Integrating sin(1000x)/sinx

How To Find Modular Multiplicative Inverses

Quadratic Diophantine Equations with One Variable

Simultaneous Logarithm Equations

Fermat's Little Theorem Reviewer

Sketch y=x^(1/x)

How To Find the Minimum Distance from a Surface to the Origin

One Minute Proof that i to power i = e to power (- π/2)

16 'Must Know' Complex Numbers - great exam revision

Adding an Exponential Form Complex Number to a General Form Complex Number

Is Santa Claus Real or Imaginary in 2023?

A Complex Quadratic Equation with a Twist

There are ten solutions to this equation - only one is obvious!

How to Calculate when Complex Number Expressions are Real or Imaginary

How to Solve Simultaneous Equations with Complex Variables

How to Evaluate Complex Expressions inside a Modulus

How to Solve Complex Exponential Equations

How to Find all Complex Solutions of cos (z) = 3

How to integrate sin (x) to the power of n for any odd 'n'

How to integrate cos (x) to the power of n for any odd 'n'

Express powers of cos(θ) and sin(θ) in terms of cos(nθ) and sin(nθ) using de Moivre's Theorem

Express cos(nθ) and sin(nθ) in terms of powers of cos(θ) and sin(θ) using de Moivre's Theorem

How to integrate sin (x) to the power of n for any even 'n'

How to integrate cos (x) to the power of n for any even 'n'

Summing cos(θ) + cos(2θ) + .. + cos(nθ) and sin(θ) + sin(2θ) + .. + sin(nθ)

Summing an infinite series involving cos(kθ)

Solving Exponential Equations with Logs as Exponents

How to find f-1(a) from f(x) without Calculating the Inverse Function

Domain of Composite of Three Functions - most people get this wrong

Summing BY INSPECTION Series with nth term 1/[n(n+1)(n+2)...(n+p)]

Counting All Solutions of a Three Variable Diophantine Equation

How to Solve a Three Variable Linear Diophantine Equation

A Cricket Scoreboard Malfunction Solved with a Three Variable Linear Diophantine Equation

How to Find all Solutions of a Cubic Diophantine Equation

A Seemingly Tricky Word Puzzle Solved Effortlessly Courtesy of Diophantus

Solving a Binomial Theorem Coefficient Question Using a Geometric Series Sum Shortcut

JEE Main - Two Binomial Theorem Remainder Questions Explained

2025^2025 (mod 35) - Three Quick Methods Explained

Maths Olympiad - A Neat Remainder Trick Solves this Question Instantaneously

Summing a Series with nCr (Combinations) in each Term

Summing an Alternating Series with nCr (Combinations) in each Term

Vandermonde's Identity for Simplifying Sums of nCr x nCr Combinations

Exam Time Saver - Summing Instantaneously an nCr Series where (n-r) is constant

Must Know (and Simple) Trick for Summing 'a^r x nCr' Series

How to Sum Series with Terms (ar^2+br+c) x nCr

How to Solve Double Summation Questions with Dependent Indices

How to Solve Basic Double Summation Questions

Solving Double Summation Questions with 'i x j' as a Term

Cool Proof Using Double Summation that (Sum of n^3) = (Sum of n)^2

Quick Method to Solve Double Summation with (nCi x iCj) as a Term

How to Answer 'Fundamental Theorem of Calculus' Exam Questions

More 'Fundamental Theorem of Calculus' Exam Questions

Oh Goody ! Even More 'Fundamental Theorem of Calculus' Exam Questions Answered

How to Solve First Order Homogeneous Differential Equations

Great Trick to Quickly Solve Certain Types of First Order Differential Equations

How to Solve a 'Nearly' Homogeneous Differential Equation

How to Solve First Order non-Homogeneous Differential Equations of the form dy/dx+f(x)y=g(x)

Recognising ALL Forms of dy/dx+f(x)y=g(x) - Great Exam Revision

Solving Differential Equations Involving the Fundamental Theorem of Calculus

Dealing with e^y in First Order Differential Equations

Ten Increasingly Scary MUST KNOW Integrating Factors

Great Olympiad Trick - No need find f(x) to solve this.

What is f(3)?

How to Use the Chain Rule on Compositions of Multiple Functions

Counting Number of Possible Functions Given Constraints

Counting Possible INJECTIVE (one-to-one) Functions Given Constraints

Counting Possible BIJECTIVE Functions Given Constraints

Counting Possible SURJECTIVE (onto) Functions Given Constraints

Finding the Domain of a Function Consisting of Multiple Functions

Distributing IDENTICAL Objects between DISTINCT Recipients with Lower Limit Constraint

Dealing with Powers of Roots of Quadratic Equations

Distributing IDENTICAL Objects between DISTINCT Recipients with Upper and Lower Limit Constraints

Counting non-Negative Integer Solutions to x + y + z = 21 with Constraints

Changing Base of Powers and Logs to Simplify a Tricky Expression

Distributing IDENTICAL Objects between IDENTICAL Containers

Distributing DISTINCT Objects between IDENTICAL Boxes

Distributing DISTINCT Objects between DISTINCT Recipients

Using Well Known Trig and Log Limits to Find more Complex Limits

Simplifying a Logic Statement Containing Nested Implications

Finding the Square Root of a Complex Number to Solve a Quadratic Equation with Complex Coefficients

How to Solve 'Exact' First Order Differential Equations

Solving 'Exact' First Order Differential Equations When One Integral is Much Tougher than the Other

How to Solve 'Non-Exact' First Order Differential Equations

How to Solve a Bernoulli Differential Equation

How to Calculate a Homogeneous Transformation Matrix

Which Sequence of Transformations Solves this Puzzle? #transformations #mathstricks #mathshorts

An Interesting Inverse Matrix Teaser #matrices #mathshorts #inverseofmatrix

Determinants of Transpose and Inverse of Matrices

Three Modular Exponentiation Methods for Exponent Towers Explained

How To Evaluate a 3x3 Determinant

Simplifying a Determinant by Taking out Factors #determinants #3x3matrix #matrices

Determinant of the Adjoint of a Matrix

Useful Trick To Solve 'Infinitely Many Solutions' to System of Equations Questions

Changing the Order of Integration of Double Integrals #doubleintegrals #integrals #maths

How to Find the Average Value of a Function z=f(x,y) Over a Region Using a Double Integral

Using a Scalar Line Integral to Find the Area of a Vertical Fence along a Curve

Scalar Line Integrals and 'Wire/Spring' Questions

Parameterisation of a Line Segment #lineintegrals #maths

Line Integrals With Respect to dx, dy, and dz

Vector Line Integrals and Work Done

Test if a Vector Field is Conservative

Finding the Potential Function f(x,y,z) of a Conservative Vector Field F(x, y, z)

Fundamental Theorem of Calculus for Line Integrals of Conservative Vector Fields F(x,y,z)

Integrating a Conservative Vector Field Around a Simple Closed Path #maths #vectorfields

How to do Double Integrals using Polar Coordinates

Three Methods to Find the Area of an Ellipse (and One Method that Doesn't Work)

Green's Theorem Typical Questions Reviewer

Absorbing Markov Chains, Total Probabilities and Recursion

Absorbing Markov Chains Solved with Transition and Solution Matrices

Finding all Real and Complex Solutions of a Trigonometric Equation

Understanding Complex Solutions of cos (θ) = a

Understanding Complex Solutions of sin (θ) = a

Investigating Trigonometric Identities with Complex Numbers

Differentiating Trigonometric Identities Cos z and Sin z for Complex z

Three Questions on Complex Differentiation and the Cauchy-Riemann Equations

Finding the Harmonic Conjugates of a Complex Differentiable Function

Integrating Complex Valued Functions of a Real Variable

Complex Line Integrals and the Fundamental Theorem of Calculus

Can You Correctly Evaluate this Composite Function? #compositefunction #maths

How to Solve Coin Toss Problems Using Markov Chains

Can You Evaluate this Nested Composite Function? #compositefunction #maths

Reconciling Two Seemingly Completely Different Lambert W Solutions

How to Solve an Exponential Equation with the Lambert W Function

Finding ALL Solutions with the Lambert W Function

Avoiding Extraneous Solutions with the Lambert W Function

Lambert W Fun Solving an Exponential Equation #maths #lambertwfunction

Connecting Definite Integrals, Limits to Infinity of Sums and Riemann Sums

What is i to power i? #mathsshorts #maths #complexnumbers

Volume of Solid of Revolution and Rate of Change Question - Great Practice!

Introduction to Premises, Conclusions and Valid or Invalid Arguments

Partial Differentiation but Keeping which Variables Constant?

Implicit Partial Differentiation and Independent Variables

Can You Do This Complex Integral? #maths #mathsshorts #complexintegration

Partial and Total Differentiation and Independent and Dependent Variables

L'Hopital Trap for the Unwary

Maclaurin Series Expansions and Partial Fractions

Taylor Series Expansions and Approximations

Two Correct (and One Incorrect) Methods to Find this Limit

Quick Method to Find Interval of Convergence of Taylor Series Expansion of a/(bx+c) about a Point

Can You Evaluate this Horrific Looking Limit? #mathsshorts #maths #fundamentaltheoremofcalculus

A Familiar Looking Integral made Much Harder with Complex Coefficients

Laurent Series Expansions Reviewer

Cauchy's Integral Theorem and When to Use It

Informal Proof of Cauchy's Integral Formula and Cauchy's Integral Formula for Derivatives

Cauchy Integral Questions Revision and Practice Part ONE

Cauchy Integral Questions Revision and Practice Part TWO

Cauchy Integral Questions Revision and Practice Part THREE

Residue Theorem (aka Cauchy's Residue Theorem) Refresher

GR 3768 Question 49 Solved with both Cauchy Integral Formula for Derivatives and the Residue Theorem

Can you Correctly Calculate these Playing Card Probabilities?

The Tower of Hanoi, Recurrence Relations and Proof by Induction

An Intriguing Exponential Equation - the answer isnt 6!

Can you Find the Remainder Using Modular Exponentiation? #remainders #mathsshorts #mathstricks

Can You Evaluate this Complex Number to Power 100? #mathsshorts #polarform #complexnumbers

There is a Trick to Sum this Series - Can you Find It? #mathsshorts #mathstricks #summingseries

Can Shubman Kohli Win the Cricket Match with a Six on the Last Ball? #mathsshorts #wordproblems

Can you Solve this Tricky Log (Log) Equation? #logarithms #mathsshorts

Can you Correctly Simplify this Tricky Log (Log) Expression? #logarithms #mathsshorts

How Many Digits in the Number 8 to Power 888? #mathsshorts #mathstricks

Can you Solve this First Order Differential Equation? #mathsshorts #maths #differentialequation

Solving a Quartic Polynomial Question with Vieta's Formulae

Can you Find the Smallest Value of xy which Satisfies this Equation? #mathshorts #primenumbers

A Cool Method Solves this Quickly Without Using Vieta's Formulae

Can You Complete this Complex Trigonometric Equation? #mathsshorts #complexnumbers #trigonometry

Introduction to L'Hopital's Rule for Limits of Indeterminate Forms

An Intriguing Mosquito Population Differential Equation Question #mathsshorts #differentialequation

Great Practice using L'Hopital's Rule

Can You Find the Square Root of a Complex Number? #mathsshorts #complexnumbers #squareroot

Can you Differentiate this Complex-Valued Function? #mathsshorts #differentiation #complexnumbers

How Many Vertices in this Graph Given the Number of Edges? #mathsshorts #graphtheory

Can You Find the Area of a 3D Triangle Given its Vertices? #mathsshorts #crossproduct #triangle

Can you Find the Maximum Value of the Function Given the Constraint? #mathsshorts #differentiation

Two Arcsin Under a Square Root - Double Ouch! #mathsshorts #maths #trigonometry

Can You Convert This Language Statement to a Logic Statement? #logicalreasoning #mathsshorts

Introduction to Volumes of Solids of Revolution

Finding the Volume about Both x and y axis of the Solid of Revolution of a Region

Can You Multiply the Multiplicative and Additive Inverse of a Complex Number? #mathsshorts

How To Solve Composite Function Limits by L'Hopital's Rule - Two Methods

Can You Calculate the Second Partial Derivative Given this Set of Equations? #mathsshorts

How Good Are You at Simplifying Logic Statements? #logicalreasoning #mathsshorts

Can you Find the Limit of this Complex-Valued Function? #mathsshorts #lhopital #complexnumbers

nCr + nCr+1 = ? #mathsshorts #combinatorics

How to Solve this Seemingly Tough Integral by Inspection

How Good Are You at Changing Bases of Logs? #logarithms #mathsshorts

How Are You at Maclaurin Series Expansions? #mathsshorts #maclaurinseries #maclaurinexpansion

This is a Tough Partial Differentiation - Can You Do It? #mathsshorts #partialdifferentiation

How to Find the Limit of a Complex-Valued Function

Can You Solve this Matrix Equation? #matrices #mathshorts #imatrixequation

Can You Solve these Congruence Simultaneous Equations? #mathsshorts #modularmaths #congruence

A Very Common Spanning Tree Exam Question - Don't Lose Easy Marks #mathsshorts #graphtheory

Can You Sort Out This Power Series Expansion? #mathsshorts #maclaurinseries #maclaurinexpansion

Can You Do This Tricky Riemann Sum? #mathsshorts #riemann #integration

How To Find Volumes of Solids of Revolution Using the Cylindrical Shells Method

How To Find Volumes of Solids of Revolution about Diagonal Axes

Can You Correctly Evaluate This Complex Integral With Real Variables? #mathsshorts

How To Find Volumes of Solids of Revolution Using Double Integrals

Can You Evaluate This Logic Statement With Help From a Venn Diagram? #maths #logic #venndiagram

Introduction to Volumes Bounded by Surfaces

How to Calculate a Volume Bounded by Surfaces Where There is No z=f(x,y) Surface

This Teaser Looks Far Harder Than It Actually Is #mathsshorts #maclaurinseries #maclaurinexpansion