Tin Ka Ping Secondary School 05-06 F. Mathematics Syllabus Chapter Linear Inequalities in One Unknown Time Guide. Basic Concept of Inequalities A. What are Inequalities? B. Solutions of Inequalities C. Graphical Representations of the Solutions of Inequalities. Basic Properties of Inequalities Learn the inequalities and the inequality signs. Understand the law of trichotomy. Learn how to represent the solutions of inequalities graphically. Learn the basic properties of inequalities. Learn the law of trichotomy through Activity.. Introduce some common inequality signs and the meanings of inequalities. Learn the graphical representations of the solutions of inequalities. Learn the additive property, multiplicative property and the reciprocal property of two distinct numbers through Activities..4. Basic Concept of Inequalities Basic Properties of Inequalities. Linear Inequalities in One Unknown A. Solving Linear Inequalities in One Unknown B. Using Inequalities to Solve Simple Problems Introduce the meaning of linear inequalities in one unknown. Learn the techniques of solving linear inequalities in one unknown. Learn how to apply inequalities to solve simple problems. Learn the meaning of linear inequalities in one unknown. Introduce the techniques of solving linear inequalities in one unknown through worked Learn how to use inequalities to solve simple problems through worked Consolidate the techniques of solving linear inequalities in one unknown with the help of the basic topical worksheet 8. Solving Linear Inequalities in One Unknown
Chapter Percentages (II) Time Guide 4 5. More about Percentage Increase and Decrease A. Percentage Changes B. Successive Percentage Changes C. Percentage Changes in Different Parts. Increase or Decrease at a Constant Rate A. Increase at a Constant Rate B. Decrease at a Constant Rate. Interest A. Simple Interest B. Compound Interest Learn the formula for percentage change. Apply percentages to solve problems involving successive changes. Apply percentages to solve further practical problems involving changes in different parts. Learn the formulas for a value which increases/decreases at a constant rate. Understand the concepts of simple interest and compound interest. Apply percentages to solve problems involving simple interest and compound interest. Students should be able to identify original value, new value and percentage change from a given question. Emphasize the distinction between overall percentage change and successive percentage change. Learn to find the overall percentage change in problems involving percentage changes in different parts. Students should be able to deduce the formula for values increasing at a constant rate through Activity.. Consolidate the concepts of increase or decrease at a constant rate with the help of the basic topical worksheet 40. Explore the formula relating the simple interest and the deposit period through Activity.. Lead students to investigate the concept of simple interest and compound interest through Activity.. Students should be able to distinguish simple interest and compound interest. Illustrate the applications of formulas for simple interest and compound interest with worked Teachers should remind students that r% in the compound interest formula refers to the compound interest per period rather than the annual interest rate. Consolidate the techniques of solving problems involving simple interest and compound interest with the help of the basic topical worksheet 4.. Percentage Changes. Successive Percentage Changes Drilling Program: Problems about Percentages Increase or Decrease at a Constant Rate. Simple Interest. Compound Interest Drilling Program: Problems about Percentages Software Demonstration: Calculating Compound Interest Activity.: Simple interest and compound interest
Chapter Special Lines and Centres in a Triangle Time Guide 4. Important Lines in a Triangle Recognize the important lines in a triangle, including angle bisector, median, altitude and perpendicular bisector. Use the definition of the important lines in a triangle to find unknowns and perform proofs. Students should be able to identify angle bisectors, medians, altitudes and perpendicular bisectors in a triangle. Remind students that angle bisectors and medians must lie inside a triangle. On the other hand, altitudes may not. Illustrate simple proofs involving lines of a triangle with worked Consolidate the concepts of important lines in a triangle with the help of the basic topical worksheet 60. Important Lines in a Triangle. Relationship among the Three Sides of a Triangle (Non-foundation) Explore and recognize the relationship among the lengths of the three sides in a triangle, i.e. the triangle inequality. Explore the triangle inequality through Activity.. Relationship among the Three Sides of a Triangle 5. Centres of a Triangle A. Properties of the Centres of a Triangle B. Construction of Centres of a Triangle Using Compasses and Straight Edge (Non-foundation) Explore and recognize the properties of centres of a triangle, including incentre, circumcentre, centroid and orthocentre. Construct the centres of a triangle by compasses and straight edge. Explore the properties of all Animation: the centres of a triangle by drawing lines in a triangle through Activity.. Students should be able to identify different centres of a triangle. Remind students that the orthocentre and circumcentre of an obtuse-angled triangle always lie outside the triangle. Point out the relationships between incentre and inscribed circle; circumcentre and circumscribed circle. Point out that the centroid divides each median in the ratio :. Students should know how to locate different centres for a given triangle. Consolidate the concept of different centres of a triangle through Extra Activity. Centres of a Triangle Extra Activity: Centres of a triangle
Chapter 4 Quadrilaterals Time Guide 4 4 4. Quadrilaterals 4. Parallelograms A. Properties of Parallelograms B. Identifying Parallelograms (Non-foundation) 4. Rectangles, Squares, Rhombuses, Trapeziums and Kites A. Rectangles B. Squares C. Rhombuses D. Trapeziums E. Kites 4.4 Simple Proofs related to Parallelograms (Non-foundation) 4.5 Mid-point Theorem (Non-foundation) Realize the definition of quadrilaterals and the related terminology and properties. Investigate the properties of parallelograms. Use the properties of paralellograms to solve problems. Realize the conditions for parallelograms, and learn to identify parallelograms. (Non-foundation) Realize the properties of other special quadrilaterals, including rectangles, squares, rhombuses, trapeziums and kites. Apply the properties of rectangles, squares, rhombuses, trapeziums and kites to solve problems. Use the properties of different kinds of parallelograms to perform simple proofs. Realize the mid-point theorem and use it to solve problems. Introduce the definition of quadrilaterals. Introduce the related terminologies and properties of quadrilaterals. Investigate the properties of parallelograms through Activity 4.. Consolidate the properties of parallelograms with the help of the basic topical worksheet 6. Deduce the conditions for a given quadrilateral to be a parallelogram through Activity 4.. Emphasize the difference between the properties of parallelograms and the conditions for a quadrilateral to be a parallelogram in solving problems. Students should be able to apply the properties of parallelogram and write their corresponding abbreviations in solving problems. Introduce the definitions of rectangles, squares, rhombuses, trapeziums and kites. Students should be able to distinguish rectangles, squares, rhombuses, trapeziums and kites. Point out the relationships among different kinds of quadrilateral with the diagram in p. 4.. Consolidate the properties of other quadrilaterals with the help of the basic topical worksheets 6 & 6. Illustrate with worked examples the proofs related to parallelograms. Introduce the mid-point theorem and emphasize the usefulness of different geometrical properties. Illustrate with worked examples the application of mid-point theorem in solving problems. Parallelograms Software Demonstration: Construction of Parallelograms. Rectangles, Squares and Rhombuses. Trapeziums and Kites Software Demonstration: Construction of Rectangles Mid-point Theorem and Intercept Theorem
Time Guide 4.6 Intercept Theorem (Non-foundation) Realize the intercept theorem and apply it to solve problems. Introduce the intercept theorem through Activity 4.. Distinguish the difference between the mid-point theorem and the intercept theorem. Illustrate with worked examples the application of intercept theorem in solving problems.
Chapter 5 More about -D Figures Time Guide 5. Understand the concepts of Symmetries of reflectional and rotational Solids symmetries of solids. A. Reflectional Recognize the reflectional and and Rotational rotational symmetries of cubes Symmetries of and regular tetrahedra. Solids Explore the reflectional and B. Symmetries of rotational symmetries of other Regular regular polyhedra. Polyhedra (Enrichment topic) (Enrichment: Other Regular Polyhedra) 5. Nets of Solids 5. -D Representations of Solids A. Orthographic Views of Solids B. Identifying Solids from their Orthographic Views (Enrichment: Drawing Solids on Isometric Grid) Understand and learn to design a net for a solid. Realize the relationships among the vertices and the faces of a solid formed by a net. Understand the limitations of a -D representation. Learn to draw the orthographic views of a solid and understand the related concepts. Sketch the solid according to its orthographic views. Draw the solid on isometric grid paper according to its orthographic views. (Enrichment topic) Help students to extend the concepts of reflectional and rotational symmetries from rectilinear figures to solids. Teachers may use the teaching tools provided in the teaching CD-ROM to illustrate the idea of rotational symmetry of different regular polyhedra. Encourage students to investigate the symmetric properties of other regular polyhedra on their own. Explore the relationships between a solid and its net through Activity 5.. Students should realize that there may be more than one net for a solid. Ask students to design nets for a given solid to consolidate their understanding on the topic. Learn to draw the orthographic views of a solid through Activity 5.. Help students to realize the limitation of -D representation of a solid. Introduce the steps in drawing the solid on the isometric grid according to its orthographic views. Symmetries of Solids Tools:. Rotational Symmetry of Cube. Rotational Symmetry of Tetrahedron,. Rotational Symmetry of Octahedron, 4. Rotational Symmetry of Dodecahedron 5. Rotational Symmetry of Icosahedron Animation: Rotational Symmetry of Cube Nets of Solids Tools:. A Net of the Tetrahedron. A Net of the Cube. A Net of the Octahedron 4. A Net of the Dodecahedron 5. A Net of the Icosahedron -D Representations of Solids
Time Guide 5.4 Understand the concept of the Points, Lines and projection of a point or a line Planes in Solids segment on a plane. A. Relationships Learn to identify the angle between Lines between a line and a plane. and Planes Learn to identify the angle B. Relationships between two planes. between Two Solve practical problems Planes involving lines and planes in a solid. 5.5 More about Solids A. Euler s Formula B. Duality of Regular Polyhedra Realize the Euler s formula. Explore the duality of regular polyhedra. Introduce the concept of the projection of a point or a line segment on a plane. Students should be able to identify the angle between a line and a plane, and the angle between two planes. Explore the Euler s formula through Activity 5.. Remind students that for every pair of dual polyhedra, their numbers of vertices and faces must be interchangeable. Points, Lines and Planes in Solids Tools:. Projection of a Line on a Plane. Trigonometry in Three Dimensions Tools:. Duality of Cube and Octahedron. Duality of Dodecahedron and Icosahedron
Chapter 6 Measures of Central Tendency Time Guide 6. Introduction to Central Tendency Learn the concept of central tendency. Learn that averages are used to reflect the central tendency of data sets. Point out that averages are important in reflecting the central tendency of data. 6. Arithmetic Means A. Arithmetic Means of Ungrouped Data B. Arithmetic Means of Grouped Data 6. Medians A. Medians of Ungrouped Data B. Medians of Grouped Data Learn the definition of arithmetic mean and its applications. Learn to find arithmetic means of ungrouped data. Learn to find arithmetic means of ungrouped and grouped data from frequency distribution tables. Learn the definition of median and its applications. Learn to find medians of data from frequency distribution tables. Review how to find medians of data from cumulative frequency polygons/curves. Emphasize the difference between averages and arithmetic means. Arithmetic Means Demonstrate the calculation and application of arithmetic means of ungrouped data using worked Review how data can be grouped and organized in frequency distribution tables. Introduce the method for calculating arithmetic means of ungrouped / grouped data from frequency distribution table. Emphasize that the arithmetic means obtained in grouped data are approximations only and are affected by how the data are grouped. Introduce the definition of median. Illustrate how to find medians for odd or even number of data. Demonstrate how to find medians from frequency distribution tables through worked Review with students how to find the median of grouped data from a cumulative frequency polygon/curve learnt in Book A Chapter 7. Emphasize that the medians obtained from cumulative frequency polygons/curves are approximations only since they are affected by how the data are grouped. Medians
Time Guide 6.4 Learn the definition of Modes and mode/modal class and its Modal Classes applications. A. Introduction Learn to find modal classes to Modes of grouped data from B. Modal Classes frequency distribution of Grouped tables. Data 6.5 Comparing Different Types of Average A. Choosing the most Appropriate Measure of Central Tendency B. Comparing Two Sets of Data with Different Types of Average 6.6 Misuses of Averages and the Consequences of Misues A. Misuses of Averages B. Consequences of Misusing Averages 6.7 Further Investigations on Averages (Non-foundation) Compare the characteristics of the three averages. Learn to choose the appropriate averages in different situations to reflect the central tendency. Compare two sets of data by using different types of average. Understand how business people may use averages to mislead customers. Learn to determine whether the averages used to reflect central tendency are appropriate. Understand the consequences of the misuses of averages. Learn the effects on the averages when the data sets are modified. Explore the concept of mode. Emphasize that there may be no modes or more than one mode in a data set. Demonstrate the applications of modes with worked Point out that modal class is the class interval with the highest frequency for grouped data. Point out that modal classes are affected by how the data are grouped. Consolidate the concepts of means, medians and modes with the help of the basic topical worksheet 70. Learn to choose an appropriate measure of central tendency through a daily-life scenario through Activity 6.. Explore how to choose appropriate averages to reflect central tendency of data with Compare the properties of different averages and remind students to choose the appropriate average(s) according to the actual situations. Learn to compare two sets of data with different types of average with worked Explore the difficulties in comparing two sets of data with only one or two averages. Explore the effects of using different averages to reflect the same data set through Activity 6.. Show students how some shop owners misleads the customers using averages with worked Explore the inappropriate comparisons using arithmetic means through Activity 6. to develop students analyzing skills. Explore the effects on averages after the following modifications of data: Adding a constant C to each datum Multiplying a constant k to each datum Inserting the datum 0 Deleting a datum Modes and Modal Classes Software Demonstration: Calculating the Mean, Median and Mode for Ungrouped Data Comparing Different Types of Average Extra Activity: Properties of the averages Misuses of Averages Further Investigations on Averages
Time Guide 6.8 Weighted Mean Learn the definition of weighted mean. Learn to find the weighted means of data sets. Introduce the concept of weighted mean and formula for calculating weighted mean through real-life situation. Illustrate how to calculate weighted mean from frequency distribution table with worked Weighted Mean
Chapter 7 Areas and Volumes (III) Time Guide 4 4 7. Pyramids A. Volumes of Pyramids B. Total Surface Areas of Pyramids Learn the names of different parts Students can deduce the of a pyramid. formula for calculating the Learn the properties of right volume of a pyramid pyramids and regular pyramids. through Activity 7.. Understand and learn how to use By studying the net of a formulas to calculate the volume pyramid, students can have and the total surface area of a a better understanding on pyramid. how to calculate the total Learn the definition of a frustum of surface area of a pyramid. a pyramid. Introduce the definition of a frustum of a pyramid. Show the relationship between the heights and lengths of a frustum and its corresponding pyramid by using the properties of 7. Learn the names of different parts Circular Cones of a circular cone. A. Volumes of Right Understand and learn how to use Circular Cones formulas to calculate the volume B. Total Surface and the total surface area of a Areas of Right circular cone. Circular Cones similar triangles. Realize that Pythagoras theorem can be used to express the relationships among the base radius, the height and the slant height of a circular cone. Through increasing the number of sides of the base of a right pyramid, students can explore the relationship between the formulas for calculating the volume of a circular cone and the volume of a right pyramid. Introduce the definition of a frustum of a circular cone. Show the relationship between the base radii and heights of a frustum and its corresponding circular cone by using the properties of similar triangles. Students can deduce the formula for calculating the curved surface area of a right circular cone through Activity 7.. Pyramids Extra Activity: Volumes of Pyramids (Three Pyramids in a Prism) Circular Cones Animation: Volume of a Circular Cone
Time Guide 7. Spheres A. Volumes of Spheres B. Surface Areas of Spheres 7.4 Formulas for Lengths, Areas and Volumes 7.5 Similar Shapes A. Similar Plane Figures B. Similar Solids Learn the names of different parts of a sphere. Understand and use formulas to calculate the volume and the total surface area of a sphere. Learn how to distinguish the formulas for lengths, areas and volumes. Explore the relationship between lengths and areas of similar plane figures. Explore the relationship between lengths, areas and volumes of similar solids. Understand and use the relationship between lengths, areas and volumes of similar figures to do calculation. Introduce the formulas for calculating the volume and the surface area of a sphere. Illustrate how to calculate the volume and the total surface area of a hemisphere through Consolidate the techniques of finding the total surface areas and volumes of pyramids, circular cones and spheres with the help of the basic topical worksheet 44. Introduce the concept that the measurement of length is a linear measurement. Guide students to distinguish between quadratic measurement for area and cubic measurement for volume through Activity 7.. Guide students to deduce the relationship between the lengths and areas of similar plane figures through Activity 7.4. Guide students to deduce the relationships among lengths, areas and volumes of similar solids through Activity 7.5. Spheres Extra Activity: Volumes of Spheres Formulas for Lengths, Areas and Volumes Similar Shapes Drilling Program: Similar Figures
Chapter 8 Coordinates Geometry of Striaght Lines Time Guide 8. Distance between Any Two Points on a Plane 8. Slope of a Straight Line A. Slope B. Inclination 8. Parallel and Perpendicular Lines A. Parallel Lines B. Perpendicular Lines Understand and apply the distance formula to find the distance between any two points on a plane. Understand the concept of the slope of a straight line on a coordinate plane. Realize and apply the slope formula. Realize the conditions for two straight lines to be parallel or perpendicular on a coordinate plane. Use the relationship between the slopes of a pair of parallel lines or perpendicular lines to solve some geometric problems. Review the method of finding distance between two points lying on the same horizontal line or vertical line on a rectangular coordinate plane and derive the distance formula using the Pythagoras theorem through Activity 8.. Illustrate with examples the application of distance formula to solve problems in coordinate geometry. Consolidate the techniques of finding the distance between any two points on a rectangular coordinate plane using distance formula with the help of the basic topical worksheet 5. Develop the concept of the slope of a line in coordinate geometry by using the steepness of an inclined road. Remind students that different pairs of points on a straight line give the same slope. Point out how the sign and numerical value of the slope affect the steepness and orientation of a straight line. Verify the properties of the slopes of horizontal lines and vertical lines. Teachers should not use inclination to define steepness of a straight line as only acute angle is considered at this stage. Consolidate the techniques of finding the slope and inclination of a straight line with the help of the basic topical worksheet 5. Point out the relationship between the slopes of a pair of parallel lines or perpendicular lines and illustrate how to use these properties to solve geometrical problems. Consolidate the concepts of the relationships between the slopes and parallel lines or perpendicular lines with the help of the basic topical worksheet 5. Distance between Any Two Points on a Plane Slope and Inclination of a Straight Line Parallel and Perpendicular Lines
Time Guide 8.4 Learn the mid-point Point of formula. Division Learn the section formula A. Mid-point for internal division. B. Internal Point (Non-foundation) of Division (Nonfoundation) 8.5 Learn to use the analytic Using Analytic approach to prove results Approach to relating to rectilinear Prove Results figures. Relating to Learn to choose between Rectilinear the analytic approach and Figures the deductive approach in (Non-foundation) performing proofs. Explore the relationship between the coordinates of the end-points of a line segment and the coordinates of its mid-point through Activity 9.4. Consolidate the techniques of applying mid-point formula to solve problems with the help of the basic topical worksheet 54. Derive the section formula for internal division by considering the properties of similar triangles. Help students understand how to apply the section formula for internal division through worked Through Activity 8.5, students can have a basic concept of how the analytic approach can be applied to prove geometric results. Guide students to perform proofs involving special quadrilaterals to reinforce students understanding of the analytic approach. Point of Division Drilling Program: Point of Division Using Analytic Approach to Prove Results Relating to Rectilinear Figures
Chapter 9 Trigonometric s Time Guide 9. Trigonometric s of Special Angles 9. Finding Trigonometric s by Constructing Right-Angled Triangles Explore the exact values of trigonometric ratios of the special angles 0, 45 and 60. Learn how to construct a right-angled triangle from a given trigonometric ratio, so as to find the other two trigonometric ratios. From the results of Activity 9., tabulate the exact values of the trigonometric ratios of special angles. Explain that the exact values of the trigonometric ratios of some special angles cannot be obtained using calculators and ask them to memorize the table on p. 9.5. Demonstrate how to find the values of the expressions involving trigonometric ratios of special angles. Explain in details how to find trigonometric ratios by constructing right-angled triangles. Remind students that it is not necessary to construct the triangles to scale. Consolidate the techniques of trigonometric ratios by constructing right-angled triangles with the help of the basic topical worksheet 65. Trigonometric s of Special Angles Finding Trigonometric s by Constructing Right-Angled Triangles
Time Guide 9. Trigonometric Identities A. Basic Trigonometric Identities B. Trigonometric s of Complementary Angles C. Proofs of Simple Trigonometric Identities Explore the basic trigonometric identities, and use them to simplify expressions. Learn how to use trigonometric identities to find the other two trigonometric ratios from a given trigonometric ratio. Explore the trigonometric identities for complementary angles, and use them to simplify expressions. Learn how to use trigonometric identities to solve trigonometric equations. Learn how to prove simple trigonometric identities. Guide students to derive two basic trigonometric identities sin tan and cos sin cos through Activity 9.. Demonstrate the use of trigonometric identities to simplify expressions and find the other two trigonometric ratios using the given trigonometric ratio through Explore the three trigonometric identities for complementary angles through Activity 8.. Demonstrate how to use trigonometric identities for complementary angles to simplify expressions through Introduce how to use the identities to solve simple trigonometric equations. As suggested in the syllabus, teachers may briefly introduce the proof of simple trigonometric identities, depending on the ability of students. Consolidate the techniques of applying trigonometric identities in solving equations, simplifying expressions and proving identites with the help of the basic topical worksheet 66. Trigonometric Identities
Chapter 0 Application of Trigonometry Time Guide 0. Gradients A. Gradient of a Road B. Finding Gradient from a Map 0. Angles of Elevation and Depression 0. Bearings A. Simple Bearings B. Problems Involving Bearings 0.4 Applications of Trigonometry to Rectilinear Figures Learn the concept of gradient of a road. Learn how to find gradients from a map. Learn how to solve daily-life problems on gradients. Learn the concepts of angles of elevation and depression. Learn how to solve problems on angles of elevation and depression. Learn the concepts of two kinds of bearing, which are true bearing and compass bearing. Learn how to solve problems on bearings. Learn how to apply trigonometric ratios to solve problems on rectilinear figures. Teachers may review with students the related knowledge about the slope of a straight line. Teachers may first use the ratio shown on the road sign to introduce the definition of the gradient of an inclined road. Then, introduce the relationship between the gradient and the inclination of a straight road using the definition of tangent. With the help of a contour map, introduce the definition of the gradient of a straight road between two points. Then, introduce the relationship between the gradient and the inclination of a straight road between two points on a map. Introduce the concept of angle of elevation and the angle of depression first. Then, show how to use trigonometric ratios to solve related practical problems. Teachers may show students the teaching aid Inclinometer. Explain in details the concept of true bearing and compass bearing. Make sure that students understand the two systems and know how to convert from one system to another. Illustrate with examples on how to use trigonometric ratios to solve practical problems involving bearings. Demonstrate the use of subsidiary lines or points in solve ing problems about bearings. Remind students to note the parallel lines related to two (or more) observation points. Demonstrate the need of adding line segments to solve more complicated trigonometric problems involving rectilinear figures through worked Encourage students to practise more to master the skills in applying trigonometric ratios to solve problems on rectilinear figures. 5-Minute Lecture: Gradients 5-Minute Lecture: Angles of Elevation and Depression 5-Minute Lecture: Bearings
Chapter Introduction of Probability Time Guide. Probability A. The Meaning of Probability B. Possible Outcomes C. Calculation of Probabilities D. Impossible Events and Certain Events. Further Problems on Probability A. Listing Possible Outcomes by Tree Diagrams or in Tables B. Geometric Probability. Experimental Probability Learn the basic concept of probability and the definitions of related terms. Learn the nature of probability. Know the application and calculation of probability in daily life. Learn to use tree diagrams and tables to solve further problems on probability. Learn the idea of geometric probability. Learn that the probability introduced previously is the theoretical probability. Learn the meaning of experimental probability and how to find it. Understand the difference and relationship between theoretical probability and experimental probability. Introduce the idea of chance of occurrence of an event through Activity.. Explore the likelihood for an event to occur and introduce the definition of equally likely outcomes. Define the term probability using the number of equally likely outcomes and the number of outcomes favourable to the event. Demonstrate how to solve problems involving probability through worked Introduce the definitions of impossible event and certain event, and deduce the range of the value of probability. Meaning of Probability Through the scenario in the textbook, introduce how to use tree. Finding Probability diagram to list all possible Using Tree Diagrams outcomes. or Tables Introduce how to use tables to list. Geometric all possible outcomes. Probability Discuss with students the advantages and disadvantages of using tree diagrams and tables. Introduce the definition of geometric probability and the techniques for solving related problems. Consolidate the techniques of finding probability with the help of the basic topical worksheet 7. Introduce the term theoretical probability for the probability encountered in previous sections. Introduce the meaning of experimental probability and how to calculate it through worked Realize that for a large number of trials, the experimental probability is close to the theoretical probability. Demonstrate how to solve problems involving experimental probability through worked Experimental Probability Tools: Experimental Probability and Expected Value Activity.: Experimental probability Extra Activity: Experimental Probability of Throwing a Dice Consolidate the techniques of finding experimental probability with the help of the basic topical worksheet 7.
Time Guide.4 Expected Value Learn the meaning of expected value and solve related problems. Learn the use of expected value in decision making. Help students grasp the meaning of expected value through the scenarios in the textbook. Point out that expected values are calculated based on theoretical probability and then introduce the definition of expected value. Demonstrate how the expected value is calculated through worked Remind students that the expected value is only an average of what we expect for each trial, it is not necessarily the same as the actual result. Expected Value