How to get top marks in VCE Mathematical Methods Units 3 & 4

Pass your VCE Mathematical Methods Units 3 & 4 with flying colours You aspire to get high marks in your[...]

Tips on how to study VCE specialist mathematics Units 3 & 4

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How to improve on your VCE Mathematics

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Follow these Preliminary Chemistry study tips and success will be guaranteed

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Hack your way to success in HSC Chemistry

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How to Ace the HSC Maths Exams

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Preliminary Physics Study Guide for year 11

Preliminary Physics Study Guide The preliminary physics syllabus is required study for your 11 students in New South Wales Australia[...]

How to Succeed in IB Maths

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The HSC physics Exam is a requirement for year 12 students in New South Wales. This university entrance exam otherwise[...]

Logarithmic Differentiation

Basic Rule of Logarithmic Differentiation $$ \displaystyle \dfrac{d}{dx}\log_e{x} = \dfrac{1}{x} \\ \dfrac{d}{dx}\log_e{f(x)} = \dfrac{f'(x)}{f(x)} $$ Practice Questions Question 1 Differentiate[...]

Binomial Expansion | Binomial Theorem

Binomial Expansion is based on two terms, that is binomial. Any expression of the form \( (a+b)^n \) is called[...]

Compound Interest | Series and Sequences

Compound Interest is being used to calculate the total investment across over time. Suppose John invests $1000 in the bank.[...]

Geometric Sequence | Math Help

A geometric sequence is also referred as a geometric progression. Each term of a geometric sequence can be obtained from[...]

Arithmetic Sequence | Maths Help

An Arithmetic Sequence is a sequence in which each term differs from the previous one by the same fixed number.[...]

General Term of a Number Sequence

The general term of a number sequence is one of many ways of defining sequences. Consider the tower of bricks.[...]

Understanding Number Sequence

Number Sequence or progression is ordered list of numbers defined by a pattern or rule. The numbers in the sequence[...]

Implicit Differentiation | Calculus Help

Implicit Differentiation for Calculus Problems This very powerful differentiation process follows from the chain rule. $$u = g(f(x)) \\ \frac{du}{dx}[...]

Surd Equations Reducible to Quadratic | Math Algebra

Surd Equations Reducible to Quadratic | Math Algebra Surd Equations Reducible to Quadratic for Math Algebra is done squaring both[...]

Trigonometric Equations Reducible to Quadratic | Math Skills

Trigonometric Equations Reducible to Quadratic for Math Skills Trigonometric Equations Reducible to Quadratic for Math Skills are based on trigonometric[...]

Exponential Equations Reducible to Quadratic | Math Help

Exponential Equations Reducible to Quadratic for Math Help Exponential Equations Reducible to Quadratic for Math Help is based on various[...]

Fraction Equations Reducible to Quadratic | Free Math Help

Fraction Equations Reducible to Quadratic | Free Math Help iitutor provides full explains of Fraction Equations Reducible to Quadratic for[...]

Algebra Equations Reducible to Quadratic | Math Help

Algebra Equations Reducible to Quadratic Form | Math Help Algebra Equations Reducible to Quadratic Form for Math Help is done[...]

Best Examples of Mathematical Induction Inequality

Mathematical Induction Inequality Proofs Mathematical Induction Inequality is being used for proving inequalities. It is quite often applied for the[...]

Best Examples of Mathematical Induction Divisibility

Mathematical Induction Divisibility Proofs Mathematical Induction Divisibility can be used to prove divisibility, such as divisible by 3, 5 etc.[...]

5 Important Patterns of First Principles

First Principles The First Principles defines how basic rule of derivative of a function. $$\displaystyle f'(x) = \lim_{h\to\infty} \frac{f(x+h)-f(x)}{h}$$ Patterns[...]

10 Deadly Common Algebra Mistakes

Common Patterns of Algebra Mistakes Students often make Common Algebra Mistakes due to confusions such as expand and simplify rules,[...]

Mathematical Induction Fundamentals

Mathematical Induction Fundamentals The Mathematical Induction Fundamentals are defined for applying 3 steps, such as step 1 for showing its[...]

Integrating Trigonometric Functions by Double Angle Formula

Integrating Trigonometric Functions by Double Angle Formula Integrating Trigonometric Functions can be done by Double Angle Formula reducing the power[...]

Trigonometric Integration by Substitution

Trigonometric Integration by Substitution Trigonometric Integration by Substitution can be handled using the basic rules such as \( \displaystyle \frac{d}{dx}[...]

Definite Integration by Substitution

Definite Integration by Substitution Definite Integration by Substitution requires to convert upper and lower limits of definite integration. $$ \displaystyle[...]

Integration by Substitution

Integration by Substitution Integration by Substitution is performed by replacing the pronumeral (variable) to other pronumeral to simplify the expression[...]

Definite Integrals

Background of Definite Integrals Definite Integrals are calculated by subtracting the function values of upper and lower limits. $$\displaystyle \int_{a}^{b}{f(x)}dx[...]

Indefinite Integral of Rational Functions

Understanding Indefinite Integral of Rational Functions Using Indefinite Integral of Rational Functions requires that the format of the expression must[...]

Radical Indefinite Integrals

Radical Indefinite Integrals should be performed after converting its radical or surd notations into index form. $$\displaystyle \sqrt[n]{x^m} = x^{\frac{m}{n}}$$[...]

Indefinite Integral Formula

Basics of Indefinite Integral Formula Indefinite Integral Formula ahs been made from the reverse operations of differentiation or anti-differentiation. \([...]

Geometric Sequence using Logarithms

Applications of Geometric Sequence using Logarithms Geometric Sequence using Logarithms is being used for finding the number of terms of[...]

4 important types of absolute value equation

Absolute Value Equation There are 4 main type of absolute value equation regarding whether there are; absolute value and a[...]

Logarithmic Inequalities

Solving logarithmic inequalities, it is important to understand the direction of the inequality changes if the base of the logarithms[...]

Quartic Graph Sketching

Quartic Graph Sketching is based on their concavities and x-intercepts to determine the basic shape of the quartic graphs. Question[...]

Cubic Graph Sketching

Basics of Cubic Graph Sketching Cubic Graph Sketching start considering from the \(x\)-intercepts and whether the leading coefficient is either[...]

Harder Factorise

Algebra - Harder Factorise or Factoring can be done by collecting common factors and using sums and products of factors.[...]

Sketching Quadratic Graphs

Sketching Quadratic Graphs using Transfomration Sketching Quadratic Graphs are drawn based on \( y=x^2 \) graph for transforming and translating.[...]

Internal Division

Internal Division of Line Segments Internal Division an interval in a given ratio is that if the interval \( (x_1,y_1)[...]

Angle Between Lines

Linear Functions - Angle Between Lines If the acute angle \( \theta \) between two straight lines \( y =[...]

Solving Radical Equations

Solving radical equations are required to isolate the radicals or surds to one side of the equations. Then square both[...]

Integration Reverse Chain Rule

By recalling the chain rule, Integration Reverse Chain Rule comes from the usual chain rule of differentiation. This skill is[...]

Inequality with Variables in the Denominator

Solving Inequality with Variables in the Denominator requires special cares due to the direction of the inequalities. Let's have a[...]

12 Patterns of Logarithmic Equations

Solving logarithmic equations is done many ways using properties of logarithmic functions, such as multiply of logs, change the base[...]

Geometric Series for Time Payments

Time payments is are calculated based on Geometric Series for reducible compound interests. Basically geometric series formula is used for[...]

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Complex Numbers with Vector Addition is obtained using the sides of triangles, the sum of sides of two sides of[...]

Rates of Change involving Integration

Rates of Change for finding height and time can be solved by integration. Once integrated, find the integral constant using[...]

Three Dimensional Trigonometry

One of the most effective ways to solve Three Dimensional Trigonometry questions is to list all of the trigonometric ratios[...]

Quadratic Equations in Square Roots

For solving Quadratic Equations in Square Roots, it is required to square both sides entirely, but not individually. For instance,[...]

Area of a Triangle using Radius and Perimeter

Area of a triangle can be calculated using its perimeter and the radius of the circle which is inscribed in[...]

Collision of Projectile Motion

Collision of Projectile Motion is handled by setting the same vertical height and horizontal distance at a given time. Worked[...]

Collinear Proof in Circle Geometry

Collinear Proof can be done in Circle Geometry by showing Three or more points lie on a single straight line.[...]

Integration by Parts

Integration by Parts is made of product rule of differentiation. The derivative of \(uv\) is \(u'v + uv'\) and integrate[...]

Volumes by Cross Sections

Volumes by Cross Sections can be setting a unit volume, \( \delta V \) of a cross section. Then establish[...]

Mathematical Induction Inequality Proof with Factorials

Mathematical Induction Inequality Proof with Factorials uses one of the properties of factorials, \( n! = n(n-1)! = n(n-1)(n-2)! \).[...]

Cyclic Quadrilateral in Circle Geometry

Cyclic Quadrilateral is inscribed into a circle, whose vertices all lie on a circle. The properties of Cyclic Quadrilateral in[...]

Locus of Complex Numbers

Locus of Complex Numbers is obtained by letting \( z = x+yi \) and simplifying the expressions. Operations of modulus,[...]

Mechanics Circular Motions

Mechanics Circular Motions are handled by resolving forces horizontally and vertically in conjunction with the tension of the string, normal[...]

Ellipse Geometry

Ellipse Geometry is used for proving ellipse questions relating to geometry such as similar triangles and circle geometry. Worked Examples[...]

Inequality Proofs

Inequality Proofs can be done many ways. For proving \(A \ge B \), one of the easiest ways is to[...]

Complex Number Regions

Regions defined by complex numbers \( \displaystyle z = x + yi \) where \(x\) and \(y\) are real numbers,[...]

Ellipse Discriminant Eccentricity

Discriminant can be used to ellipses for identifying the status of their intersections in conjunction with eccentricity. The eccentricity of[...]

Rationalising Denominators

Rationalising Denominators simplifies the fractions by multiplying the conjugates of the denominators. Worked Example of Rationalising Denominators Simplify \( \displaystyle\frac{1}{\sqrt{1}[...]

Probability with Replacement

Probability with Replacement is used for questions where the outcomes is returned back to the sample space again. Which means[...]

Integration Recurrence Formula

For Integration Recurrence Formula or reduction formula, it is important set a relationship between two consecutive terms by using mostly[...]

Polynomial Equation and Maximum Coefficient

If \( \alpha \) is a root of a polynomial equation \( P(x) = 0 \), then \( P(\alpha) =[...]

Absolute Value Inequalities

Absolute Value Inequalities are usually proved by the absolute value of a certain value is greater than or equal to[...]

Integration using Trigonometric Properties

Trigonometric properties such as the sum of squares of sine and cosine with the same angle is one, $$ \displaystyle[...]

Circle Geometry with Semicircles

There are many properties of circle geometry with semi circles, such as equal arcs on circles of equal radii subtend[...]

Volumes by Cylindrical Shells Method

Let’s consider the problem of finding the volume of the solid obtained by rotating about the \(x\)-axis or parallel to[...]

Integrating Binomial Expansion

Integrating Binomial Expansion is being used for evaluating certain series or expansions by substituting particular values after integrating binomial expansion.[...]

Probability Ratio using Combination

Counting Techniques for Probability Ratio using Combination The probability ratio of an event is the likelihood of the chance that[...]

Inequalities using Arithmetic Mean Geometric Mean

Arithmetic Mean of \(a\) and \(b\) is always greater than or equal to the Geometric Mean of \(a\) and \(b\),[...]

Mathematical Induction Inequality Proof with Two Initials

Usually, mathematical induction inequality proof requires one initial value, but in some cases, two initials are to be required, such[...]

Trigonometric Proof using Compound Angle Formula

There are many areas to apply the compound angle formulas, and trigonometric proof using compound angle formula is one of[...]

Finding a Function from Differential Equation

The solution of a differential equation is to find an expression without \(\displaystyle \frac{d}{dx} \) notations using given conditions. Note[...]

3 Ways of Evaluating Nested Square Roots

Nested square roots or nested radical problems are quite interesting to solve. The key skill for this question is to[...]