GRADE 10-12 MATHEMATICS
GENERAL OUTCOMES
Provide clear mathematical thinking and expression in the learner
Develop the learners’ mathematical knowledge and skills
Enrich the learners’ understanding of mathematical concepts in order to facilitate further study of the discipline
Build up an appreciation of mathematical concepts so that the learner can apply these for problem solving in everyday life.
Enable the learner represent, interpret and use data in a variety of formsInculcate a desire to develop different career paths in the learners
Key competences
· Assimilate necessary mathematical concepts for use in everyday life such as environment and other related disciplines.
· Think mathematically and accurately in problem solving skills and apply these skills to formulate and solve mathematical and other related problems.
· Develop necessary skills needed to apply mathematical concepts and skills in other disciplines.
· Produce imaginative and creative work from mathematical concepts and ideas.
· Develop abilities and ideas drawn from mathematics to reason logically, communicate mathematically, and learn independently without too much supervision (self-discipline).
· Develop positive attitudes towards mathematics and use it in other subjects such as science and technology
· Apply mathematical tools such as information and communication technology in the learning of other subjects
Use mathematics for enjoyment and pleasure
Develop understanding of algebra, geometry, measurements and shapes.
SET OPERATIONS
Specific Outcomes
Carry out operations on sets
Apply higher operations on sets
Introduction: Set Theory
Watch this video: Sets: full Lesson
Media Resource
Basic Operation on Sets Union, Intersection, Complement Basic Set Theory, Part 3 Basic Set Theory, Part 4 Basic Set Theory, Part 5
Intersection, Union and Complement 2 Set Operations & Venn Diagrams
Set Operations & Venn Diagrams, part 2 Defining Sets Set Equality and Subsets
Venn Diagrams, Unions, and Intersections
Complement and Relative Complement Venn Diagrams with 3 sets
Quiz: Set Operations
Index Notation/Indices
Specific Outcomes
Apply laws of indices
Simplify positive, negative and zero indices
Simplify fractional indices
Solve equations involving indices
Introduction:
Intro to indices Algebra Introducing Indices
Media Resource
Rules of Indices Law of indices (all index laws)
Laws of Indices Part 2: Negatives and Fractions Law of indices (all index laws) Solving Indices Equation
Solving Exponential Equations With Different Bases Using Logarithms Solving Exponential Equations
Base and Power, Rules, Results and Examples Solving equations with an unknown Index part 2
How to work with indices (powers) Laws of Indices - Adding & subtracting powers of numbers Adding and Subtracting Powers Fractional Exponents How to deal with fractional powers
What happens when the power isn't a whole number? (Fractional Indices)
Fractional and Negative indices Index form (power of unit fractions)
Quiz: Index Notation/Indices
ALGEBRA BASIC PROCESSES
Specific Outcomes
Expand and simplify expressions
Factorise algebraic expressions
Simplify Algebraic fractions
Introduction: Algebra Basics: What Is Algebra?
Media Resource:
Solving Basic Equations Part 2 What Are Polynomials?
Solving 2-Step Equations Laws Of Exponents What Are Functions? Graphing On The Coordinate Plane
Exponents In Algebra Simplifying Polynomials
Solving Basic Equations Factorising Algebraic Expressions Factorising Algebraic Expressions (All Positives) Factorising Algebraic Expressions ( With Negatives) Factorising Algebraic Expressions (Grouping)
Factorising Algebraic Expressions (Non-Monic Quadratic) Factorising Algebraic Expressions
Simulation:Area Model Algebra
Matrices
Specific Outcomes
Find a Transpose of a matrix
Multiply matrices (up to 3x3 matrices)
Calculate the determinant of a 2 by 2 matrix
Find the inverse of a 2 by 2 matrix
Solve systems of linear equations in two variables
Apply matrices to solve real life problems
Introduction:
Introduction to matrices An Introduction to Matrices 2
Media Resource
Matrices Introduction to Matrices 3
Transpose of a matrix Transpose of a Matrix 2 Multiplying Matrices Multiplying Matrices 2
Matrix & its Inverse Inverse of a Matrix Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors Inverse of a 2x2 matrix Inverse of a 3x3 Matrix
Similarity and Congruence
Specific Outcomes
Calculate the scale on a map
Calculate length and area using a given scale and vice versa
Calculate areas and volumes of similar figures
Apply ratio, proportion, to solve problems on similarity and congruence
Introduction:
Media Resource
How to calculate distances on the map or in reality using the map scale
Map and simple conversion scale: converting Using map scales and ratios 2 Using Scale Maps Distance
Mapwork: Ratio scale Scaling Up and Scaling Down Ratios
How to convert map scales Ratio on a Map
Similar Shapes Length, Area and Volume
Areas and Volumes of Similar Solids
Surface Areas and Volumes of Similar Solids Similar Solids Ratios And Rates
Scales of Measurement - Nominal, Ordinal, Interval, Ratio
Travel Graphs
Specific Outcomes
Compute average speed, distance and time
Determine acceleration and retardation/deceleration
Draw travel graphs
Calculate the distance under a velocity time graph
Relate area under the graph to distance travelled
Introduction:
Distance Time Graphs - Basic Introduction
Media Resource
Distance Time Graphs explained in maths
Conversion between Speed-Time and Distance-Time graphs Conversion of Speed time to Distance time Graph Distance Time Graphs Velocity Time Graphs(speed) Average Speed Word Problems
Time Speed Distance Tricks – Average Speed
Acceleration Calculations - Initial Velocity Acceleration Calculation - Solve for Distance and Velocity
Acceleration Calculations - Deceleration Acceleration Calculations - Velocity and Distance Acceleration Concept Retardation Explained Calculating Distance from a velocity versus time graph
Why distance is area under velocity-time line Velocity - speed, distance and time
Displacement Velocity Acceleration Time Graphs - Slope & Area
Distance Time Graphs distance time graphs Velocity Time Graphs Speed, velocity and acceleration
Velocity-time graphs Velocity Time Graphs 2 Area Under Velocity Time Graphs Kinematic Equations of Motion.
Equations of Motion Velocity Time Graph - Problem Velocity vs. Time Graph Revision Question and answer Estimating distance travelled under a curved V/t graph Displacement time graphs
Social and Commercial Arithmetic
Specific Outcomes
Carry out calculations that involve Shares, dividends and investment Bonds
Media Resource
Simple Interest Calculate Percentages: 5 Easy Methods Solving an Investment Problem
Simple Interest Formula Percentage Trick - Solve precentages mentally How to calculate ratio - sharing money Dividend Calculations Word problems Shares & dividends
How To Compute Dividends How to Calculate EPS (Earnings Per Share) The Price-to-Earnings (P/E) Ratio
Bearings
Specific Outcomes
Draw/sketch diagrams to represent position and direction
Use bearing and scale drawing in real life
Introductions
Media Resource
Bearings Bearings Problem Bearing Problems & Navigation Finding Bearings
Bearings 2 Calculating Bearings Bearings 3 bearings and scale drawings
Bearings 4 practice loci and scale drawing Bearings problems Practice bearings and scale drawing
True Bearings and Trigonometry Angle of Elevation/Angle of Depression Problems
Symmetry
Specific Outcomes
Determine order of rotational symmetry
Determine symmetry of solids
Determine plane symmetry
Introduction:
Media Resource
Symmetry Lines of Symmetry Symmetry in Solid Shapes Planes of Symmetry Symmetry Planes
Symmetry Properties of 3D Shapes Planes of Symmetry in 3D Shapes 2 Reflection and Rotation
Order of Rotational Symmetry Rotational Symmetry Plane symmetry and axis symmetry
Computer and Calculator
Demonstrate the use of different functions on a calculator
Describe components of a computer
Describe various methods of implementing an algorithm
Outline problem solving stages
Introduction: Introduction to Flow Charts
Media Resource
Watch These Lessons: Flow Chart Tutorials
How to use a Scientific Calculator Casio Calculator Tutorial - Overview of Essential Buttons
Complete a table and graph using mode PC Components System Parts
What Are the 4 Basic Functions of a Computer? Computer Operations Intro to Computer Architecture
Introduction to Algorithms What's an algorithm?
Algorithms Algorithms 2 Algorithms Implementing an algorithm from a flow chart Basic Fast Multiplication Division standard algorithm method Division Algorithm for Polynomials
Read notes here: Computer
APPROXIMATION
Specific Outcomes
Work with relative and absolute errors
Introduction:
Media Resource
Absolute, Relative, Relative Percentage Percent Error Made Easy Error and Percent Error
How to Calculate Relative Error Relative Error and Percent Error Percentage Error in Measurement
Approximation & Estimation Estimation and Approximation
Rounding Estimation approximation rounding How to approximate square roots
Estimation and Approximation 2 Estimation Limit of Accuracy Solving Limits of Accuracy Problems
Introduction to Limits How to Find the Limit at Infinity How to Find Any Limit
Quiz: ApproximationsSEQUENCES AND SERIES
Specific Outcomes
Identify an arithmetic progression (AP)
Find the nth term of the AP
Find the sum of an AP
Find the arithmetic mean
Identify a geometric progression (GP)
Find the nth term of a GP
Find the geometric mean
Find the sum of a geometric progression
Find the sum to infinity of a Geometric progression
Calculate the length of a straight line
Calculate the mid-point of two points
Calculate the gradient of a line segment
Find the equation of a straight line
Find the gradients of parallel and perpendicular lines
Use gradients of parallel and perpendicular lines to find equations
Introduction:
Introduction to Arithmetic Progressions Introduction to Arithmetic Progressions 2
Media Resource
Arithmetic Progression part 1 Arithmetic Progression part 2 Arithmetic Progression part 3
Nth term of AP Arithematic Progression Nth term of AP Find missing terms of AP Example nth term of AP
Example nth term of AP 2 Example nth term of AP 3 Sum of n terms of AP Arithmetic Progression cont. Arithmetic Progression cont. 2 Example and Summary What is a geometric progression?
Intro to Geometric Progressions
Intro to Geometric Progressions (1 of 2) Intro to Geometric Progressions (2 of 2)
COORDINATE GEOMETRY
Specific outcomes
Calculate the length of a straight line
Calculate the mid-point of two points
Calculate the gradient of a line segment
Find the equation of a straight line
Find the gradients of parallel and perpendicular lines
Use gradients of parallel and perpendicular lines to find equations
Introduction
Media Resource
Watch this video:Full Lesson
Explore More:
Introduction To Coordinate Geometry How to Find the Distance Between Two Points
Find the Distance Between Two Points-Pythagorean Theorem
Find Distance Between 2 Points on Coordinate Plane Pythagorean Theorem on a Coordinate Plane
Midpoint Using The Midpoint Formula
Midpoint Formula Midpoint of a line segment Gradient of a straight line
Gradient, midpoint, equation and length of a line Midpoint, Distance, Gradient of an Interval.
Gradients of lines find the equation of a straight line graph with two points Finding the Equation of a Line Linear Equations Finding the Equation of a Line in Slope Y-Intercept Gradient of a straight line
Parallel and Perpendicular Lines Parallel and Perpendicular Lines
Equations of Lines Parallel and Perpendicular to a Given Line
Simulations: Graphing Linear
Graphing Slope-intercept
FUNCTIONS AND RELATIONS
Specific Outcomes
Find inverses of one- to- one function
Simplify composite functions
Solve problems involving linear functions
Introduction:
Introduction - Relations and functions What Are Functions?
Media Resource
Find The Inverse of a Function Inverse Functions Verifying Inverse Functions Finding the inverse of a function Find the Inverse of a Function
Composite Functions Domain Fractions & Square Roots Composite and Inverse Functions
Evaluating composite functions example Composite Functions Relations & Functions
Quadratic Functions
Specific Outcomes
Explain the quadratic function and its graph
Sketch the graph of a quadratic function
Introduction
Intro to Quadratic Functions (Relations)
Media Resource
The Vertex Form of Quadratic Functions
Vertical Reflection of Quadratic Functions Horizontal Translation of Quadratic Functions
Maximum and Minimum of a Quadratic Function Factored Form of a Quadratic Equation
How to Factor Quadratic Equations Solving Quadratic Equations (by Factoring)
Solving Quadratic Equations (by the Quadratic Formula)
Finding the Vertex through Partial FactoringQuadratic Equations
Specific Outcomes
Explain the meaning of the quadratic equation
Solve quadratic equations by graphical method
Solve quadratic equations using factorisation method
Solve quadratic equations using completing of square method
Solve quadratic equations using quadratic formula method
Apply quadratic equations to solve real life problems
Introduction
ntroduction to the quadratic equation
Media Resource
Quadratic Equations How to Solve Quadratic Equations
Solve Quadratic Equations by Completing the Square How To Solve Quadratic Equations By Factoring
Introduction to Quadratic Theory Introduction to Quadratic Theory 2 5 Ways to Solve Quadratic Equations
4 Methods of Solving Quadratic Equations Solve Quadratic Equations using Quadratic Formula
Variation
Specific Outcomes
Describe variation
Distinguish between direct and inverse variation
Distinguish between joint and partial variation
Draw and Interpret graphs of variation
Solve problems involving variations
Introduction:
Introduction to Variation Functions
Media Resource
Introduction to Variation; Choosing Variation, Interactive
Direct and inverse variation Direct Inverse and Joint Variation Direct Variation VS Inverse Variation
Inverse Variation Direct Variation Direct Variation: Multiple Representations
Direct Variation Tables and Graphs Graph in Direct Variation Direct Variation Graphing Inverse Variation Graphing Inverse Variations with shifts Direct and Inverse Variation Equations
Circle Theorems
Specific Outcomes
Analyse the parts of a circle
Solve problems using angle properties of a circles
Solve problems involving tangent properties
Introduction:
Media Resource
Everything About Circle Theorems Circle Theorem: Part 1 Circle Theorems Properties of Circles
Angle Properties of Circle Introduction Angles in a Circle Inscribed Angles in Circles Circles and Angle Properties Angles in Circles
Circle Theorems Circle Theorems 2 Circumference, Area, Arc Length, Inscribed Angles & Chords
Circle Theorems-revision Circle Theorem revision 2 Circle Theorems -revisions 3 Circle Theorem-revision 4
Tangent lines and circles Tangent Lines to a Circle Tangents of Circles
Construction and Loci
Specific Outcome
Construct line and angle bisectors
Explain the meaning of Locus
Describe locus of point in two and three dimensions
Construct locus of point in two dimensions
Introduction
Media Resource
Four basic types of loci Construction Of Basic Angles And Loci Construction and Loci Locus Constructions and Loci 2 Loci and Locus
Loci and Drawing Accurately-Examples
Loci in two dimensions Loci in two dimensions-Revision
Trigonometry
Specific Outcomes
Relate right angled triangle to the three trigonometric ratios
Describe the three trigonometric ratios on a right angled triangle
Calculate sides and angles of a right angled triangle
Work with special angles (60o, 45o and 30o)
Find sides and angles of non right angled triangles.
Calculate areas of a non right angled triangle
Determine the signs of the three trigonometric ratios in the quadrants
Draw graphs for sine, cosine and tangent curves
1Solve trigonometric equations
Use trigonometry to solve practical problems
Introduction
An Introduction To Trigonometry
Media Resource
Basic trigonometry Trigonometric Ratios Trigonometry SOH CAH TOA
Sine Cosine Tangent Find Exact Values of Trig Functions Trigonometry SOHCAHTOA 2 Sine and Cosine Rule Area of a Triangle, Given 3 Sides
Area Of A Non-Right Angle Triangle Area of a Triangle Using Trigonometry
How To Solve Two Triangle Trigonometry Problems Law of Sines & Cosines Area of a Triangle
Graphing Sine and Cosine Trig Functions
Trigonometric Equations Using Identities Solving Trigonometric Equations By Finding All Solutions
Simulation: Trig Tour
Mensuration
Specific Outcomes
Calculate the area of a sector
Calculate surface area of three dimensional figures
Calculate volume of prisms
Solve problems involving area and volume
Introduction
Media Resource
Mensuration Introduction Mensuration Area Surface Area of a Pyramid & Volume of Square Pyramids
Arc Length of a Circle Formula Triangular Prism Rectangular Prism
Volume How to find the Surface Area and Volume of Prisms Volume of a Cylinder and Surface Area of a Cylinder Tricks To Understand Mensuration Formulas Area and volume of common solids
Probability
Specific Outcomes
Compute probabilities using the laws of probability
Calculate probabilities using tree diagrams and grids.
Calculate probabilities of mutually exclusive events and compound events
Find probabilities of independent events
Apply probability to real life problems
Introduction
Media Resource
Probability explained Probability Addition rule for probability Total Probability Rule Laws of Probability Probability Sample Space & Tree Diagrams Probability Tree Diagrams
Probability trees-revision Probability of Compound Events & Tree Diagrams Compound Events with Tree Diagrams and Tables Independent Events Example Independence of Two Events
Probability Concepts and Applications How Is Probability Used in Real Life? Practical Applications of probability
Statistics
Specific Outcomes
Construct cumulative frequency tables using grouped and ungrouped data
Draw cumulative frequency curves
Draw relative cumulative curves
Calculate the range, inter quartile range, and semi inter quartile range
Calculate the percentiles
Calculate variance and standard deviation for ungrouped and grouped data
Introduction
Media Resource
Introduction to Statistics 2 Mean, median, and mode Finding Cumulative Frequency Cumulative Relative Frequency Table Cumulative Frequency Constructing a Frequency Distribution
Mean, Median, and Mode of Grouped Data
Quartiles, Deciles, & Percentiles Cumulative & Relative Frequency Ungrouped frequency tables Analyzing a cumulative relative frequency graph Analyzing a cumulative relative frequency graph
Finding Percentiles & Outliers Cumulative Frequency Curves Estimated Mean, Median and Quartiles
Standard Deviation of Grouped Data standard deviation for grouped data 2 variance for grouped data
Quiz: Statistics
Graphs of Functions
Specific Outcomes
Draw graphs of cubic functions
Use graphs to find solutions
Determine gradients of curves
Estimate areas under curves
Draw graphs of inverse functions
Application of graphs of functions
Introduction
Media Resource
Graphing On The Coordinate Plane Graphing Inverse Functions Graphing Cubic Functions Calculate the gradient of a curve Gradient at a point on a curve Intro to Area Under a Curve
Estimating the Area Under a Curve Domain & range- With Fractions, Square Roots, & Graphs
Quiz: Graphs of FunctionsLinear Programming
Specific Outcomes
Draw graphs of linear equations and inequations in one and two variables (as a recap)
Shade the wanted and unwanted regions
Describe the wanted or unwanted regions.
Determine maximum and minimum values
Use the search line to determine the maximum and minimum values
Apply knowledge of linear programming in real life
Introduction
Introduction to Linear programming
Media Resource
Linear Programming - Introduction 2 Linear Programming
Linear Programming - Formulation Linear programming lesson
Linear Programming - Formulation 2 Graphical Solution Introduction to graphing inequalities
Two-variable linear equations and their graphs Graphing Linear Inequalities in Two Variables
Graphing systems-Two variables Find the Minimum of an Objective Function
Find the Max and Min of an Objective Function Find the Maximum of an Objective Function
Finding the Minimum or Maximum value Graphical Solution - Minimization Problem
Linear programming in real life 1 Linear programming real life 2 Linear programming in real life 3
Vectors
Specific Outcomes
Describe a vector
Represent and denote a vector
Add and subtract vectors
Apply translations on vectors and find magnitude
Multiply vectors by scalars
Determine collinearity of points
Solve geometrical problems involving vectors
Introduction
Media Resource
Introduction to Vectors 2 What is a vector? Adding vectors
Adding and subtracting vectors Adding and Subtracting Vectors Graphically
Subtracting vectors Transformations - translating a shape
Transformations Rotating Shapes Transformations - Reflecting Shapes Transformations - enlarging shapes Vectors and Translations Multiplying a vector by a scalar Addition, Subtraction, and Scalar Multiplication
Understanding multiplying vectors by scalars How to Show Points are Collinear
Geometric Proofs Using Vectors Geometric Vectors
Simulation:Vector Addition -Equations
Simulation: Vector Addition
Geometrical Transformations
Specific Outcomes
Explain the concept of transformation
Use a column vector to translate an object
Reflect objects by different methods
Rotate objects by different methods
Enlarge objects by different methods
Stretch objects by different methods
Find area, scale factors of a stretch by determinant method
Shear objects by different methods
Solve problems involving combined transformations
Introduction
Introduction to transformations
Media Resource
Geometry - Translations Translations Translations Reflections and Rotations Geometry- Reflections Common Core Geometry Transformations Reflections How Do I Rotate a Figure?
Rotating Objects 90 Degrees Around The Origin
Enlargement Center of Enlargement How to Enlarge with a Positive Scale Factor Transformations stretch Stretch and shear Linear Transformation Scaling and Shearing Transformations Combining Transformations 1
Combining Transformations 2 Combining Transformations 3 Combining Transformations 4
Earth Geometry
Specific Outcomes
Explain the concept of Earth Geometry
Distinguish between small and great circles
Calculate distance along parallels of latitudes and longitude in kilometres and nautical miles
Calculate the shortest distance between two points on the surface of the earth
Calculate speed in knots and time
Introduction
Earth Geometry Great and Small Circles Great Circle Distance Distance between two points on small circle Small Circles Longitude and Latitude Latitude and Longittude Latitudes and Longitudes
Finding distance with latitude and longitude
Calculating Distance (in degrees) with Latitude Distance between two points on great circle Parallel lines of latitude Vs distance greater circle Angular & Linear Speed of a Circle Nautical miles and knots
Nautical Miles & Knots Minutes and Nautical miles What`s 1 knot?
Distance along an arc on the surface of the earth
Introduction to Calculus
Specific Outcomes
Explain concept of differentiation
Differentiate functions from first principles.
Use the formula for differentiation
Calculate equations of tangents and normals
Explain integration
Find Indefinite integrals
Evaluate simple definite integrals
Find the area under the curve
Introduction
Media Resource
Introduction, Basic Review Calculus in 10 Minutes Differential Calculus
Tips in Differential Calculus Differentiation Differentiation Rules Differentiation from 1st Principles
Slope and Equation of Normal & Tangent Line of Curve at Given Point Tangents and Normals
How to find Equations of Tangents and Normals Basic Integration Problems Indefinite Integral Basic Integration Intro to Area Under a Curve Finding the Area Under a Curve
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