# The Sign of One

Make the following numbers using FOUR 1s and any mathematics operators and/or symbols, such as $\dfrac{x}{y}$, $\sqrt{x}$, decimal dots, $+$, $-$, $\times$, $\div$, $($ $)$, etc by the Sign of One. Click the numbers below to see the answers. The first one is done for you.

# Number Curiosity

Are these number beautiful? \begin{align} \displaystyle 1 \times 8 + 1 &= 9 \\ 12 \times 8 + 2 &= 98 \\ 123 \times 8 + 3 &= 987 \\ 1234 \times 8 + 4 &= 9876 \\ 12345 \times 8 + 5 &= 98765 \\ 123456 \times 8 + 6 &= 987654 \\ 1234567 […]

# Nicomachus Theorem

$\textbf{Nicomachus}$ discovered “Nicomachus Theorem” interesting number patterns involving cubes and sums of odd numbers. Nicommachus was born in Roman Syria (now, Jerash, Jordan) around 100 AD. He wrote in Greek was a Pythagorean. $\textbf{Nicomachus Theorem: Cubes and Sums of Odd numbers}$ \begin{eqnarray*} 1 &=& 1^3 \\ 3 + 5 &=& 8 = 2^3 \\ 7 […]

# 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 VCE Mathematical Methods Units 3 & 4, which is getting a score of forty or above. It isn’t going to be easy but with dedication, hard work and adequate practice you’ll get a boost for […]

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

You don’t need to be a genius to pass VCE specialist mathematics units 3 & 4 I’m sure you’ve read those articles that claim VCE specialist mathematics units 3 & 4 is only for geniuses. They tell us that you have to be very good in math to make it in this subject. The truth […]

# How to improve on your VCE Mathematics

Share0 Share +10 Tweet0 VCE Mathematics VCE Mathematics Subscription Improve your VCE Mathematics skills The Victorian Certificate of Education (VCE) in mathematics can be challenging, many students find themselves struggling. An assumption that the majority of learners have a good background in VCE Mathematics already may be one of the contributors. The fact of the […]

# Follow these Preliminary Chemistry study tips and success will be guaranteed

Share0 Share +10 Tweet0 Preliminary Chemistry Course Preliminary Chemistry Subscription Preliminary Chemistry Study Tips For finding Preliminary Chemistry Study Tips, preliminary chemistry marks for year eleven may not count towards your HSC chemistry exam results but it will definitely influence how you perform and also your future life. It pays to give it the deserved […]

# Hack your way to success in HSC Chemistry

Share0 Share +10 Tweet0 HSC Chemistry Course HSC Chemistry Subscription Success in HSC Chemistry We all want a good marks in chemistry, not just to make you feel good but also to improve your chances of landing a good job. Knowing how to maximise your HSC Chemistry mark is crucial, forget about those saying that […]

# How to Ace the HSC Maths Exams

Share0 Share +10 Tweet0 HSC Maths HSC Maths Extension 1 HSC Maths Extension 2 HSC Maths General 2 Tips for Success in HSC Maths, Extension 1, Extension 2, and Maths General Our team works with students all over the world, and we are aware that there are different testing and courses found in various areas […]

# Preliminary Physics Study Guide for year 11

Share0 Share +10 Tweet0 Preliminary Physics Course Preliminary Physics Subscription Preliminary Physics Study Guide The preliminary physics syllabus is required study for your 11 students in New South Wales Australia who are going to be preparing for the HSC physics exam. Preliminary physics syllabus requirements of the introductory concepts which will eventually be required for […]

# How to Succeed in IB Maths

Share0 Share +10 Tweet0 IB Maths Courses IB Maths Subscriptions Your One-Stop, Five-Step Guide for SL and HL Maths Victory There’s no feeling like the pride of completing a course and doing a great job. When it comes to IB Maths, we know all too well the challenges faced. That’s why our team does what […]

# How to succeed at HSC Physics Exam

Share0 Share +10 Tweet0 The HSC physics Exam is a requirement for year 12 students in New South Wales. This university entrance exam otherwise called a higher school certificate is the international equivalent to an IB or SAT. We know many students internationally and locally will require this type of qualification in order to enter […]

# Logarithmic Differentiation

Share0 Share +10 Tweet0 Our Courses 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 \( y = \log_{e}(3x) \). \( \begin{aligned} \displaystyle \dfrac{d}{dx}\log_{e}(3x) &= \dfrac{(3x)’}{3x} \\ &= \dfrac{3}{3x} \\ &= \dfrac{1}{x} \end{aligned} \) Question 2 Differentiate \( y = \log_{e}(2x-1) \). \( \begin{aligned} […]

# Binomial Expansion | Binomial Theorem

Share0 Share +10 Tweet0 Our Courses Binomial Expansion is based on two terms, that is binomial. Any expression of the form \( (a+b)^n \) is called power of a binomial. All binomials raised to a power can be expanded using the same general principles. \( \begin{aligned} \displaystyle (a+b)^1 &= a+b \\ (a+b)^2 &= (a+b)(a+b) \\ […]

# Compound Interest | Series and Sequences

Share0 Share +10 Tweet0 Our Courses Compound Interest is being used to calculate the total investment across over time. Suppose John invests $1000 in the bank. He leaves the money in the bank for 4 years, and are paid an interest rate of 10% per annum. The interest is added to his investment each year, […]

# Geometric Sequence | Math Help

Share0 Share +10 Tweet0 Our Courses A geometric sequence is also referred as a geometric progression. Each term of a geometric sequence can be obtained from the previous one my multiplying by the same non-zero constant. For example, \(2, \ 6, \ 18, \ 54, \cdots \) is a geometric sequence as each term can […]

# Arithmetic Sequence | Maths Help

Share0 Share +10 Tweet0 An Arithmetic Sequence is a sequence in which each term differs from the previous one by the same fixed number. It cal also be referred to as an arithmetic progression. For example, 2, 5, 8, 11, … 10, 20, 30, 40, … 6, 4, 2, 0, 02, … Algebraic Definition of […]

# General Term of a Number Sequence

Share0 Share +10 Tweet0 The general term of a number sequence is one of many ways of defining sequences. Consider the tower of bricks. The first row has five bricks on top of the pile, the second row has six bricks, and the third row has seven bricks. If \( T_n \) represents the number […]

# Understanding Number Sequence

Share0 Share +10 Tweet0 Number Sequence or progression is ordered list of numbers defined by a pattern or rule. The numbers in the sequence are said to be its numbers or its terms. A sequence which continues indefinitely is called an infinite sequence. A sequence which ends is called finite sequence. For example, 2, 5, […]

# Implicit Differentiation | Calculus Help

Share0 Share +10 Tweet0 Implicit Differentiation for Calculus Problems This very powerful differentiation process follows from the chain rule. $$u = g(f(x)) \\ \frac{du}{dx} = g'(f(x)) \times f'(x)$$ We’ve done quite a few differentiation and derivatives, but they all have been differentiation of functions of the form \( y = f(x) \). Not all the […]