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Matholicism
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Primary School
Primary 1
P1.1 Numbers to 100
P1.1.1 Counting to 10
P1.1.2 Add & Subtract 1 to 10
P1.1.3 Digit
P1.1.4 Add & Subtract Numbers to 100
Addition
Addition & Subtraction Checkpoint
Addition of Length
P1.2 Ordinal Numbers
Primary 2
P2.1 Numbers to 1000
P2.1.1 Counting to 1000
P2.1.2 Spelling Numbers to 1000
P2.1.3 Ordering numbers to 1000
P2.2 Addition & Subtraction to 1000
P.2.2.3 Addition and Subtraction to 1000
P2.3 Multiplication and Division (2,3,4,5, and 10)
P2.4 Lengths & Mass
P2.4.1 Lengths
P2.6 Fractions Part 1
P2.6.1 What is a Fraction?
P2.6.3 Ordering Fractions
P2.7 Time
Clock Activity 2
P2.8 2D & 3D Shapes
P2.8.1 2D Shapes (2)
P2.10 Pictograms
Primary 3
P3.1 Numbers to 10 000
P3.3 Multiplication
P3.4 Division
P3.6 Time
P3.7 Fractions (Part 2)
P3.7.1 Equivalent Fractions
P3.9 Angles
P3.11 Perimeter & Area
P3.12 Bar Graphs
Workbook Tasks
P3. Revision
Mental Sums Quiz
Arithmetic Game
Mathjong Game
Primary 4
P4.1 Numbers to 100 000
P4.2 Rounding & Estimation
P4.3 Factors & Multiples
P4.5 Fractions
4.7 Decimals
P4.7.1 Decimals
4.7.3 Convert Fractions to Decimals
P4.9 Angles
P4.9.4 8 Point Compass
Cardinal Quiz
P4.5.2 Improper Fractions
Primary 5
P5.2 Order of Operations
P5.6 Rate
P5.7 Percentage
P5.8 Triangles
P5.8.1 Area of Triangle
P5.9 Volume
P5.9.1 Volume of Cube / Cuboid
P5.10 Angles
P5.10.3 Vertically Opposite Angles
P5.11 Quadrilaterals
Primary 6
6.4 Percentage
6.6 Angles
6.7 Circles
6.7.1 Estimating Pi
6.7.2 Circumference of Circle
6.7.3 Area of Circle Proofs
6.8 Volume of a Cuboid
Sec 1
1.1 Factors & Multiples
1.1.1 Natural Numbers
1.1.2 Factors
Amicable & Perfect Numbers
1.1.3 Prime Numbers
1.1.4 Prime Factorisation
1.1.5 Highest Common Factor
Euclidean Algorithm
1.1.6 Lowest Common Multiple
1.1.7 Squares and Cubes
(Olympiad) Trailing Zeroes
(Olympiad) Divisibility Tests
1.2 Real Numbers
1.2.1 Negative Numbers
Poem: A Positive Reminder
1.2.2 Integers
Palindromic Numbers
1.2.3 Rational Numbers
1.2.4 Irrational Numbers
1.2.5 BODMAS on Real Numbers
1.3 Approximation & Estimation
1.3.1 Rounding
1.3.2 Decimal Places
1.3.3 Significant Figures
1.4 Introduction to Algebra
1.4.0 History of Algebra
1.4.1 Algebraic Expressions
1.4.2 Like & Unlike Terms
1.4.3 Algebraic Expressions
1.4.4 Expand Algebraic Expressions
1.4.5 Factorise Algebraic Expressions
1.4.6 Linear Equations
1.4.7 Linear Inequalities
1.5 Introduction to Geometry
1.5.1 Definitions of Point & Lines
1.5.2 Angle Properties
1.5.3 Parallel Lines & Transversals
1.5.4 Line of Symmetry
1.5.5 Rotational Symmetry
1.5.6 Loci & Construction
1.5.6.1 More Loci
1.5.6.2. Voronoi Diagrams
NUSH Loci Problems
Challenging Questions (Geometry I)
(Enrichment) Centres of a Triangle
1.6 Triangles, Quadrilaterals & Polygons
1.6.1 Special Triangles
1.6.2 Triangle Properties
1.6.3 Types of Quadrilaterals
1.6.4 Types of Polygons
1.6.5 Polygon Properties
Checkpoint (Geometry)
Challenging Question (Polygon)
(Olympiad) Useful Property (2 Squares)
(Olympiad) Area of Dodecagon
(Olympiad) Viviani's Theorem
1.7 Ratio, Rate & Speed
1.7.1 Ratio
1.7.3 Speed
1.8 Percentages
1.8.1 Calculating Percentages
1.9 Number Patterns
1.10 Coordinate Geometry
1.10.0 Basic Definitions
1.10.1 Coordinates System
1.10.2 Gradient of a Straight Line
Optical Illusion
1.10.3 Equation of a Straight Line
1.10.3.1 Intercept & General Form
1.10.4 Drawing a Straight Line Graph
1.10.5 Real World Context
1.11 Perimeters and Areas of Plane Figures
1.11.1 Squares & Rectangles
1.11.2 Parallelograms
1.11.3 Rhombus
1.11.4 Trapezium
1.12 Volumes & Areas of Solids
1.12.1 Prism
1.12.2 Cylinders
(BL) Prisms and Cylinders
Nets of Cubes (all 11)
Cube Rotation & Shadows
(Enrichment) Platonic Solids
Truncated Hexahedron
Nets of Polyhedrons
(Enrichment) Net of a 4D Hypercube
(Enrichment) Olympiad Questions
Sec 2
2.1 Proportions
2.1.1 Direct Proportions
2.1.2 Inverse Proportions
2.1.3 Map Scales
2.2 Algebraic Expansion & Factorisation
2.2.1 Quadratic Identities
2.2.2 Quadratic Expansion
2.2.3 Quadratic Factorisation
2.2.4 Group Factorisation
(Olympiad) Mental Square Roots
2.3 Simple Algebraic Fractions
2.3.1 Simplify Algebraic Fraction
2.3.2 Product of Algebraic Fractions
2.3.3 Sum of Algebraic Fractions
2.3.4 Change Subject
2.4 Quadratic Equations
2.4.1 Solving Quadratic Equations (Factorisation)
2.5 Simultaneous Equations
2.5.2 Elimination Method
2.5.3 Graphical Solution
Cow & Chicken
2.6 Congruency & Similarity
2.7 Pythagoras' Theorem
2.7.1 Proof of Pythagoras' Theorem
2.7.2 Application of Pythagoras' Theorem
2.7.3 Converse of Pythagoras' Theorem
2.7.4 Beauty of Pythagoras' Theorem
(Olympiad) Corollaries & Challenging Problems
2.8 Trigonometric Ratios
2.8.1 Trigonometric Ratios
2.8.2 Inverse Trigonometric Functions
Challenging Questions
2.9 Mensuration of Pyramids, Cones & Spheres
2.9.1 Surface Area of Pyramids
2.9.2 Volume of Pyramids
2.9.3 Surface Area of a Cone
2.9.5 Surface Area of Sphere
2.9.6 Volume of Sphere
NUSH Y1 Mensuration Problems
2.10 Statistics Part 2
2.10.2 Stem & Leaf Diagrams
2.10.3 Histogram (Ungrouped)
Histogram vs Bar Chart
2.11 Probability
2.11.1 Sample Space
Sec 3
3.1 Indices
3.1.1 Laws of Indices
3.1.2 Index Law of Addition & Subtraction
3.1.3 Index Power Law
3.1.4 Index Distribution Law
3.1.5 Zero Index Law
3.1.6 Negative Index Law
3.1.7 Fractional Index Law
3.1.8 Solve Index Equations
3.1.9 Standard Form
Prefixes
3.1.10 Compound Interest
CPF
3.1.11 Exponential Graph
TDD Challenge
Password Math
3.2 Quadratics Equations
3.2.1 Completing the Square
Completing the Square Method
Graph of Complete-the-Square Form
3.2.2 Quadratic Formula
Quadratic Word Problems
3.2.3 Fractional Equations
3.2.4 Quadratic Word Problems
3.2.5 Sketching Quadratic Graphs
Quadratic Graph
Sketching Quadratic Graphs Checkpoint
Checkpoint for Sketching Quadratic Curves
3.2.6 Graphical Method
Projectile Motion
Satellite Dish
3.3 Linear Inequalities
3.3.5 JIM Questions
3.4 Congruency & Similarity
3.4.1 Congruency Tests
3.4.2 Similarity Tests
3.4.3 Scale Factor
3.4.4 Triangles of Common Heights
Frustum
3.5 Coordinate Geometry
3.5.1 Length of Line Segment
3.5.2 Gradient of Line Segment
3.5.3 Equation of a Straight Line
3.6 Functions & Graphs
3.6.1 Power Functions
降龙十八Graphs (上)
降龙十八Graphs (下)
Graph Matching Game
3.6.2 Drawing a Graph
3.6.3 Gradient of a Curve
3.6.4 Approximate Solution (Intersection of 2 graphs)
3.6.5 Kinematic Graphs
3.6.6 Flow Rate Graphs
3.6.7 Misc Graphs in Practical Situation
The Paper Bag Challenge
3.7 Trigonometry
3.7.1 Obtuse Angles
3.7.2 Area of Triangle (Trigo)
3.7.3 Sine Rule
3.7.4 Cosine Rule
3.7.5 Bearings
3.7.6 Angles of Elevation & Depression
3.7.7 3D Geometry Problems
NUSH Y2 Problems
Shing Lee Textbook
National Exam Questions (3D Models)
2017 O-Level P2 Q5
2016 O-Level P2 Q8
2015 O-Level P2 Q7
2015 N-Level P2 Q5
3.8 Circular Measure
3.8.1 Radian
Gradian
3.8.2 Arc Length
3.8.3 Sector Area
3.8.4 Area of a Segment
Fuhua's Green House
Challenging
3.9 Circle Properties
3.9.1 Parts of a Circle (Extended)
3.9.2 Equal Chords Equidistant from Centre
3.9.3 Perpendicular Bisector of Chord
3.9.4 Angle at Centre = 2x Angle at Circumference
3.9.5 Right Angle in Semicircle
3.9.6 Angles in the Same Segment
3.9.7 Opposite Angles of Cyclic Quad
3.9.8 Tangent perpendicular to Radius
3.9.9 Tangents from an external Pt
Sec 4
4.1 Set Language Notation
4.1.1 Set Notation
4.1.2 Complement, Union & Intersection
Checkpoint of Set Notations
4.1.3 Venn Diagrams
4.2 Probability
4.2.1 Sample Space
Dice
Guessing Game
Pi Generator
Buffon's Needle
4.3 Statistics
4.3.1 Cumulative Frequency Graphs
4.3.2 Box & Whisker Plot
4.3.3 Mean & Standard Deviation
4.3.3.1 Mean & S.D (Frequency)
4.3.3.2 Group Mean & S.D
IQ
4.3.4 Statistical Misrepresentation
4.3.4.1 Bias Collection of Data
4.3.4.2 Statistical Diagrams
4.3.4.3 Fallacious Analysis
Bar Graph
4.4 Matrix
4.4.1 Order of a Matrix
4.4.2 Matrix Addition & Subtraction
4.4.3 Matrix Multiplication
Determinant
The Formula for Love
4.5 Vectors
4.5.2 Vector Addition & Subtraction
4.5.3 Scalar Multiplication
4.5.6 Vector Sum
Additional Mathematics
0. What is a function?
1. Quadratic Functions
1.1 Complete-the-Square
1.2 Simultaneous Equations
1.3 Quadratic Inequality
1.4 Nature of Roots
1.4.1 NUSH Questions
1.5 Vieta's Formulas
2. Surds
2.1 Simplifying Surds
2.2 Conjugate Surd
2.3 Surd Equations
2.4 Nested Surds
3. Polynomial Functions
3.1 Polynomial Long Division
3.2 Remainder Theorem
3.3 Factor Theorem
3.4 Sum & Difference of 2 Cubes
3.5 Solving Cubic Equations
3.6 Partial Fractions
3.7 Power Functions
4. Exponential Functions
4.1 Indice Laws
4.2 Exponential Equations
4.3 Substitution Method
4.4 Euler's Number, e
4.5 Exponential Graph
Epidemics
Radioactive Decay
5. Logarithmic Functions
5.1 Conversion to Logarithmic Form
5.2 Product & Quotient Law
5.2.1 Slide Rule
5.3 Power Law
5.4 Change of Base & Reciprocal Law
5.5 Logarithmic Equations
5.6 Logarithmic Graph
pH Value
Richter Scale
6. Binomial Theorem
6.1 Pascal's Triangle
6.2 Cubic Expansion
6.3 Factorial Function
6.4 Combination Function
Binomial Expansion Practice
7. Coordinate Geometry
7.1 Angle of Inclination
7.2 Parallel Lines
7.3 Perpendicular Lines
7.4 Midpoint
7.5 Shoelace Method
Coordinate Geometry Checkpoint
7.6 Equation of a Circle
7.6.1 Circle Transformations
7.6.2 Tangent to a Circle
7.6.3 Circumcircle
7.6.4 Int & Ext point of a Circle
(Enrichment) Pick's Theorem
8. Linear Law
8.1 Forming a non-linear equation
8.2 Transforming a non-linear Equation
9. Trigonometry
9.1 Special Angles
9.2 Complementary Angles
9.3 The Unit Circle
9.4 Solving Trigo Equations (1)
9.5 Negative Angles and angles larger than 360°
9.6 Secant, Cosecant & Cotangent
9.7 Principal Values
9.8 Axis of Curve, Amplitude & Period
9.9 Trigonometric Graph
Ferris Wheel
9.10 Pythagorean Identities
9.11 Angle Addition Formulas
9.12 Double Angle Formula
9.13 Proving Trigonometric Identities
9.14 Solving Trigo Equations (2)
9.15 R-Formulae
NUSH Assignment 1 Q3
Trigo Among Us!
Olympiad Identities
10. Differentiation
10.1 Differentiation of Power Functions
10.2 Chain Rule
10.3 Product Rule
10.4 Quotient Rule
10.5 Tangent & Normal to a Curve
10.6 Increasing/Decreasing Functions
10.7 Connected Rates of Change
10.8 Stationary Points
NUSH Problems
Differentiation of Trigonometric Functions
11. Integration
11.3 Practice Time!
12. Kinematics
12.1 Kinematic Terms
13. Plane Geometry
13.2 Midpoint Theorem
13.4 Alternate Segment Theorem
(Olympiad) Intersecting Chord Theorem
(Olympiad) Tangent-Secant Theorem
(Olympiad) Intercept Theorem
(Olympiad) Angle Bisector Theorem
JC (A-Level) H2 Math
J1. Functions & Graphs
J1.1 Intro to Function
J1.4 Inverse Functions
J1.6 Modulus Functions
J1.7 Conic Sections
J1.7.1 Eccentricity, Directrix & Focus
J1.8 Ellipses
J1.9 Hyperbolas
J1.10 Rational Functions
NUSH Questions (Rational)
J1.11 Graph Transformations
J2. Sequence & Series
J2.1 Summation Notation
J2.2 Method of Difference
J2.3 Arithmetic Series
The Handshake Problem
J2.4 Geometric Series
Sum of Squares
Sum to Infinity
Nicomachus's Theorem
J3. 3D Vectors
J3.3 Magnitude of Vector
J3.4 Unit Vectors
J3.4.1 Directional Cosines
J3.5 Dot Product
J3.6 Applications of the Dot Product
J3.7 Cross Product
J3.8 Equation of a Line
J3.9 Equation of a Plane
J4. Complex Numbers
J4.1 Quadratic Equations (Complex Roots)
J4.3 Complex Conjugate
J4.4 Argand Diagram
J4.5 Polar Form
J4.6 Euler's Identity
J4.8 Roots of Unity
J5. Calculus
J5.3 Implicit Differentiation
J5.4 Parametric Equation
NUSH Y4 Questions
J5.5 Maclaurin Series
J5.5.1 Generalised Binomial Theorem
J5.5.2 Taylor Series
J5.6 Integrate by Substitution
Integration Practice
J5.7 Volume of Revolution
NUSH Problems
J5.8 Differential Equations
Euler's Method
Slope Fields
Riemann Sums
J6. Probability & Statistics
J6.1 Permutations
J6.3 Conditional Probability
J6.4 Binomial Distribution
Squid Game #5
J6.5 Normal Distribution
Poisson Distribution
Geometric Distribution
Exponential Distribution
University Math
Real Analysis
Bounds
Sequences
Convergence
Divergence
Cauchy Sequence
Continuous Function
Bolzano–Weierstrass Theorem
Graph Theory
Tree
Fourier Series
Physics
1) Measurement
1.1 Basic Quantities & SI Units
1.2 Prefixes
Vernier Calipers
Scalars & Vectors
3) Forces
Inclined Plane
8) Thermal Physics
Brownian Motion
Ideal Gas
9) Light
Convex Lens
Snell's Law
Chemistry
3D Molecular Models
Solubility of Salts
Periodic Table
Enrichment
Study Skills
Memory Games
SASMO Training
SASMO (Geometry Questions)
Mathematical Modelling
S.I.R Model
Math & Science Jokes
Squid Game #4
Geoboard
Cycloid
Fractals
Koch Snowflake
Sierpinski Triangle
Fractal Canopy
Spherical Geometry
Lissajous Curves
Common Passwords
Speech Day Heritage Challenge
Heritage Challenge 1
Heritage Challenge 2
Heritage Challenge 3
Heritage Challenge 4
National Day 2021 Challenge
Christmas 2022
Brain Teasers
Infinite Chocolate Illusion
Mind Reading Trick
Missing Square Illusion
Templates
Links
Feedback
Matholicism
Ratio, Rate & Speed
Success Criteria
At the end of this chapter, students are able to:
Convert a ratio into a fraction and vice-versa.
Find and simplify the ratio of 2 to 3 quantities.
Calculate the speed of an object.
Overview of Ratio, Rate & Speed
A
ratio
is a comparison of two or more quantities of the same type.
A
rate
is a comparison of two quantities of different types.
Speed
is the rate of change of distance with respect to time.
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