Q1 Math Exam 2023 Paper

Q2 Math 2023 exam past paper

Q3 Math 2023 exam

Q4 math 2023 Exam past paper

Q5 Math 2023 exam past paper

Q6 Math 2023 exam past paper

Q7 MATH1120 2023 EXAM PAPER

Q1 MATH1100 2023 EXAM PAPER

Q2 Math1100 Exam 2023 Paper

Q3 Math 1100 EXAM 2023

Q4 MATH1100 2023 EXAM PAPER

Q5 MATH1100 2023 EXAM PAPER

Q6 MATH1100 2023 EXAM PAPER

Q7 MATH1100 2023 EXAM PAPER

MSM112 2022 & 2023

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MSM112 Q1 to Q9 2023

MSM112 2023 Q10 to Q13

MSM112 2023 Q13 SEC A to Q1b SEC B

MSM112 2023 Q1c to Q1d SEC B

MSM112 2023 Q1d(ii) to Q2b(ii) SEC B

MSM112 2023 section B Q2c

MSM112 2023 section B Q2d

MSM112 2023 SECTION B Q3

MATH1100 2024 PAPER

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math1120 2024 paper

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MATH1120 2024 EXAM FULL VIDEO

2024 Test 1 paper

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Math1120 Quiz 1 2024

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Trigonometry

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Intro Class - 03/02/25