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Express Math HBL
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Lessons
Secondary 1
Chp 1: Primes, Highest Common Factor and Lowest Common Multiple
1.1: Prime Numbers
1.2: Square Roots and Cube Roots
1.3: Highest Common Factors and Lowest Common Multiple
Chp 2: Integers, Rational Numbers and Real Numbers
2.1: Negative Numbers
2.2: Addition and subtraction involving negative integers
2.3: Multiplication, division and combined operations for negative integers
2.4: Fractions and mixed numbers
2.5: Decimals
2.6: Rational, irrational and real numbers
Chp 3: Approximation and Estimation
3.1: Rounding and significant figures
3.2: Approximation and approximation errors in real-world contexts
3.3: Estimation and estimation errors in real-world contexts
Chp 4: Basic Algebra and Algebraic Manipulation
4.1: Basic algebraic concepts and notations
4.2: Addition and subtraction of linear terms
4.3: Expansion and factorisation of linear expressions
4.4: Linear expressions with fractional coefficients
Chp 5: Linear Equations
5.1: Linear Equations
5.2: Linear Equations with Fractional Coefficients and Factional Equations
5.3: Application of linear equations in real-world contexts
5.4: Mathematical Formulae
Chp 6: Linear Functions and Graphs
6.1 and 6.2: Cartesian coordinates and Functions
6.3: Linear Functions
6.4: Applications of linear graphs in real-world contexts
Chp 7: Number Patterns
7.1: Number Sequences
7.2: Number Sequences and Patterns
Chp 8: Percentage
8.1: Percentage
8.2: Percentage change, percentage point and reverse percentage
8.3: Percentage in real-world contexts
Chp 9: Ratio and Rate
9.1: Ratio
9.2: Rate
9.3: Speed
Chp 10: Basic Geometry
10.1: Basic geometry concepts and notations
10.2: Properties of angles formed by intersecting lines (Recap)
10.3: Properties of angles formed by two parallel lines and transversal
Chp 11: Polygons and Geometrical Constructions
11.1: Triangles
11.2: Quadrilaterals
11.3: Geometrical constructions of triangles and quadrilaterals
11.4: Polygons
Chp 12: Perimeter and Area of Plane Figures
12.1: Conversion of Units
12.2: Perimeter and Area of basic plane figures
12.3: Perimeter and Area of parallelograms
12.4: Perimeter and Area of Trapeziums
Chp 13: Volume and Surface Area of Prism and Cylinders
13.1: Conversion of Units
13.2: Three-dimensional solids
13.3: Volume and surface area of cubes and cuboids
13.4: Volume and surface area of prisms
13.5: Volume and surface area of cylinders
13.6: Volume and surface area of composite solids
Chp 14: Statistical Data Handling
14.1: Frequency table
14.2: Pictogram
14.3: Bar Graph
14.4: Pie Chart
14.5: Line Graph
14.6: Evaluation of statistical representations
14.7: Statistical investigation
Secondary 2
Chp 1: Linear Graphs and Simultaneous Linear Equations
1.1: Equations of straight lines
1.2: Graphs of linear equations in the form ax + by = k
1.3: Solving simultaneous linear equations using graphical method
1.4: Solving simultaneous linear equations using algebraic method
1.5: Applications of simultaneous equations in real-world contexts
Chp 2: Linear Inequalities
2.1: Simple Inequalities
2.2: Solving simple linear inequalities
2.3: Solving problems involving linear inequalities
Chp 3: Expansion and Factorisation of Algebraic Expressions
3.1: Addition and Subtraction of quadratic expressions
3.2: Expansion of algebraic expressions of the form (a+b)(c+d)
3.3: Expansion of quadratic expressions
3.4: Factorisation of quadratic expressions
3.5: Factorisation of algebraic expressions into the form (a+b)(c+d)
Chp 4: Expansion and Factorisation using Special Algebraic Identities
4.1: Expansion using Special algebraic identities
4.2: Factorisation using special algebraic identities
Chp 5: Quadratic Equations and Graphs
5.1: Solving quadratic equations by factorisation
5.2: Quadratic functions and graphs
Chp 6: Algebraic Fractions and Formulae
6.1: Algebraic fractions
6.2: Multiplication and division of algebraic fraction
6.3: Addition and subtraction of algebraic fractions
6.4: Solving equations involving algebraic fractions
6.5: Manipulation of algebraic formulae
Chp 7: Direct and Inverse Proportions
7.1: Direct proportion
7.2: Algebraic and graphical representations of direct proportion
7.3: Other forms of direct proportion
7.4: Inverse proportion
7.5: Algebraic and graphical representations of inverse proportion
7.6: Other forms of inverse proportion
Chp 8: Congruency and Similarity
8.1: Congruent Figures
8.2: Similar Figures
8.3: Similarity and enlargement
Chp 9: Pythagoras' Theorem
9.1: Pythagoras' Theorem
9.2: Application of Pythagoras' Theorem in real-world contexts
9.3: Converse of Pythagoras' Theorem
Chp 10: Trigonometric Ratios
10.1: Trigonometric Ratios
10.2: Applications of trigonometric ratios to find unknown sides
10.3: Applications of trigonometric ratios to find unknown angles
10.4: Applications of Trigonometric ratios in real-world
Chp 11: Volume and Surface Area of Pyramid, Cones and Spheres
11.1: Volume and Surface Area of Pyramids
11.2: Volume and Surface Area of Cones
11.3: Volume and Surface Area of Spheres
11.4: Volume and Surface Area of Composite Figures
Chp 12: Probability of Single Events
12.1: Probability experiment and sample space
12.2: Probability of single events
12.3: Further examples of probability of single events
12.4: Experimental approach to finding probability
Chp 13: Statistical Diagrams
13.1: Dot diagrams
13.2: Histograms for ungrouped data
13.3: Stem-and-leaf diagrams
13.4: Histogram for grouped data
Chp 14: Averages of Statistical Data
14.1: Mean
14.2: Median
14.3: Mode
14.4: Measures of central tendency
Notes
Sec 1 Notes
Sec 2 Notes
Chp 7: Inverse and Direct Proportion
Homework Submission, Marked Assignments and Corrections
Sec 1: Homework Submission and Marked Assignments
Sec 2: Homework Submission and Marked Assignments
Video Answers
2E Homework Video Answers
2E Worksheets Video Answers
2E Quiz Video Answers
2E School Papers Video Answers
School Papers and Worksheets
Solutions and Answers
Sec 1: Video Answers
Chp 1: Video Answers
Chp 4: Video Answers
Chp 6: Video Answers
Chp 7: Video Answers
Chp 10: Video Answers
Exam Papers Video Answers
Express Math HBL
Home
Lessons
Secondary 1
Chp 1: Primes, Highest Common Factor and Lowest Common Multiple
1.1: Prime Numbers
1.2: Square Roots and Cube Roots
1.3: Highest Common Factors and Lowest Common Multiple
Chp 2: Integers, Rational Numbers and Real Numbers
2.1: Negative Numbers
2.2: Addition and subtraction involving negative integers
2.3: Multiplication, division and combined operations for negative integers
2.4: Fractions and mixed numbers
2.5: Decimals
2.6: Rational, irrational and real numbers
Chp 3: Approximation and Estimation
3.1: Rounding and significant figures
3.2: Approximation and approximation errors in real-world contexts
3.3: Estimation and estimation errors in real-world contexts
Chp 4: Basic Algebra and Algebraic Manipulation
4.1: Basic algebraic concepts and notations
4.2: Addition and subtraction of linear terms
4.3: Expansion and factorisation of linear expressions
4.4: Linear expressions with fractional coefficients
Chp 5: Linear Equations
5.1: Linear Equations
5.2: Linear Equations with Fractional Coefficients and Factional Equations
5.3: Application of linear equations in real-world contexts
5.4: Mathematical Formulae
Chp 6: Linear Functions and Graphs
6.1 and 6.2: Cartesian coordinates and Functions
6.3: Linear Functions
6.4: Applications of linear graphs in real-world contexts
Chp 7: Number Patterns
7.1: Number Sequences
7.2: Number Sequences and Patterns
Chp 8: Percentage
8.1: Percentage
8.2: Percentage change, percentage point and reverse percentage
8.3: Percentage in real-world contexts
Chp 9: Ratio and Rate
9.1: Ratio
9.2: Rate
9.3: Speed
Chp 10: Basic Geometry
10.1: Basic geometry concepts and notations
10.2: Properties of angles formed by intersecting lines (Recap)
10.3: Properties of angles formed by two parallel lines and transversal
Chp 11: Polygons and Geometrical Constructions
11.1: Triangles
11.2: Quadrilaterals
11.3: Geometrical constructions of triangles and quadrilaterals
11.4: Polygons
Chp 12: Perimeter and Area of Plane Figures
12.1: Conversion of Units
12.2: Perimeter and Area of basic plane figures
12.3: Perimeter and Area of parallelograms
12.4: Perimeter and Area of Trapeziums
Chp 13: Volume and Surface Area of Prism and Cylinders
13.1: Conversion of Units
13.2: Three-dimensional solids
13.3: Volume and surface area of cubes and cuboids
13.4: Volume and surface area of prisms
13.5: Volume and surface area of cylinders
13.6: Volume and surface area of composite solids
Chp 14: Statistical Data Handling
14.1: Frequency table
14.2: Pictogram
14.3: Bar Graph
14.4: Pie Chart
14.5: Line Graph
14.6: Evaluation of statistical representations
14.7: Statistical investigation
Secondary 2
Chp 1: Linear Graphs and Simultaneous Linear Equations
1.1: Equations of straight lines
1.2: Graphs of linear equations in the form ax + by = k
1.3: Solving simultaneous linear equations using graphical method
1.4: Solving simultaneous linear equations using algebraic method
1.5: Applications of simultaneous equations in real-world contexts
Chp 2: Linear Inequalities
2.1: Simple Inequalities
2.2: Solving simple linear inequalities
2.3: Solving problems involving linear inequalities
Chp 3: Expansion and Factorisation of Algebraic Expressions
3.1: Addition and Subtraction of quadratic expressions
3.2: Expansion of algebraic expressions of the form (a+b)(c+d)
3.3: Expansion of quadratic expressions
3.4: Factorisation of quadratic expressions
3.5: Factorisation of algebraic expressions into the form (a+b)(c+d)
Chp 4: Expansion and Factorisation using Special Algebraic Identities
4.1: Expansion using Special algebraic identities
4.2: Factorisation using special algebraic identities
Chp 5: Quadratic Equations and Graphs
5.1: Solving quadratic equations by factorisation
5.2: Quadratic functions and graphs
Chp 6: Algebraic Fractions and Formulae
6.1: Algebraic fractions
6.2: Multiplication and division of algebraic fraction
6.3: Addition and subtraction of algebraic fractions
6.4: Solving equations involving algebraic fractions
6.5: Manipulation of algebraic formulae
Chp 7: Direct and Inverse Proportions
7.1: Direct proportion
7.2: Algebraic and graphical representations of direct proportion
7.3: Other forms of direct proportion
7.4: Inverse proportion
7.5: Algebraic and graphical representations of inverse proportion
7.6: Other forms of inverse proportion
Chp 8: Congruency and Similarity
8.1: Congruent Figures
8.2: Similar Figures
8.3: Similarity and enlargement
Chp 9: Pythagoras' Theorem
9.1: Pythagoras' Theorem
9.2: Application of Pythagoras' Theorem in real-world contexts
9.3: Converse of Pythagoras' Theorem
Chp 10: Trigonometric Ratios
10.1: Trigonometric Ratios
10.2: Applications of trigonometric ratios to find unknown sides
10.3: Applications of trigonometric ratios to find unknown angles
10.4: Applications of Trigonometric ratios in real-world
Chp 11: Volume and Surface Area of Pyramid, Cones and Spheres
11.1: Volume and Surface Area of Pyramids
11.2: Volume and Surface Area of Cones
11.3: Volume and Surface Area of Spheres
11.4: Volume and Surface Area of Composite Figures
Chp 12: Probability of Single Events
12.1: Probability experiment and sample space
12.2: Probability of single events
12.3: Further examples of probability of single events
12.4: Experimental approach to finding probability
Chp 13: Statistical Diagrams
13.1: Dot diagrams
13.2: Histograms for ungrouped data
13.3: Stem-and-leaf diagrams
13.4: Histogram for grouped data
Chp 14: Averages of Statistical Data
14.1: Mean
14.2: Median
14.3: Mode
14.4: Measures of central tendency
Notes
Sec 1 Notes
Sec 2 Notes
Chp 7: Inverse and Direct Proportion
Homework Submission, Marked Assignments and Corrections
Sec 1: Homework Submission and Marked Assignments
Sec 2: Homework Submission and Marked Assignments
Video Answers
2E Homework Video Answers
2E Worksheets Video Answers
2E Quiz Video Answers
2E School Papers Video Answers
School Papers and Worksheets
Solutions and Answers
Sec 1: Video Answers
Chp 1: Video Answers
Chp 4: Video Answers
Chp 6: Video Answers
Chp 7: Video Answers
Chp 10: Video Answers
Exam Papers Video Answers
More
Home
Lessons
Secondary 1
Chp 1: Primes, Highest Common Factor and Lowest Common Multiple
1.1: Prime Numbers
1.2: Square Roots and Cube Roots
1.3: Highest Common Factors and Lowest Common Multiple
Chp 2: Integers, Rational Numbers and Real Numbers
2.1: Negative Numbers
2.2: Addition and subtraction involving negative integers
2.3: Multiplication, division and combined operations for negative integers
2.4: Fractions and mixed numbers
2.5: Decimals
2.6: Rational, irrational and real numbers
Chp 3: Approximation and Estimation
3.1: Rounding and significant figures
3.2: Approximation and approximation errors in real-world contexts
3.3: Estimation and estimation errors in real-world contexts
Chp 4: Basic Algebra and Algebraic Manipulation
4.1: Basic algebraic concepts and notations
4.2: Addition and subtraction of linear terms
4.3: Expansion and factorisation of linear expressions
4.4: Linear expressions with fractional coefficients
Chp 5: Linear Equations
5.1: Linear Equations
5.2: Linear Equations with Fractional Coefficients and Factional Equations
5.3: Application of linear equations in real-world contexts
5.4: Mathematical Formulae
Chp 6: Linear Functions and Graphs
6.1 and 6.2: Cartesian coordinates and Functions
6.3: Linear Functions
6.4: Applications of linear graphs in real-world contexts
Chp 7: Number Patterns
7.1: Number Sequences
7.2: Number Sequences and Patterns
Chp 8: Percentage
8.1: Percentage
8.2: Percentage change, percentage point and reverse percentage
8.3: Percentage in real-world contexts
Chp 9: Ratio and Rate
9.1: Ratio
9.2: Rate
9.3: Speed
Chp 10: Basic Geometry
10.1: Basic geometry concepts and notations
10.2: Properties of angles formed by intersecting lines (Recap)
10.3: Properties of angles formed by two parallel lines and transversal
Chp 11: Polygons and Geometrical Constructions
11.1: Triangles
11.2: Quadrilaterals
11.3: Geometrical constructions of triangles and quadrilaterals
11.4: Polygons
Chp 12: Perimeter and Area of Plane Figures
12.1: Conversion of Units
12.2: Perimeter and Area of basic plane figures
12.3: Perimeter and Area of parallelograms
12.4: Perimeter and Area of Trapeziums
Chp 13: Volume and Surface Area of Prism and Cylinders
13.1: Conversion of Units
13.2: Three-dimensional solids
13.3: Volume and surface area of cubes and cuboids
13.4: Volume and surface area of prisms
13.5: Volume and surface area of cylinders
13.6: Volume and surface area of composite solids
Chp 14: Statistical Data Handling
14.1: Frequency table
14.2: Pictogram
14.3: Bar Graph
14.4: Pie Chart
14.5: Line Graph
14.6: Evaluation of statistical representations
14.7: Statistical investigation
Secondary 2
Chp 1: Linear Graphs and Simultaneous Linear Equations
1.1: Equations of straight lines
1.2: Graphs of linear equations in the form ax + by = k
1.3: Solving simultaneous linear equations using graphical method
1.4: Solving simultaneous linear equations using algebraic method
1.5: Applications of simultaneous equations in real-world contexts
Chp 2: Linear Inequalities
2.1: Simple Inequalities
2.2: Solving simple linear inequalities
2.3: Solving problems involving linear inequalities
Chp 3: Expansion and Factorisation of Algebraic Expressions
3.1: Addition and Subtraction of quadratic expressions
3.2: Expansion of algebraic expressions of the form (a+b)(c+d)
3.3: Expansion of quadratic expressions
3.4: Factorisation of quadratic expressions
3.5: Factorisation of algebraic expressions into the form (a+b)(c+d)
Chp 4: Expansion and Factorisation using Special Algebraic Identities
4.1: Expansion using Special algebraic identities
4.2: Factorisation using special algebraic identities
Chp 5: Quadratic Equations and Graphs
5.1: Solving quadratic equations by factorisation
5.2: Quadratic functions and graphs
Chp 6: Algebraic Fractions and Formulae
6.1: Algebraic fractions
6.2: Multiplication and division of algebraic fraction
6.3: Addition and subtraction of algebraic fractions
6.4: Solving equations involving algebraic fractions
6.5: Manipulation of algebraic formulae
Chp 7: Direct and Inverse Proportions
7.1: Direct proportion
7.2: Algebraic and graphical representations of direct proportion
7.3: Other forms of direct proportion
7.4: Inverse proportion
7.5: Algebraic and graphical representations of inverse proportion
7.6: Other forms of inverse proportion
Chp 8: Congruency and Similarity
8.1: Congruent Figures
8.2: Similar Figures
8.3: Similarity and enlargement
Chp 9: Pythagoras' Theorem
9.1: Pythagoras' Theorem
9.2: Application of Pythagoras' Theorem in real-world contexts
9.3: Converse of Pythagoras' Theorem
Chp 10: Trigonometric Ratios
10.1: Trigonometric Ratios
10.2: Applications of trigonometric ratios to find unknown sides
10.3: Applications of trigonometric ratios to find unknown angles
10.4: Applications of Trigonometric ratios in real-world
Chp 11: Volume and Surface Area of Pyramid, Cones and Spheres
11.1: Volume and Surface Area of Pyramids
11.2: Volume and Surface Area of Cones
11.3: Volume and Surface Area of Spheres
11.4: Volume and Surface Area of Composite Figures
Chp 12: Probability of Single Events
12.1: Probability experiment and sample space
12.2: Probability of single events
12.3: Further examples of probability of single events
12.4: Experimental approach to finding probability
Chp 13: Statistical Diagrams
13.1: Dot diagrams
13.2: Histograms for ungrouped data
13.3: Stem-and-leaf diagrams
13.4: Histogram for grouped data
Chp 14: Averages of Statistical Data
14.1: Mean
14.2: Median
14.3: Mode
14.4: Measures of central tendency
Notes
Sec 1 Notes
Sec 2 Notes
Chp 7: Inverse and Direct Proportion
Homework Submission, Marked Assignments and Corrections
Sec 1: Homework Submission and Marked Assignments
Sec 2: Homework Submission and Marked Assignments
Video Answers
2E Homework Video Answers
2E Worksheets Video Answers
2E Quiz Video Answers
2E School Papers Video Answers
School Papers and Worksheets
Solutions and Answers
Sec 1: Video Answers
Chp 1: Video Answers
Chp 4: Video Answers
Chp 6: Video Answers
Chp 7: Video Answers
Chp 10: Video Answers
Exam Papers Video Answers
5.3: Application of linear equations in real-world contexts
1) Lesson Objectives:
You should be able to
convert information from word problem into mathematical statements using 3Cs
Formulating Linear Equation Video 1
TB Ex 5B Qtn 1
Formulating Linear Equation Video 2
TB Ex 5B Qtn 1
Alternative Method
Formulating Linear Equation Video 3
TB Ex 5B Qtn 10
Formulating Linear Equation Video 4
TB Ex 5B Qtn 10 Alternative Method
Formulating Linear Equation Video 5
TB Ex 5B Qtn 7
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