Revision Note

Division Algorithm

When $f(x)$ is divided by $d(x)$, if the quotient is $Q(x)$ a… Read

Math

Enlargement of $y=f(x)$

For the function $y=f(ax)$.

If $a 1$, the graph of $y=f(x)$ c

… Read

Math

Equations of Circle

Standard form
For a circle $\mathscr{C}$ with centre $(h,k

… Read

Coordinates

Equations of Straight Line

Point slope form
For a straight line $\ell$ with slope $m$ an

… Read

Coordinates

Errors

For known actual value.
1. Absolute error $=$ Actual value $-$

… Read

Errors and Estimations

Estimations

Round up
1. $12345 \approx 12350$ (rounding up to 4 sig. fig.)
2. $

… Read

Errors and Estimations

Expectation

For an event with $n$ possible outcomes, each outcome corre… Read

Data Handling

Experimental Probability

Let $E$ be an event in a certain experiment.
\begin{equatio… Read

Data Handling

Exterior Angle of Triangle

Result: $a+b=c$

Reference: ext. $\angle$ of $\Delta$… Read

Math

Factor Theorem

If $f(x)$ is divisible by $(x-a)$, where $a$ is a real number

… Read

Math

Factorial

For $n$ different objects, if we have a queue of all $n$ objec… Read

Data Handling

Fibonacci Sequence

The sequence of numbers $1$, $1$, $2$, $3$, $5$, $8$, $13$, $… Read

Math

Geometric Sequences

Let $T(1)$, $T(2)$, …, $T(n)$ be an geometric sequen… Read

Math

Growth and Decay

Denote $O$ and $N$ the old value and new value respectively, … Read

Math

Identities of Cubes

For any real numbers $a$ and $b$.

Sum of cubes
$a^3+b^3 \equi

… Read

Identities

Identities of Squares

For any real numbers $a$ and $b$.

Difference of squares
$a^2

… Read

Identities

Index of Earthquakes – the Richter Scale

The relation between the magnitude ($M$) of an earthquake a… Read

Exponential and Logarithm

Inter-quartile Range

Let $Q_3$ and $Q_1$ be the upper and lower quartile respecti… Read

Data Handling

Intercept Theorem

Condition: $AB=BC$ and $AD//BE//CF$

Result: $DE=EF$

Refe… Read

Math

Interests

Simple interest
Denote $P$ the principal, $r\%$ the intere

… Read

Math