$$ \large \begin{align} a &= 4 \\ b &= 3 \\ x &= 25 \\ y &= -8 \end{align} $$ Question 1 If \( a=4 \) and \( b=3 \), evaluate \( ab \). \( \begin{align} ab &= a \times b \\ &= 4 \times 3 \\ &= 12 \end{align} \) Question 2 If \( […]
Tag Archives: Algebra
Expand and Simplify Linear Expressions
Transcript It says to expand and simplify this. So we’ve got two sets of brackets we want to expand it all out.So here I want to multiply a with the a and also the positive one, and this time I want to multiply, this time it’s negative a in front, isn’t it? So I want […]
Everything You Need to Know about Perfect Numbers
Some of the first patterns of natural numbers spotted and studied by Pythagoreans were $\textit{perfect numbers}$. These are natural numbers with bizarre properties that can be formed by adding up all the smaller numbers that make up their divisors. The number $6$ is the first perfect number because it may be divided by $1$, $2$ […]
Method of Exhaustion
Eudoxus, a Greek mathematician 408-355 BC, developed the idea of seeking mathematical solutions using the $\textit{Method on Exhaustion}$: at this stage, you achieve a more accurate figure. For example, he produced a ladder of numbers to find an increasingly accurate solution to $\sqrt{2}$. Starting with $1$ and $1$ as the first row, he added those […]
The Golden Ratio
Since the days of old, artists, as well as mathematicians, have known that there is a special, aesthetically pleasing rectangle with width $1$, length $x$, and the following property:When a square of side $1$ is removed, the remaining rectangle has the same proportions as the original rectangle. Since the new rectangle has a width $x-1$ […]
Index Notation
A convenient way to write a product of $\textit{identical factors}$ is to use $\textbf{exponential}$ or $\textbf{index notation}$.Rather than writing $5 \times 5 \times 5 \times 5$, we can write this product as $5^4$. The small $4$ is called the $\textbf{exponent}$ or $\textbf{index}$, and the $5$ is called the $\textbf{base}$.If $n$ is a positive integer, then […]
The Sign of One
Make the following numbers using FOUR 1s using 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.
Surd Equations Reducible to Quadratics
Surd Equations Reducible to Quadratic for Math Algebra is done squaring both sides for removing surds and radical expressions. Make sure to check whether the solutions are correct by substituting them into the original surd equations. Question 1 Solve \( x = \sqrt{x+2} \). \( \begin{aligned} \displaystyle \require{AMSsymbols} \require{color}x^2 &= x+2 &\color{red} \text{square both sides} […]
Trigonometric Equations Reducible to Quadratics
Trigonometric Equations Reducible to Quadratic for Math Skills are based on trigonometric identities such as;$$ \large \begin{align}\sin^2{x} + \cos^2{x} &= 1 \\1 + \cot^2{x} &= \csc^2{x} \\\tan^2{x} + 1 &= \sec^2{x} \\end{align} $$ Question 1 Solve \( 2 \cos^2{x}-3 \cos{x} + 1 = 0 \) for \( 0^\circ \le x \le 360^\circ \). \( \begin{aligned} […]
4 Important Types of Absolute Value Equations
There are 4 main types of absolute value equations regarding whether there are; absolute value and a static value absolute value and an expression involving unknown pronumerals two absolute values in both sides two absolute values and a value Type 1: One Absolute Value and a Constant Solve \( | x-2 | = 5 \). […]
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