mapping document This document outlines the mapping of Hong Kong Curriculum outcomes to particular topics and subtopics within Mathspace.
Key Stage 2 K4-K6 – Page
Key Stage 3 S1-S3– Page Number and Algebra Measures, Shape and Space Data Handling
NF – Non foundation ** - exemplars of enrichment topics # coming soon
Key Stage 4 – Compulsory Module S4-S5 - Page Number and Algebra Measures, Shape and Space Data Handling
KS3
Number and Algebra
Number and Number Systems Directed Numbers and the Number Line understand and accept intuitively the concept and uses of negative numbers
Directed Numbers:
have simple ideas of ordering on the number line
Directed Numbers:
explore and discuss the manipulation of directed numbers
manipulate directed numbers
Directed Numbers:
Representation of Directed Numbers Comparisons of Directed Number Statements Integer Number Line Comparing Sizes of Integers Negative Number Placement and Opposites# Comparisons of Directed Number Statements Negative Number Placement and Opposites# Comparisons of Directed Number Statements Addition of Integers Subtraction of Integers Adjacent Signs Multiplication of Integers Division of Integers Addition of Integers Subtraction of Integers Adjacent Signs Multiplication of Integers Division of Integers Negative Squares and Cubes Order of Operations Order of operations with directed rational numbers
Numerical Esimation Not yet covered
be aware of the need to use estimation strategies in real-life situations and appreciate the past attempts to approximate values such as π determine whether to estimate values or to compute the exact values select and use estimation strategies to estimate values and to judge the reasonableness of results choose appropriate means for calculation such as mental computation, calculators or paper and pencil etc.
Not yet covered Not yet covered Not yet covered
Approximation and Errors acquire further concepts and skills of rounding off numbers to a required number of significant figures understand the meaning of scientific notation use scientific notation in practical problems
be aware of the size of errors during estimation and approximation understand and calculate different types of errors such as absolute errors, relative errors and percentage errors Page 2
Approximation and Errors:
Significant Figures
Approximation and Errors: Approximation and Errors:
Introducing Scientific Notation #
Approximation and Errors: Approximation and Errors:
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Scientific Notation I Scientific Notation II Using a Calculator for Scientific Notation # Errors in Measurement # Errors in Measurement #
Rational and Irrational Numbers be aware of the existence of irrational numbers and surds
Surds:
Rationals and Irrationals Answers that result in irrational numbers Rational and Irrational Operations # Exact Answers VS Decimal Evaluations Approximating Irrational Numbers #
explore the representations of irrational numbers in the number line (NF) manipulate commonly encountered surds including the rationalization of the denominator in the form of √a
Surds: Surds:
Addition and subtaction of Surds Multiplication and Division of Surds Rationalising the Denominator
(NF) appreciate the expressions of surds could be expressed in a more concise form
Surds:
Simplifying Surds Addition and subtaction of Surds Multiplication and Division of Surds
Comparing Quantities Using Percentages understand the meaning of percentages and percentage changes
Percentages:
apply percentage changes to solve simple selling problems
Percentages:
apply percentages to solve problems involving simple and compound interests, growth and depreciation
Percentages:
Percentage of a Quantity Percentage Composition Percentage Change Unitary Method Business Applications of Percentages Best Buys and Discounts Deferred Payment Plans Payment Methods Simple Interest Compound Interest Introduction Compound Interest - Compound Variations Compound Interest - Finding Other Values Applicaions of Compound Interest Depreciation Applications of Compound Interest Growth and Decay
More About Percentages apply percentages to solve further practical problems involving successive and component changes apply percentages to solve simple real-life problems involving taxation and rates
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Percentages:
Repeated Percentage Change #
Percentages:
Wages and Salaries Commission and Other Income Profit and Loss Overtime and Extra Income Wage Deductions and Net Income Effective Interest Rates Loans Credit Cards
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Rate and Ratio understand the meaning of rate and ratio
Ratios and Rates:
recognize the notation of a : b, a : b : c
Ratios and Rates:
apply the ability in using rate, ratio to solve reallife problems including mensuration problems
Ratios and Rates:
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Introduction to Ratios and Rates Ratio Tables Rates I Rates II Introduction to Ratios and Rates Ratio Tables Simplifying Ratios I Simplifying Ratios II Simplifying Ratios III Dividing a Quantity into a Given Ratio Ratios with Fractions Ratios with Fractions and Percents # Decimal Ratios Applications of Ratios I Applications of Ratios II Applications of Ratios III Applications of Ratios IV Scales, Maps and Ratios I Scales, Maps and Ratios II
Observing Patterns and Expressing Generality Formulating Problems with Algebraic Language appreciate the use of letters to represent numbers
Algebra:
Pictorial Representations of Algebra Describing Number Patterns Algebraic Expressions Components in an expression # Algebraic Conventions
understand the language of algebra including translating word phrases into algebraic expressions or write descriptive statement for algebraic expressions note the differences between the language of arithmetic and the language of algebra recognize some common and simple formulas which can be expressed as algebraic forms and be able to substitute values
Algebra:
Modelling Algebraic Expressions Rules for Describing Sequences Worded Problems
Algebra:
Substitution into Expressions Table of values Substitution into Algebraic Expressions Substitution in to complete a table of values Substitution into common formulas Formulas arising from Substitution Algebra in Measurement
formulate simple algebraic equations/ inequalities to solve problems
Algebra:
Algebraic Equations Equations Number Sentences Introduction to Equations Values that Satisfy Equations Balancing Equations Backtracking Building Expressions Using Backtracking One Step Equations Two Step Equations Number Problems Problem Solving with Equations Introduction to Inequalities One Step Inequalities Creating Inequalities with 1 Variable # Creating Inequalities with 2 Variables # Introduction to Arithmetic Progressions # Introduction to Geometric Progressions #
Not yet covered
Equations:
Inequalities:
Algebra:
investigate, appreciate and observe the patterns of various number sequences such as polygonal numbers, arithmetic and geometric sequences, Fibonacci sequence etc. use algebraic symbols to represent the number patterns obtain a preliminary idea of function such as input-processing-output concept
Algebra:
Polynomials and Other Functions:
Modelling Algebraic Expressions Rules for Describing Sequences Worded Problems Function Notations ^
Manipulations of Simple Polynomials recognize polynomial as a special example of algebraic expressions recognize the meaning of the terminology involved
Polynomials and Other Functions:
Polynomials and Notation ^
Polynomials and Other Functions:
add, subtract, multiply polynomials involving more than one variable
Polynomials and Other Functions:
Functions and Relations Definitions Function Notations Polynomials and Notation Addition and Subtraction of Polynomials # Multiplication of Polynomials #
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Laws of Integral Indices Indices:
extend and explore the meaning of the index notation of numbers with negative exponents
Algebra:
explore, understand and use the laws of integral indices to simplify simple algebraic expressions (up to 2 variables only) (NF) understand and compare numbers expressed in various bases in real-life situations (NF) foster a sense of place values in different numeral systems
Indices:
Numbers in Other Bases #
Indices:
* Roman Numerals * Egyptian Numbers * Binary Number System Numbers in Other Bases #
Indices:
(NF) inter-convert between simple binary/hexadecimal numbers to decimal numbers
Negative Indices Numerical Bases with Negative Indices Numerical Bases with Negative Indices (mult and division) Numerical Bases with Negative Indices (power of power) Numerical Bases with Negative Indices (mixed) Mixed Index Laws Negative Indices Multiplciation Law with Negative Indices Division Law with Negative Indices Power of Power with Negative Indices Products and Quotients with Negative Indices Algebraic Multiplication and Division Using the Index Laws
Factorization of Simple Polynomials understand factorization as a reverse process of exapnsion factorize polynomials by using common factors and grouping of terms
Expansions and Factorisations:
Difference of Two Squares ^ Perfect Squares ^
Expansions and Factorisations:
factorize polynomials by using identifies including difference of two squares; perfect square expressions; difference and sum of two cubes (NF – difference and sum of two cubes)
Expansions and Factorisations:
factorize polynomials by cross-method
Expansions and Factorisations:
Factorising the HCF I Factorising Algebriac Factors Factorising the HCF II Highest Common Factor Grouping in Pairs Difference of Two Squares Perfect Squares Monic Quadratic Trinomials Micellaneous Factorisations Further Factorisations Non-Monic Quadratic Trinomials
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Algebraic Relations and Functions Linear Equations in One Unknown formulate and solve linear equations in one unknown
Equations:
**solve literal equations
Equations:
One Step Equations Two Step Equations Number Problems Problem Solving with Equations Identifying Patterns Simple Number Problems Keeping Equations Balanced Simple Equations Three Step Equations Grouping with Pronumerals I Grouping with Pronumerals II Problem solving with Equations Solutions to Linear Equations # Comparing Linear Equations Solve Equations (add/sub) with rational expressions # Solve Equations (mult) with rational expressions # Solve Equations (div) with rational expressions # Equations involving Fractions Formulae and Substitution Measurement Equations Creating Equations with 1 Variable # Changing the subject of a formula
Linear Equations in Two Unknowns plot and explore the graphs of linear equations in 2 unknowns
Coordinate Geometry:
formulate and solve simultaneous equations by algebraic and graphical methods
Simultaneous Equations:
be aware of the approximate nature of the graphical method **explore simultaneous equations that are inconsistent or that have no unique solution
Simultaneous Equations: Simultaneous Equations:
Interpreting Graphs Horizontal and Vertical Lines Points on a Line Intercepts Identifying Linear Equations - Graphs Linear Relationships - graphs Solving Equations with Straight Lines Practical Linear Relationships Sketching Linear Graphs Modelling Linear Relationships - graphs Problem Solving Introduction to Simulataneous Equations The Graphical Method The Substitution Method The Elimination Method Problems with Simultaneous Equations The Graphical Method ^ The Substitution Method ^ The Elimination Method ^ Problems with Simultaneous Equations ^
Identities explore the meaning of identities and distinguish between equations and identities discover and use the identities : difference of two squares; the perfect square expression; difference and sum of two cubes (NF – difference and sum of two cubes)
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Not yet covered Expansions and Factorisations:
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Expanding Difference of two Squares Expanding Perfect Squares Miscellaneous Expansion
Formulas manipulate algebraic fractions with linear factors as denominators
Algebra:
develop an intuitive idea of factorization of polynomials explore familiar formulas and substitute values of formulas
Polynomials and Other Functions:
perform change of subject in simple formulas but not including radical sign
Equations:
Algebra: Equations:
Algebriac Fractions I Algebraic Fractions II Addition and Subtaction of Algebraic Fractions Multiplication and Division of Algebraic Fractions Mixed Operations with Algebraic Fractions Simplifying Algebraic Fractions Factorising Algebraic Fractions I Factorising Algebraic Fractions II Extending concepts of curve sketching # Substitution into common formulas Formulas arising from Substitution Formulae and Substitution Changing the subject of a formula Formulae and Substitution Changing the subject of a formula
Linear Inequalities in one unknown understand the meaning of inequality signs ≥ , > , ≤ and < explore the fundamental properties and some laws of inequalities solve simple linear inequalities in one unknown and represent the solution on the number line
Inequalities:
Introduction to Inequalities One Step Inequalities
Inequalities:
Introduction to Inequalities ^
Inequalities:
Two Step inequalities Problem Solving with Inequalities # Identifying Solutions to Inequalities # Three step Inequalitites Compound Inequalities #
Included as background and supporting work Algebra:
Whilst not explicitly required as part of the curriculum, these subtopics are included for background and supporting work for the benefit it can add to student learning and understanding.
Indices:
Polynomials and Other Functions: Expansions and Factorisations: Coordinate Geometry:
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Equivalent Expressions Laws of Arithmetic with Algebraic Terms Addition and subtraction of Like Terms Addition and subtraction of Algebriac Terms Multiplication of Algebraic Terms Division of Algebraic Terms Distributive Law Simplifying expressions with grouping symbols Relationships between two Quantities Index Notation The Zero Index Multiplication Law I Multiplication Law II Division Law I Division Law II Power of a Power Further Application of Index Laws Polynomial Division # Complete the Square Unit Rates and Graphs # Comparing unit rates # Simple Proportional Relationships # Intercepts and The Intersection of Lines
KS3
Measures, Shape and Space
Measures in 2-D and 3-D Figures Estimation in Measurement Not yet covered
recognize the approximate nature of measurement and choose an appropriate measuring tool and technique for a particular purpose choose an appropriate unit and the degree of accuracy for a particular purpose develop estimation strategies in measurement handle and reduce errors in measurement estimate, measure and calculate lengths, areas, capacities, volumes, weights, rates, etc.
Not yet covered Not yet covered Not yet covered Not yet covered
Simple Ideas of Areas and Volumes find areas of simple polygons
Measurement:
explore the formula for the area of a circle calculate circumferences and areas of circles
Measurement: Measurement:
understand and use the formulas for surface areas and volumes of cubes, cuboids, prisms and cylinders
Measurement:
appreciate the application of formulas, besides measurement, in finding measures and be aware of the accumulated errors arisen **explore the maximum area of figures for a given perimeter **design a container by cutting squares from the 4 corners of a sheet of A4 paper to maximize the capacity of the container
Measurement:
Area of Rectangles and Squares Area of a Triangles Area of Parallelograms Area of Composite Shapes I Area of Composite Shapes II Exploring the area of special quadrilaterals# Area of Special Quadrilaterals Area of a Circle Circumference Area of a Circle Volume of Rectangular Prisms Volume Volume of Prisms I Volume of Prisms II Volume of Cylinders I Volume of Cylinders II Volume of Composite Solids I Volume of Composite Solids II Applications of Volume Surface Area of Prisms I Surface Area of Prisms II Surface Area of Cylinders I Surface Area of Cylinders II Surface Area of Simple Composite Solids Surface Area of Composite Solids Surface Area of Complex Composite Solids Error in Measurement #
Measurement:
Area of Rectangles and Squares (i)
Measurement:
Volume of Prisms II
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More About Areas and Volumes calculate arc lengths and areas of sectors understand and use the formulas for volumes of pyramids, circular cones and spheres
Measurement: Measurement:
understand and use the formulas for surface areas of right circular cones and spheres
Measurement:
understand and use the relationships between sides, surface areas and volumes of similar figures distinguish between formulas for length, area, volume by considering dimensions
Area and Perimeter of Sectors Volume of Right Pyramids Volume of Right Cones Volume of Spheres Volume of Composite Solids I Volume of Composite Solids II Applications of Volume Surface Area of Right Pryamids and Cones Surface Area of a Sphere Surface Area of Complex Composite Solids Not yet covered
Not yet covered
Learning Geometry Through an Intuitive Approach Introduction to Geometry recognize the common terms and notations in geometry such as line segments, angles, regular polygons, cubes and regular polyhedra (Platonic solids) etc. identify types of angles and polygons
Geometry:
Polygons Lines, Intervals and Rays
Geometry:
construct 3-D solids and explore their properties, such as Euler’s formula sketch the 2-D representation of simple solids
Geometry:
Polygons Classification of Solids Faces, Edges and Vertices in Polyhedra Nets of solids Naming Angles Measuring, Estimating and Drawing Angles# Complementary and Supplementary Angles Faces, Edges and Vertices in Polyhedra
sketch the cross-sections of the solids
Geometry:
overview tools of geometry and explore ways of using them to construct polygons, circles, parallel and perpendicular lines **recognize some semi-regular polyhedra (Archimedean Solids)
Geometry:
Nets of solids Constructing 3D Shapes # Drawing and Recognising Shapes with Properties # Visualising Prisms Cross Sections of Prisms Constructions with a Compass (i) #
Geometry:
Classification of Solids (i) ^
Geometry:
Transformation and Similarity recognize reflectional and rotational symmetries in 2-dimensional (2-D) shapes recognize the effect on 2-D shapes after the transformation including reflection, rotation, translation, dilation/contraction etc. appreciate the symmetrical shapes around and transformations on shapes used in daily-life **construct and design tile patterns
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Geometry: Congruence and Similarity: Congruence and Similarity:
Geometry: Congruence and Similarity:
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Symmetry Line and Rotational Symmetries Translations on the Cartesian Plane Reflections on the Cartesian Plane Rotations on the Cartesian Plane Combined Transformations on the Cartesian Plane Symmetry (i) ^ Tesselations (i) #
Congruence and Similarity recognize the properties for congruent and similar triangles
Congruence and Similarity:
Congruence in Triangles # Similarity in Triangles Using similarity proportion to solve problems # Trigonometry and Similarity # Conditions of Similarity Transformations and Congruence # Transformations and Similarity #
extend the ideas of transformation and symmetry to explore the conditions for congruent and similar triangles recognize the minimal conditions in fixing a triangle identify whether 2 triangles are congruent/similar with simple reasons
Congruence and Similarity:
(NF) explore and justify the methods to construct angle bisectors, perpendicular bisectors and special angles by compasses and straight edges (NF) appreciate the construction of lines and angles with minimal tools at hand
Geometry:
** discuss the possibility of trisecting an angle by compasses and straight edges **explore some shapes in fractal geometry
Geometry:
Constructions with a compass # Measring, Estimating and Drawing Angles(i)# Constructions with a Compass (i) #
Geometry:
Introduction to Fractal Geometry (i) #
recognize different types of angles explore and use the angle properties associated with intersecting lines and parallel lines
Geometry: Geometry:
explore and use the properties of lines and angles of triangles
Geometry:
Naming Angles Angles at a Point & vertically Opposite Angles Cointerior Angles Alternate Angles Corresponding Angles Angles and Parallel Lines Identifying Parallel Lines Angles on Parallel Lines Revision Harder Angles on Parallel Lines Types of Triangles Angles in Triangles Triangle problems Angles in Triangles Revision
explore and use the formulas for the angle sum of the interior angles and exterior angles of polygons explore regular polygons that tessellate (NF) appreciate the past attempts in constructing some special regular polygons with minimal tools at hand (NF) construct some special regular polygons using straight edges and compasses
Geometry:
Interior and Exterior Angles of Polygons Exterior Angle Sum and other Calculations
Geometry:
Polygons Not yet covered
Geometry:
Constructions with a compass # Drawing and Recognising Shapes with Properties # Not yet covered
Congruence and Similarity:
Similarity in Triangles ^
Congruence and Similarity:
Simple Proofs for Congruence in Triangles Congruence in Triangles # Similarity in Triangles Using similarity proportion to solve problems # Trigonometry and Similarity # Conditions of Similarity Constructions with a Compass (i) #
Geometry:
Angles related with Lines and Rectilinear Figures
**discuss past attempts in constructing some special regular polygons such as 17-sided regular polygons
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extend the idea of symmetry in 2-D figures to recognize and appreciate the reflectional and rotational symmetries in cubes and tetrahedron explore and identify the net of a given solid imagine and sketch the 3-D objects from given 2D representations from various views recognize the limitation of 2-D representations in identifying the solid explore the properties of simple 3-D object, such as identifying; ‹ the projection of an edge on one plane, ‹ the angle between a line and a plane, ‹ the angle between 2 planes **investigate the reflectional and rotational symmetries in other regular polyhedra **assemble a set of Soma Cube into a larger cube **explore the number of regular polyhedra
Geometry:
Symmetries in 3-D Shapes (i) #
Geometry: Geometry:
Nets of solids Visualising Prisms Not yet covered
Trigonometry:
Pythagoras in 3D
Geometry:
Symmetries in 3-D Shapes(i) #
Geometry: Geometry:
Soma Cubes Investigation (i)# Polygons (i)^
Learning Geometry through a Deductive Approach Simple Introduction to Deductive Geometry Not yet covered
develop a deductive approach to study geometric properties through studying the story of Euclid and his book - Elements develop an intuitive idea of deductive reasoning by presenting proofs of geometric problems relating with angles and lines understand and use the conditions for congruent and similar triangles to perform simple proofs
Congruence and Similarity:
identify lines in a triangle such as medians, perpendicular bisectors etc. (NF) explore and recognize the relations between the lines of triangles such as the triangle inequality, concurrence of intersecting points of medians etc. (NF) explore and justify the methods of constructing centres of a triangle such as incentre, circumcentre, orthocentre, centroids etc. **prove some properties of the centres of the triangle
Geometry:
Geometrical Calculations Deductive Proofs Proofs with Triangles Proofs with Quadrilaterals Simple Proofs for Congruence in Triangles Find sides and angles with congruent relationships # Congruence in Triangles # Centres of Triangles #
Geometry:
Centres of Triangles #
Geometry:
Centres of Triangles #
Geometry:
Centres of Triangles #
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Geometry:
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Pythagoras’ Theorem recognize and appreciate different proofs of Pythagoras’ Theorem including those in Ancient China recognize the existence of irrational numbers and surds use Pythagoras’ Theorem and its converse to solve problems
Not yet covered
Surds: Trigonometry:
(NF) appreciate the dynamic element of mathematics knowledge through studying the story of the first crisis of mathematics **investigate and compare the approaches behind in proving Pythagoras’ Theorem in different cultures **explore various methods in finding square root
Rationals and Irrationals Answers that result in irrational numbers PYTHAG - The Right-Angled Triangle PYTHAG - Pythagorean Triads PYTHAG - Calculating Side Lengths Using Pythagoras Pythagoras in 3D Not yet covered
Not yet covered
Not yet covered
Quadrilaterals extend the idea of deductive reasoning in handling geometric problems involving quadrilaterals
Geometry:
deduce the properties of various types of quadrilaterals but with focus on parallelograms and special quadrilaterals
Geometry:
(NF) perform simple proofs related with parallelograms
Geometry: Congruence and Similarity:
(NF) understand and use the mid-point and intercept theorems to find unknowns
Angles in Quadrilaterals Lengths in Quadrilaterals Properties of Quadrilaterals Proofs with Quadrilaterals Types of Quadrilaterals Lengths in Polygons on the Plane # Identifying Polygons from angle conditions# Angles and Lengths in Quadrilaterals Revision Proofs with Quadrilaterals Congruence in Quadrilaterals # Using similarity proportion to solve problems # Not yet covered
Learning Geometry through an Analytic Approach Introduction to Coordinates understand and use the rectangular and polar coordinate systems to describe positions of points in a plane able to locate a point in a plane by means of an ordered pair in the rectangular coordinate system describe intuitively the effects of transformation such as translation, reflection with respect to lines parallel to x-axis, y-axis and rotation about the origin through multiples of 90° on points in coordinate planes calculate areas of figures that can be cut into or formed by common 2-D rectilinear figures
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Coordinate Geometry:
The Number Plane
Not yet covered
Congruence and Similarity:
Translations on the Cartesian Plane Reflections on the Cartesian Plane Rotations on the Cartesian Plane Combined Transformations on the Cartesian Plane Not yet covered
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Coordinate Geometry of Straight Lines understand and use formulas of distance and slope
(NF) use ratio to find the coordinates of the internal point of division and mid-point understand the conditions for parallel lines and perpendicular lines
Coordinate Geometry:
Gradient of a Line The Gradient Formula Calculating Gradients Distances on the Plane The Distance Formula Not yet covered
Coordinate Geometry:
Parallel Lines II Parallel Lines II Perpendicular Lines Not yet covered
(NF) appreciate the analytic approach to prove results relating to rectilinear figures besides deductive approach (NF) choose and use appropriate methods to prove results relating to rectilinear figures **explore the formula for external point of division
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Not yet covered Not yet covered
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Trigonometry Trigonometric Ratios and Using Trigonometry understand the sine, cosine and tangent ratios for angles between 0° to 90°
Trigonometry:
explore the properties and relations of trigonometric ratios
Trigonometry:
explore the exact value of trigonometric ratios on special angles 30°, 45°, 60°
Trigonometry:
(NF) rationalize the denominators such as √2 apply trigonometric ratios to find measures of 2D figures
Surds: Trigonometry:
introduce the ideas of bearing, gradient, angle of elevation, angle of depression and solve related 2-dimensional problems
Coordinate Geometry: Trigonometry:
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Sides of a Right-Angled Triangle Ratio of Sides in Right-Angled Triangles Trigonometric Ratios I Trigonometric Ratios II Calculating Trigonometric Expressions Finding Unknown Side Lengths Using Trig Ratios Finding Unknown Angles Triangle Problems Applications to Geometry Applications to Real Life I Applications to Real Life II Sides of a Right-Angled Triangle Ratio of Sides in Right-Angled Triangles Trigonometric Ratios I Trigonometric Ratios II Calculating Trigonometric Expressions Finding Unknown Side Lengths Using Trig Ratios Finding Unknown Angles Triangle Problems Applications to Geometry Applications to Real Life I Applications to Real Life II Exact Trigonometric Values Trigonometric Equations - with Exact Values Trigonometric Equations - Complimentary Results and Ratios Rationalising the Denominator Finding Unknown Side Lengths Using Trig Ratios Finding Unknown Angles Triangle Problems Applications to Geometry Applications to Real Life I Applications to Real Life II Gradient of a Line Applications to Geometry Angles of Elevation and Depression Problems with Two Right-Angled Triangles Applications to Real Life I Applications to Real Life II Applications Including Bearings
Included as background and supporting work Whilst not explicitly required as part of the curriculum, these subtopics are included for background and supporting work for the benefit it can add to student learning and understanding.
Measurement:
Congruence and Similarity:
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Units of Mass Units of Capacity Units of Area Conversions Units from graphs # Units resulting from a formula # Quantities, Units and Modelling # Reasonable Units # Converting Units Very large and small Perimeter I Perimeter II Introduction to Area Area of Non Right Angle Triangles Parts of a Circle Introduction to Congruence Methods for Enlargements # Reproducing Images to Scale # Enlargements, Ratio and Scale Factors Introduction to Similarity
KS3
Data Handling
Organization and Representation of Data Introduction to Various Stages of Statistics recognize various stages involved in statistics
Data Analysis:
Statistical Investigations #
use simple methods to collect data so as to analyze posed problems
Data Analysis:
be aware of the existence of different types of data (discrete and continuous) understand the criteria of organizing data and discuss different ways of organizing the same set of data
Data Analysis:
Practicalities of Obtaining Data # Statistical Questions Number of Observations Statistical Attributes Types of Data I Types of Data II
Data Analysis:
Frequency Tables Grouped Data Describing Statistical Relationships #
Construction and Interpretation of Simple Diagrams and Graphs construct and interpret simple diagrams including stem-and-leaf diagrams, pie charts, histograms, scatter diagrams, broken line graphs
Data Analysis:
construct and interpret simple frequency polygons and curves, cumulative frequency polygons and curves be able to differentiate between histograms and bar charts explore the construction of diagrams and graphs with various tools besides paper and pencil
Data Analysis:
Line, Conversion and Step Graphs Stem and Leaf Plots Dot Plots Column, Bar Graphs and Histograms Travel Graphs Sector Graphs Back to back stem and leaf plots Histograms and Polygons Scatter Plots Sketch Step Graphs # Histograms and Polygons
Data Analysis:
Column, Bar Graphs and Histograms
Data Analysis:
compare the presentations of the same set of data by using various graphs or the same type of graphs but with different scales
Data Analysis:
choose appropriate diagrams/graphs to present a given set of data
Data Analysis:
read data from given frequencies in graphs (including percentiles, quartiles, median)
Data Analysis:
read frequencies from given data in diagrams and graphs
Data Analysis:
Line, Conversion and Step Graphs Stem and Leaf Plots Dot Plots Column, Bar Graphs and Histograms Travel Graphs Sector Graphs Back to back stem and leaf plots Scatter Plots Sketch Step Graphs # Comparisons and Predictions Comparing Sets of Data I Comparing Sets of Data II Real Life Data I Real Life Data II Comparisons and Predictions Comparing Sets of Data I Comparing Sets of Data II Real Life Data I Real Life Data II The Median Cumulative Frequency Frequency Distribution for Grouped Data Measures of Spread - Quartiles Frequency Tables Cumulative Frequency Frequency Distribution for Grouped Data
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use some common wordings such as ‘most popular’, ‘most likely’, ‘equally likely’ to describe trends from line graphs discuss the impressions from graphs presented in various sources identify sources of deception in misleading graphs and their accompanying statements
recognize the dangers of misinterpreting statistical data
Not yet covered
Data Analysis:
Statistics in the Media I Statistics in the Media II
Data Analysis:
Comparisons and Predictions Comparing Sets of Data I Comparing Sets of Data II Real Life Data I Real Life Data II Statistics in the Media I Statistics in the Media II Real Life Data I Real Life Data II Statistics in the Media I Statistics in the Media II
Data Analysis:
Analysis and Interpretation of Data Measures of Central Tendency find mean, median and mode from a given set of ungrouped data
Data Analysis:
find mean, median and modal class from a given set of grouped data be aware that the mean found for grouped data is an estimation compare 2 data sets with given mean, median and mode construct data sets with a given mean, median and mode discuss the relative merits of different measures of central tendency for a given situation
Data Analysis:
(NF) explore and make conjectures on the effect of the central tendency of the data such as: (i) removal of a certain item from the data; (ii) adding a common constant to the whole set of data; (iii) multiplying the whole set of data by a common constant (iv) insertion of zero in the data set understand weighted mean and be aware of its use in various real-life situations such as Hang Seng Index, calculation of marks in a report etc. discuss the misuse of averages in various daily life situations recognize the dangers of misusing averages
Data Analysis:
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The Mean The Median Range and Mode Mean, Median, Mode and Range Mean, Median, Mode and Range Frequency distribution for Grouped Data
Data Analysis:
Frequency distribution for Grouped Data
Data Analysis:
Comparing Sets of Data I Comparing Sets of Data II
Data Analysis:
Mean, Median, Mode and Range
Data Analysis:
Centre or Spread? # How the shape effects choice of centre and spread # How the shape effects choice of centre and spread (i)#
Data Analysis:
Weighted Means #
Data Analysis:
The Mean (i)^
Data Analysis:
The Mean (i)^
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Probability Simple Idea of Probability explore the meaning of probability through various activities
Probability:
have an intuitive idea about the relation between probability and the relative frequency as found in statistics or simulation activities
Probability:
investigate probability in real-life activities, including geometric probability compare the empirical and theoretical probabilities calculate the theoretical probability by listing the sample space and counting recognize the meaning of expectation
Describing Chance Experimental Probability Generating data for probability analysis # Theoretical Probability Generating data for probability analysis #Complementary Events Relatvie frequencies of And/Or events # Expectation and Fair Value Not yet covered
Probability:
Theoretical Probability Expected Outcomes
Probability:
Sample Spaces Theoretical Probability
Probability:
Expected Outcomes
Probability:
Venn Diagrams and Two Way Tables tree diagrams EXT Divided Bar Graphs EXT Area Charts and Radar Graphs
Included as Background and Supporting Work Whilst not explicitly required as part of the curriculum, these subtopics are included for background and supporting work for the benefit it can add to student learning and understanding
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Data Analysis:
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KS4-C
Number and Algebra
Observing Patterns and Expressing Generally More About Polynomials manipulate polynomials further including long division up to simple quadratic divisor (NF) recognize the concept of division algorithm
Polynomials and Other Functions:
Polynomial Division #
Polynomials and Other Functions:
Polynomial Division # Not yet covered
(NF) understand and use remainder and factor theorems to factorize polynomials up to degree 3 (NF) appreciate the power of factor theorem and also be aware of the limitation of the theorem
Not yet covered
Arithmetic and Geometric Sequences and their Summation (NF) explore further the properties of arithmetic and geometric sequences (NF) develop and use the general terms of the sequences
Sequences and Series:
Introduction to Arithmetic Progressions # Introduction to Geometric Progressions #
Sequences and Series:
(NF) investigate and use the general formulas of the sum to n terms of arithmetic and geometric sequences (NF) develop an intuitive idea on limit and deduce the formula for sum to infinity for certain geometric series (NF) solve real-life problems such as interest, growth and depreciation, geometric problems etc. **explore recurrence in some sequences
Sequences and Series:
Terms in Arithmetic Progressions # Graphs and Tables - AP's # Finding the Common Ratio # Terms in Geometric Progressions # Graphs and Tables - GP's # Arithmetic Series # Geometric Series #
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Sequences and Series:
Infinite sum for GP's #
Sequences and Series:
Applications of Arithmetic Progressions # Applications of Geometric Progressions #
Sequences and Series:
First Order Linear Recurrences Introduction# Graphs and Tables - Recurrence Relations # Solutions to Recurrence Relations # Applications of Recurrence Relations #
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Algebraic Relations and Functions Quadratic Equations in One Unknown formulate and solve quadratic equations by factor method and formula
Quadratic Relationships:
solve the equation ax^2 + bx + c = 0 by plotting the graph y = ax^2 + bx + c and reading the xintercepts be aware of the approximate nature of the graphical method choose the most appropriate strategy to solve quadratic equations
Quadratic Relationships:
recognize the conditions for the nature of roots
Quadratic Relationships:
Quadratic relationships Solving basic quadratic equations Solve by Factorisation I Graphing Quadratic Functions in Factorised Form Solving by factorisation II Solving by completing the square Solving by completing the square - with surds Graphing Quadratic Functions in Turning Point form Solving using the quadratic formula Application Problems with Quadratics Miscellaneous Quadratic Equations NonMonic Quadraitc Equations Graphing Quadratic Functions in General Form Graphing Quadratic Functions in General Form Not yet covered
Quadratic Relationships:
Application Problems with Quadratics Miscellaneous Quadratic Equations Applications of Quadratic Functions using graphs # Further Applications The Number and Nature of Solutions Not yet covered
understand the hierarchy of real-number system and be aware of the characteristics of rational numbers when expressed in decimals
More About Equations (NF) formulate and solve equations which can be transformed into quadratic equations (NF) formulate and solve one linear and one quadratic simultaneous equations by algebraic method solve equations by reading intersecting points of given graphs appreciate the power and understand the limitation of graphical method in solving equations choose the most appropriate strategy to solve equations **explore the algebraic method to solve cubic or higher degree equations
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Quadratic Relationships:
Variable substitution Method
Quadratic Relationships:
Simultaneous, linear and quadratic equations
Polynomials and Other Functions:
Intersections of polynomials by graphing # Not yet covered
Not yet covered Polynomials and Other Functions:
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Cubics Extending concepts of curve sketching # y=ax^n # Intersections of Polynomials by other methods #
Variations discuss the relations between 2 changing quantities sketch the graphs of direct and inverse variations and recognize the algebraic representations between the quantities recognize and appreciate the algebraic representations of various variations such as those in the forms of V=πr^2h or y = k_1+k_2 x etc. apply the relations to solve real-life problems
Polynomials and Other Functions:
Inverse functions Variations
Polynomials and Other Functions:
Inverse functions Variations Not yet covered
Not yet covered
Linear Inequalities in Two Unknowns Inequalities:
Graphical Solutions to systems of Inequalities
Inequalities:
Compound Inequalities
Inequalities:
One Step Inequalities Two Step inequalities Problem Solving with Inequalities Identifying Solutions to Inequalities Three step Inequalitites Creating Inequalities with 1 Variable Creating Inequalities with 2 Variables Systems of Inequalities Graphical Solutions to systems of Inequalities NF Linear Inequalities in Two Unknowns : solve systems of linear inequalities in two unknowns Not yet covered
(NF) understand and use the laws of rational indices
Logarithms and Exponentials:
(NF) understand the definition of logarithmic functions and recognize the common logarithm is not the only type of the function (NF) examine the properties of the graphs of exponential and logarithmic functions
Logarithms and Exponentials:
Numerical Bases with Fractional Indices # Fractional Bases with Fractional Indices # Fractional Bases with Fractional # Fractional Indices with Algebraic Terms # Logs and Exponential Forms # Logarithm Laws and Logarithm Properties
(NF) explore and study the relations between the properties of logarithmic function and that of exponential function
Logarithms and Exponentials:
(NF) appreciate the application of logarithm in various real-life problems
Logarithms and Exponentials:
(NF) represent the linear inequalities in 2 unknowns on a plane (NF) discuss the solution of compound linear inequalities connected by ‘and’ (NF) solve systems of linear inequalities in two unknowns
(NF) solve linear programming problems
Exponentials and Logarithmic Functions
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Logarithms and Exponentials:
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Exponential Graph Transformations of Exponential and Logarithmic graphs Logs and Exponential Forms Simplifying Exponential Expressions # Transforming Exponential Expressions # Simple exponential Equations Extended exponential and logarithmic equations Comparing Exponential Models # Applications of Exponenatial Functions Further Exponentials
Functions and Graphs relate the idea of input-processing-output to the meaning of dependent and independent variables understand the basic idea of a function from the tabular, symbolic and graphical representations of a function and the dummy nature of x use the notation for a function
Not yet covered
Not yet covered
Polynomials and Other Functions:
explore various properties of quadratic functions such as vertex, axis of symmetry, the optimum value(s) from their graphs
Quadratic Relationships:
(NF) appreciate the contribution of Arabians on the method of completing the square and use it to find the properties of quadratic functions (NF) appreciate the power of the method in generating a perfect square expression
Quadratic Relationships:
sketch and compare graphs of various types of functions solve f(x) > k, f(x) < k, f(x) ≥ k, f(x) ≤ k by reading graphs of f(x) (NF) explore the effects of transformation on the functions from tabular, symbolic and graphical perspectives (NF) visualize the effect of transformation on the graphs of functions when giving symbolic relations
Quadratic Relationships:
Describing functions # Functions and Relations Definitions Function Notations Polynomials and Notation Transformations and Quadratic Equations Transformations and Quadratic Graphs Maximum and Minimum Values of Quadratics # Maximisation and Minimisation # Solving by completing the square Solving by completing the square - with surds Complete the Square Solving by completing the square Solving by completing the square - with surds Graphing Quadratic Functions in Turning Point form Not yet covered Not yet covered
Polynomials and Other Functions:
Polynomials and Other Functions:
Translation of graphs Transformations of Functions Transformations of Exponential and Logarithmic graphs Translation of graphs Transformations of Functions Transformations of Exponential and Logarithmic graphs
Included as background and supporting work Whilst not explicitly required as part of the curriculum, these subtopics are included for background and supporting work for the benefit it can add to student learning and understanding.
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Inequalities: Polynomials and Other Functions:
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Introduction to Inequalities Graphs of Further Functions Combined Graphs Questions Addition and Subtraction of Polynomials # Multiplication of Polynomials #
KS4-C
Measures, Shape and Space
Learning Geometry Through an Intuitive Approach Qualitative Treatment of Locus describe verbally or sketch the locus of points moving under a condition or conditions
Not yet covered
appreciate different conditions which can give rise to the same type of locus
Not yet covered
Learning Geometry through a Deductive Approach Basic Properties of Circles (NF) understand and use the basic properties of chords and arcs of a circle
Circle Geometry:
(NF) understand and use the angle properties of a circle
Circle Geometry:
(NF) understand and use the basic properties of cyclic quadrilateral and tangent to a circle
Circle Geometry:
(NF) appreciate the intuitive and inductive ways of recognizing the properties of circles and see the importance of deductive approach (NF) perform geometric proofs related with circles
Circle Geometry:
Proofs using cyclic quadrilaterals # Proofs using chord theorems # Proofs using Segment theorems #
Circle Geometry:
Proofs using cyclic quadrilaterals # Proofs using chord theorems # Proofs using Segment theorems # Not yet covered
(NF) appreciate the structure of Euclidean Geometry such as definitions, axioms and postulates etc. and its deductive approach in handling geometric problems
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Names in Circles I Names in Circles II # Lengths in Circles Mixed Angles and Lengths in Circles # Names in Circles I Names in Circles II # Finding Angles in Cirlces Mixed Angles and Lengths in Circles # Proofs using cyclic quadrilaterals
Learning Geometry through an Analytic Approach Coordinate Treatment of Simple Locus Problems explore and visualize straight line as loci of moving points and describe the loci with equations recognize the characteristics of equation form that represents a straight line
understand and apply the point-slope form to find the equations of straight lines from various given conditions describe the properties of the line from a given linear equation (NF) explore and visualize circles as loci of moving points (NF) find the equation of circles from given conditions **explore other forms of equations for straight lines
Not yet covered
Coordinate Geometry:
Coordinate Geometry:
Identifying Slope and Intercepts Gradient Intercept Form Equation of a Line: General Form The Point Gradient Formula The Two Point Formula Finding the Rule The Point Gradient Formula Finding the Rule
Coordinate Geometry:
Identifying Slope and Intercepts # Sketching Linear Graphs Modelling Linear Relationships - graphs Not yet covered
Coordinate Geometry:
Circles at Origin Circles with translations Circles Equation of a Line: General Form The Two Point Formula Finding the Equation of Line Graphs of Physical Phenomena
Coordinate Geometry:
Trigonometry More about Trigonometry (NF) understand the sine, cosine and tangent functions, their graphs
Trigonometry:
(NF) use graphs to explore properties of trigonometric functions including periodicity etc. (NF) use graphs of the functions to find roots of an equation such as sin θ = constant, where 0° ≤ θ ≤ 360° (NF) recognize the limitation of Pythagoras’ Theorem in solving triangles (NF) understand and use sine and cosine formulas to solve triangles
Trigonometry:
(NF) understand and use the formula ½absinC and Heron’s formula for areas of triangles (NF) investigate and find the angle between 2 intersecting lines, between a line and a plane, between 2 intersecting planes (NF) apply trigonometric knowledge in solving 2dimensional and 3-dimensional problems
Trigonometry:
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Unit Circle and Trig Functions # Exact Trigonometric Values Symmetrical and Periodic Nature of Trig Functions # Graphing Sine Curves # Graphing Cosine Curves # Further Graphs of Trigonometric Functions# Graphical solution of trig equations # Symmetrical and Periodic Nature of Trig Functions #
Trigonometry:
Graphical solution of trig equations
Trigonometry:
Pythagoras in 3D Applications to Real Life
Trigonometry:
Sine Rule Cosine Rule Applications of the Sine Rule Applications of the Cosine Rule Area of Non-Right Angled Triangles Not yet covered
Trigonometry:
Version 3.1
Applications of Trigonometric Functions # Applications of the Sine Rule Applications of the Cosine Rule
Included as background and supporting work Whilst not explicitly required as part of the curriculum, these subtopics are included for background and supporting work for the benefit it can add to student learning and understanding.
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KS4-C
Data Handling
Analysis and Interpretation of Data Measures of Dispersion recognize range, inter-quartile range and standard deviation as measures of dispersion for a set of data
Data Analysis:
find range from a given set of data
Data Analysis:
find inter-quartile range from the cumulative frequency polygon
Data Analysis:
construct box-and-whisker diagrams and use them to compare the distributions of different sets of data interpret the basic formula of standard deviation and be able to find the standard deviation for both grouped and ungrouped data set compare the dispersions of different sets of data using appropriate measures
Data Analysis:
Data Analysis:
Data Analysis:
(NF) explore and make conjecture on the effect of the dispersion of the data such as: i. removal of a certain item from the data; ii. adding a common constant to the whole set of data; iii. multiplying the whole set of data by a constant; iv. insertion of zero in the data set.
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Recognising the spread of data Recognising the shape of data Range and Mode Centre or Spread ? # How the shape effects choice of centre and spread # Measures of Spread – Quartiles Standard Deviation Quartiles, Deciles and Percentiles # Range and Mode Cumulative Frequency Histograms and Polygons Measures of Spread - Quartiles 5 Number Summary # Box and Whisker Plots Interpreting Parallel Box Plots # Standard Deviation Applications of Standard Deviation Scatter Plots Comparing Sets of Data I Comparing Sets of Data II Shape of Bivariate Data # Describe Correlation of Bivariate Data # Comparisons of Data # Not yet covered
Simple Statistical Surveys Uses and Abuses of Statistics (NF) recognize different techniques in choosing samples and the criteria in choosing data collection method
Data Analysis:
(NF) investigate methods in which statistical surveys are used and misused in various daily-life activities (NF) discuss the strengths and weaknesses of statistical investigations presented in different sources such as news media, advertisements, etc including methods of collecting, presenting and analysing data etc. (NF) recognize the complexity in conducting surveys
Data Analysis:
Sampling Techniques and stats and society Conducting a Census # Pros and Cons of a Census # Estimation of Population from Sample # Sampling Techniques Sources of Bias # Sources of Errors # Sources of Bias # Misrepresentation of Results #
Data Analysis:
Statistics and Society Misleading Media #
Data Analysis:
Pros and Cons of Samples # Target Population # Questionnaire design #
Data Analysis:
Line of best fit - Identifying Line of best fit - Calculating # Interpreting Information from Time Series Data Planning a Statistical Investigation # Statistical Investigations # Distance/Time Graphs and Time Series Data Construct Time Series Graphs # Language of Time Series Graphs # Smoothing Data # Seasonal Indices # Least-Squares and Time Series Data # Statistical Investigation - Time Series Data #
Conducting Surveys **conduct statistical investigations including i. formulating key questions to investigate problems relating to their experience; ii. deciding appropriate data collection method which may involve designing simple questionnaire; iii. applying sampling techniques in collecting data; iv. conducting the investigations; v. making interpretation on the data collected and analyzing their findings; vi. presenting the investigations to other
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Probability More about Probability (NF) recognize the basic laws in probability
Probability:
(NF) apply the addition or multiplication laws in a wide variety of activities including real-life problems
Probability:
(NF) recognize the notion of conditional probability and the notation of P(A|B)
Probability:
Experimental Probability Theoretical Probability Relatvie frequencies of And/Or events # Replacement and non-replacement probabilities Identifying Independent and Dependent Events Independent Events Dependent Events Probability of Equally Likely Outcome Mutually Exclusive and Non-Mutually Exclusive Events Conditional Probability Relatvie frequencies of And/Or events # Identifying Independent and Dependent Events Independent Events Dependent Events Conditional Probability Conditional Probability
Included as Background and Supporting Work Whilst not explicitly required as part of the curriculum, these subtopics are included for background and supporting work for the benefit it can add to student learning and understanding
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Data Analysis:
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Sample and Population Means #
