Secondary 2 Mathematics

S2 Maths: start from laws of indices, walk through identities, percentages & interest, ratio, then geometry proof and statistics, finishing with polynomials and Pythagoras. Follow the order — shallow to deep.

The order below is the recommended shallow-to-deep path.

Units 單元

Tap a unit name to jump to its topics.

指數與冪 Indices4/4 live

  1. 1Laws of Positive Integral IndicesBasic
  2. 2Zero and Negative Integral IndicesBasic
  3. 3Scientific NotationBasic
  4. 4Using Calculator for IndicesBasic
⚡ Unit quiz 快測5 Qs

Answer on your own first, then reveal — wrong answers go to your wrong-answer book.

Q12³ × 2⁴ = ?

Q27⁰ = ?

Q3Scientific notation form?

Q4Power button usually labelled?

Q55⁶ ÷ 5² = ?

恆等式 Identities4/4 live

  1. 5What is an IdentityBasic
  2. 6Difference of SquaresAdvanced
  3. 7Perfect Square IdentitiesAdvanced
  4. 8Applications of IdentitiesAdvanced
⚡ Unit quiz 快測5 Qs

Answer on your own first, then reveal — wrong answers go to your wrong-answer book.

Q1Identity is true for what numbers?

Q2(a+b)(a-b) = ?

Q3(a+b)² = ?

Q4Three identity formulas?

Q5Normal equation is true for what numbers?

百分數與利率 Percentages & interest4/4 live

  1. 9Percentages ReviewBasic
  2. 10Percentage Increase and DecreaseBasic
  3. 11Simple InterestBasic
  4. 12Profit and LossBasic
⚡ Unit quiz 快測5 Qs

Answer on your own first, then reveal — wrong answers go to your wrong-answer book.

Q1Percentage symbol?

Q2Percentage change formula?

Q3Simple interest formula?

Q4Profit = ?

Q550% to decimal?

比與比例 Ratio & proportion3/3 live

  1. 13Introduction to RatioBasic
  2. 14Direct ProportionAdvanced
  3. 15Inverse ProportionAdvanced
⚡ Unit quiz 快測5 Qs

Answer on your own first, then reveal — wrong answers go to your wrong-answer book.

Q1Ratio symbol?

Q2Direct proportion formula?

Q3Inverse proportion formula?

Q410:15 simplify?

Q5k = ?

幾何證明初步 Geometry proof4/4 live

  1. 16Introduction to GeometryBasic
  2. 17Vertically Opposite Angles and Angles with Parallel LinesBasic
  3. 18Congruent TrianglesAdvanced
  4. 19Similar TrianglesAdvanced
⚡ Unit quiz 快測5 Qs

Answer on your own first, then reveal — wrong answers go to your wrong-answer book.

Q1Triangle angle sum?

Q2Vertically opposite angles?

Q3Congruent symbol?

Q4Similar symbol?

Q5Straight angle is how many degrees?

統計 Statistics3/3 live

  1. 20Data Organization and GraphsBasic
  2. 21Mean, Median, ModeBasic
  3. 22Frequency Distribution GraphsAdvanced
⚡ Unit quiz 快測5 Qs

Answer on your own first, then reveal — wrong answers go to your wrong-answer book.

Q1Frequency means?

Q2Mean formula?

Q3Why group data?

Q4Compare category quantities use?

Q5Before finding median must?

多項式 Polynomials4/4 live

  1. 23Introduction to PolynomialsBasic
  2. 24Adding and Subtracting PolynomialsBasic
  3. 25Multiplying PolynomialsAdvanced
  4. 26Dividing PolynomialsAdvanced
⚡ Unit quiz 快測5 Qs

Answer on your own first, then reveal — wrong answers go to your wrong-answer book.

Q1Coefficient of 3x²?

Q2+(x - 2) = ?

Q3What is FOIL?

Q4x³ ÷ x = ?

Q5How many terms in 3x² + 2x - 5?

畢氏定理 Pythagoras' theorem3/3 live

  1. 27Pythagoras' TheoremBasic
  2. 28Applications of Pythagoras' TheoremAdvanced
  3. 29Converse of Pythagoras' TheoremAdvanced
⚡ Unit quiz 快測5 Qs

Answer on your own first, then reveal — wrong answers go to your wrong-answer book.

Q1Pythagoras' formula?

Q2Rectangle diagonal cuts into?

Q3Converse used for?

Q4Hypotenuse is?

Q5Ladder against wall, ladder is?

Vocabulary book 生字簿

All terms, bilingual (printable).

I
Index指數

The small number on top right, e.g. the 3 in 2³.

B
Base底數

The big number, e.g. the 2 in 2³.

P
Power冪

The whole thing, e.g. 2³ is read "2 to the power 3".

M
Multiply indices同底相乘

Same base, add indices.

D
Divide indices同底相除

Same base, subtract indices.

P
Power of power次方的次方

Multiply the indices.

E
Expand展開

Write power as product.

S
Simplify化簡

Use formulas to make complicated expression simple.

Z
Zero index零指數

Index is 0, e.g. a⁰.

N
Negative index負指數

Index is negative, e.g. a⁻ⁿ.

R
Reciprocal倒數

Flip numerator and denominator, e.g. reciprocal of 2 is 12.

1
1

Any non-zero number to power 0 equals 1.

F
Fraction分數

Negative index turns into fraction form.

B
Base底數

The big number.

U
Undefined未定義

0⁰ is undefined, don't use randomly.

S
Simplify化簡

Use formulas to make complicated expression simple.

S
Scientific notation科學記數法

Write number as a × 10ⁿ form.

S
Significant figure有效數字

Digits starting from first non-zero digit.

L
Large number大數

Number with many digits, e.g. 1000000.

S
Small number小數

Very small number, e.g. 0.000001.

P
Power of 1010 的次方

10ⁿ, e.g. 10³ = 1000.

M
Move decimal移小數點

Move decimal point left or right.

S
Standard form標準式

Formal name for scientific notation.

C
Convert轉換

Convert normal number to scientific notation, or vice versa.

C
Calculator計算機

Calculator used in exams.

P
Power button次方掣

Usually labelled ^ or xʸ.

E
EXP buttonEXP 掣

Button for scientific notation.

D
Display顯示

Calculator screen.

E
Error錯誤

Calculator shows ERROR.

R
Round四捨五入

Round answer to certain number of digits.

C
Check驗算

Check if answer is reasonable.

P
Practice練習

Practice more to get familiar.

I
Identity恆等式

Equation true for any number.

E
Equation方程

Equation true only for certain numbers.

V
Variable變數

e.g. x, can substitute different numbers.

P
Prove證明

Prove equation is true for any number.

E
Expand展開

Open up brackets.

S
Simplify化簡

Make expression simpler.

L
Left side左邊

Expression on left of equal sign.

R
Right side右邊

Expression on right of equal sign.

D
Difference of squares平方差

Two squares subtracted, i.e. a² - b².

B
Binomial二項式

Expression with two terms, e.g. (a+b).

M
Multiply相乘

Multiply two expressions.

E
Expand展開

Open up brackets.

F
Factorise因式分解

Write expression as product form.

P
Positive正數

Greater than 0.

N
Negative負數

Less than 0.

F
Formula公式

Rule you can apply directly.

P
Perfect square完全平方

A number times itself, e.g. (a+b)².

S
Square平方

A number times itself, e.g. a².

T
Twice兩倍

Times 2, e.g. 2ab.

P
Plus加

+ sign.

M
Minus減

- sign.

E
Expand展開

Open up brackets.

F
Factorise因式分解

Write expression as product form.

F
Formula公式

Rule you can apply directly.

A
Application應用

Use formula on real problems.

C
Calculate計算

Work out answer.

F
Factorise因式分解

Write expression as product form.

S
Simplify化簡

Make expression simpler.

R
Recognise辨認

Recognise which form it is.

S
Substitute代入

Substitute numbers into formula.

F
Fast快

Using formula is much faster.

P
Practice練習

Practice more to get familiar.

P
Percentage百分數

How many parts out of 100, symbol %.

P
Percent百分比

Same as above.

D
Decimal小數

Number with decimal point.

F
Fraction分數

Numerator denominator form.

C
Convert轉換

Change from one form to another.

P
Percent sign百分號

This symbol %.

1
100%

Means whole, equals 1.

B
Base基數

The number that percentage is based on.

I
Increase增長

Become bigger or more.

D
Decrease下降

Become smaller or less.

P
Percentage change百分變動

Changed part as percentage of original.

O
Original原來

Number before change.

N
New新

Number after change.

M
Markup加價

Price increased.

M
Markdown減價

Price decreased.

D
Discount折扣

How many percent off.

I
Interest利息

Money you get when lending or saving.

P
Principal本金

Original amount borrowed or saved.

R
Rate利率

How many percent interest per period.

T
Time時間

How long saved or borrowed.

S
Simple interest單利

Interest not compounded, only calculated on principal each year.

A
Amount本利和

Principal plus interest.

P
Per annum每年

Calculated once per year.

B
Bank銀行

Place to save money.

C
Cost price成本

Price boss paid to buy goods.

S
Selling price售價

Price sold to customers.

P
Profit利潤

Money earned.

L
Loss虧損

Money lost.

P
Profit per cent利潤率

Profit as percentage of cost.

L
Loss per cent虧損率

Loss as percentage of cost.

M
Marked price標價

Price written on goods.

D
Discount折扣

How many percent off.

R
Ratio比

Comparison between two numbers, symbol :.

A
Antecedent前項

Number before colon.

C
Consequent後項

Number after colon.

S
Simplify化簡

Write ratio in simplest form.

E
Equivalent ratio等比

Same value but different form ratios.

U
Unit單位

Unit of measurement.

D
Divide除

Antecedent divided by consequent.

P
Part部分

Part of whole.

D
Direct proportion正比

Two numbers increase and decrease together, ratio stays same.

C
Constant常數

Fixed number that doesn't change.

k
k

Constant of proportionality.

y
y = kx

Direct proportion formula.

I
Increase增加

Become bigger.

D
Decrease減少

Become smaller.

G
Graph圖像

Line drawn on graph.

O
Origin原點

Point (0,0).

I
Inverse proportion反比

Two numbers change opposite, product stays same.

C
Constant常數

Fixed number that doesn't change.

k
k

Constant of proportionality.

x
xy = k

Inverse proportion formula.

I
Increase增加

Become bigger.

D
Decrease減少

Become smaller.

C
Curve曲線

Curved line.

S
Speed速度

How fast you go.

P
Point點

Most basic geometric figure.

L
Line直線

Extends infinitely both ways.

A
Angle角

Where two lines meet.

D
Degree度

Unit to measure angle, symbol °.

P
Proof證明

Prove something is correct step by step.

G
Given已知

Conditions given by question.

P
Prove求證

Conclusion to prove.

R
Reason理由

Which theorem used for each step.

V
Vertically opposite angles對頂角

Two angles opposite each other when two lines cross.

P
Parallel lines平行線

Two lines that never meet.

T
Transversal截線

Line crossing parallel lines.

C
Corresponding angles同位角

Angles in same position.

A
Alternate angles內錯角

Between parallel lines, on opposite sides.

I
Interior angles同旁內角

Between parallel lines, on same side.

E
Equal相等

Same size.

S
Supplementary互補

Two angles add up to 180°.

C
Congruent全等

Same shape, same size.

T
Triangle三角形

Figure with three sides.

S
Side邊

Side of triangle.

A
Angle角

Angle of triangle.

S
SSS

Three sides equal.

S
SAS

Two sides and included angle equal.

A
ASA

Two angles and included side equal.

A
AAS

Two angles and non-included side equal.

S
Similar相似

Same shape, but size can be different.

S
Scale factor比例因子

Ratio of sizes between two figures.

C
Corresponding sides對應邊

Sides in same position.

C
Corresponding angles對應角

Angles in same position.

A
AAA

Three angles equal = similar.

R
Ratio比例

Comparison of two numbers.

P
Proportion比例式

Equation with two equal ratios.

F
Find unknown求未知

Find unknown.

D
Data數據

Numbers collected.

F
Frequency頻數

How many times appears.

T
Table表格

Table to organize data.

B
Bar chart棒形圖

Use bars to show quantity.

P
Pie chart圓形圖

Use pie to show proportion.

L
Line graph折線圖

Use line to show trend.

P
Pictogram象形圖

Use pictures to show quantity.

T
Title標題

Title of graph.

M
Mean平均數

Sum all numbers divided by count.

M
Median中位數

Middle number when sorted.

M
Mode眾數

Number that appears most times.

D
Data set數據集

A set of data.

S
Sort排序

Arrange from small to big.

O
Outlier偏異值

Number very different from others.

C
Central tendency集中趨勢

Where data clusters around.

A
Average平均

General term for three averages.

F
Frequency distribution頻數分佈

How data is distributed in each group.

G
Group組

Group data.

C
Class interval組區間

Range of each group.

S
Stem-and-leaf幹葉圖

Use stem and leaf to show data.

S
Stem幹

Tens digit.

L
Leaf葉

Units digit.

T
Tally記錄

Counting with tally marks.

C
Cumulative frequency累積頻數

Adding up from small to big.

P
Polynomial多項式

Expression made of variables and constants added/subtracted.

T
Term項

Each part of polynomial.

C
Coefficient係數

Number in front of variable.

C
Constant term常數項

Number that doesn't change.

D
Degree次數

Highest power.

V
Variable變數

Number that can change, e.g. x, y.

L
Like terms同類項

Terms with same variable part.

M
Monomial單項式

Only one term.

A
Add加

Put together.

S
Subtract減

Take away.

B
Bracket括號

( ).

R
Remove bracket拆括號

Take away brackets.

D
Distribute分配

Multiply outside number to each inside term.

S
Simplify化簡

Make it simplest form.

E
Evaluate求值

Substitute numbers to get answer.

Z
Zero pair零對

Same number positive and negative add to 0.

M
Multiply乘

Product.

D
Distributive law分配律

a(b+c) = ab + ac.

F
FOIL

First, Outer, Inner, Last.

B
Binomial二項式

Polynomial with two terms.

P
Product積

Result after multiplication.

P
Power rule指數法則

xᵐ × xⁿ = xᵐ⁺ⁿ.

E
Expand展開

Multiply out.

C
Coefficient係數

Number in front.

D
Divide除

Divide.

D
Divisor除數

Number dividing by.

D
Dividend被除數

Number being divided.

Q
Quotient商

Answer after division.

R
Remainder餘數

Leftover.

C
Cancel約分

Cancel common factors.

E
Exponent rule指數法則

xᵐ ÷ xⁿ = xᵐ⁻ⁿ.

S
Simplify化簡

Make simplest.

R
Right angle直角

90° angle.

R
Right triangle直角三角形

Triangle with one right angle.

H
Hypotenuse斜邊

Longest side opposite right angle.

L
Leg股

Two sides forming right angle.

S
Square平方

Multiply by itself.

S
Square root平方根

Reverse of square.

T
Theorem定理

Proven rule.

P
Pythagoras畢氏

Ancient Greek mathematician.

A
Application應用

Use to solve problems.

L
Ladder梯

Ladder leaning against wall.

D
Diagonal對角線

Diagonal of rectangle.

R
Rectangle長方形

Quadrilateral with four right angles.

D
Distance距離

Length between two points.

C
Coordinate坐標

(x, y).

W
Word problem應用題

Word problem.

R
Real life現實生活

Daily life.

C
Converse逆定理

Reverse theorem.

C
Check驗證

Check if correct.

R
Right angle直角

90°.

L
Longest side最長邊

Longest side.

S
Square平方

Multiply by itself.

E
Equal相等

Same size.

T
Triangle三角形

Figure with three sides.

V
Verify驗證

Prove correct.

More units rolling out in batches — same illustrated format.