TEXTBOOK - HOTmaths



Cambridge HSC General Mathematics / HOTmaths

Integrated program

1 Aims of the program and suggestions for use

Cambridge HOTmaths teacher and student subscriptions are available to bundle with the Cambridge General Mathematics textbook series for NSW Stage 6 Preliminary and HSC courses. This program integrates the content of the two resources, linking HOTmaths lessons to the textbook sections. It is provided for the use of teachers and students (and parents).

A Cambridge HOTmaths student account allows students to use the full range of HOTmaths content in class or at home, and enables the teacher to use the Progress Tracker (a learning management system) to monitor students’ work and topic quiz scores. (Parents can also track their own student’s work). This makes it an ideal homework and revision resource.

A Cambridge HOTmaths teacher account allows HOTmaths to be run on one computer in a classroom, and is particularly useful when delivered via data projectors and interactive whiteboards.

The status of HOTmaths as of February 2011 is that it is mainly an early and middle secondary resource, so its principal use in relation to Year 11/12 General Maths is to revisit and revise work from earlier terms or years where requisite prior knowledge is lacking. Lessons written for Year 11 and 12 General Maths courses will be added to HOTmaths from late 2011, so it will steadily become a resource to support the General Maths course across the board, not just to revise prior knowledge.

|Examples of activities which can be done with student accounts on |Suggestions of types of activities to do in class (which can be |

|individual computers at home or in class: |accomplished with a teacher account): |

|Revise prior knowledge. |Display an interactive WIDGET in class to illustrate a concept. |

|Do a HOTmaths lesson as homework to prepare for a lesson using the |After going through a widget, print out multiple copies of an |

|textbook. |accompanying HOTsheet to work through |

|Test prior knowledge with a TOPIC QUIZ or a test from the TEST |Display an interactive WALKTHROUGH example for the class to suggest |

|GENERATOR (new in 2011) as homework or classwork. |answers for the embedded questions. |

|Do SCORCHER quizzes |Use the TEST GENERATOR (new in 2011) to print out a test of prior |

|Try the alternative approach of an interactive WIDGET or WALKTHROUGH|knowledge to do on paper |

|when having difficulty grasping a concept or learning a skill. |Display and discuss the HOTmaths lesson notes. |

|Use the DICTIONARY to test and reinforce understanding of |Set foundation-level students to work as a group revisiting previous|

|mathematical terminology and use the links provided to see |work (including previous years) while the rest of the class tackles |

|mathematical terms in use. |other work. |

Notes: The HOTmaths lessons contain other resources that teachers may prefer to use instead of or in addition to those listed in this program. The lessons accessed via the HOTmaths/Cambridge General Maths menu are selected from HOTmaths’ lesson database. The last column in the program shows the names that the lessons have in HOTmaths’ standard menu.

Please notify any errors in this draft or provide feedback to: rparry@

The exact design and appearance of the menus and lessons may change.

Check periodically for updates to this program at:

cambridge.edu.au/hotmaths or cambridge.edu.au/go

2 How to use the integrated program

From Term 1 2011, the HOTmaths menus will allow you to select Cambridge HSC General or Cambridge Preliminary General maths. You will then be offered a menu based on the structure of the textbook.

|1 In the textbook, note the HOTmaths icon indicating there |[pic] |

|is linked content for the topic, and the number under the | |

|icon which refers to the HOTmaths lesson number, not the | |

|textbook section number. These icons are a guide only. They | |

|will become out of date in printed copies as content is | |

|added to Hotmaths. For up-to-date links, consult online | |

|(PDF) versions of the text and updates to this document on | |

|Cambridge GO | |

|2 Log on to HOTmaths and choose Cambridge HSC General Maths |[pic] |

|and the chapter (topic). | |

| | |

|3 Choose the HOTmaths lesson number |[pic] |

|indicated by the icon. | |

|4 The matching HOTmaths lesson will open under the textbook headings: |

|[pic] |

Notes

1 HOTmaths lessons For the Progress Tracker and other features to work, all widgets, walkthroughs and HOTsheets have to be accessed from within HOTmaths lessons. In the Cambridge General Maths program these are the same as HOTmaths’ ‘native’ lessons, as shown in columns 4 & 5 of the tables. Having been written independently of the textbooks, the lessons may include some lower level material or material not required by the General Maths course. Teachers should check the lessons and direct students on which resources to use.

2 HOTmaths questions and tests The questions and tests are based on the complete HOTmaths lesson. Teachers are advised to check their scope and levels before use.

3 Frequent updates HOTmaths is a dynamic resource that is continually updated, and from late 2011 coverage of the Year 11 and 12 General Maths will be strengthened, and this will be reflected in updated versions of this program.

|Cambridge HSC General Mathematics |The following table summarises the location of linked HOTmaths content in the textbook, the name of the lesson to use in the |

|HOTmaths integrated program summary |HOTmaths menu, and the name of the HOTmaths topic and lesson from which the lesson is drawn (right hand side). |

| |A version that can be given to students with notes follows at the end. |

|TEXTBOOK |LESSON NUMBER & NAME |Original HOTmaths topic/lesson |

|Page |Chapter/sections |IN HOTMATHS MENU |Topic |Lesson |

| |Ch1 Credit and borrowing | | | |

|1 |1.1 Flat-rate loans |1.1 Buying on credit |Buying, borrowing, investing |Loans |

|1 |1.1 Flat-rate loans |1.2 Simple interest |Buying, borrowing, investing |Buying on credit |

|1 |1.1 Flat-rate loans |1.5 Loans |Buying, borrowing, investing |Simple interest |

|8 |1.2 Home loan repayments |1.5 Loans (see above) | | |

|14 |1.3 Comparing loans |1.3 Compound interest |Buying, borrowing, investing |Compound interest |

|14 |1.3 Comparing loans |1.4 Compound interest formula |Buying, borrowing, investing |Compound interest formula |

| |Ch2 Further apps of area & volume | | | |

|33 |2.1 Area of circles, annuluses and sectors |2.1 Areas of parts of a circle |Perimeter & area |Areas of parts of a circle |

|42 |2.3 Area of composite shapes |2.1A Formula for area of a triangle |Length, perimeter & area |Formula for area of a triangle |

|52 |2.5 Surface area of cylinders and spheres |2.2 Surface areas of cylinders |Surface area |Surface areas of cylinders |

|52 |2.5 Surface area of cylinders and spheres |2.3 Surface areas of spheres |Surface area |Surface areas of cones & spheres* |

| |Ch3 Algebraic skills & techniques | | | |

|71 |3.1 Substitution & evaluation |3.0 Substitution |Introducing algebra |Substitution |

|75 |3.2 Adding & Subtracting like terms |3.1 Add & subtract algebraic fractions |Algebraic expressions |Add & subtract algebraic fractions |

|75 |3.2 Adding & Subtracting like terms |3.2 Multiply & divide algebraic fractions |Algebraic expressions |Multiply & divide algebraic fractions |

|75 |3.2 Adding & Subtracting like terms |3.3 Expanding & simplifying |Algebraic expressions |Expanding & simplifying |

|78 |3.3 Multiplying & dividing of algebraic terms |3.2 Multiply & divide algebraic fractions |Algebraic expressions |Multiply & divide algebraic fractions |

|78 |3.3 Multiplying & dividing of algebraic terms |3.4 Factorising |Algebraic expressions |Factorising |

|78 |3.3 Multiplying & dividing of algebraic terms |3.5 Extending algebraic fraction |Algebraic expressions |Extending algebraic fraction |

|84 |3.4 Equations |3.6 Using algebra |Algebraic expressions |Using algebra |

|84 |3.4 Equations |3.7 Solving linear equations |Linear equations & inequalities |Solving linear equations |

|84 |3.4 Equations |3.8 Equations with brackets |Linear equations & inequalities |Equations with brackets |

|84 |3.4 Equations |3.9 Equations with fractions |Linear equations & inequalities |Equations with fractions |

|84 |3.4 Equations |3.10 Problems & formulas |Linear equations & inequalities |Problems & formulas |

|101 |3.7 Scientific notation |3.11 Scientific notation |Number notations |Scientific notation |

|TEXTBOOK |LESSON NUMBER & NAME |Original HOTmaths topic/lesson |

|Page |Chapter/sections |IN HOTMATHS MENU |Topic |Lesson |

| |Ch4 Interpreting sets of data | | | |

|109 |4.1 Mean |4.1 Exploring the mean |Analysing data |Exploring the mean |

|109 |4.1 Mean |4.3 Centres for grouped data |Data analysis |Centres for grouped data |

|116 |4.2 Median |4.2 The mode, median & range |Analysing data |The mode, the median & range |

|116 |4.2 Median, |4.3 Centres for grouped data |Data analysis |Centres for grouped data |

|120 |4.3 Measures of spread |4.2 The mode, median & range |Analysing data |The mode, the median & range |

|120 |4.3 Measures of spread |4.3 Centres for grouped data |Data analysis |Centres for grouped data |

|122 |4.3 Measures of spread |4.5 Standard deviation & distribution |Data analysis |Standard deviation & distribution |

|132 |4,5 Double stem-and-leaf plots |4.6 Stem-and-leaf plots |Representing data |Stem-and-leaf plots |

|135 |4.4 Double box-and-whisker plots |4.4 Box-and-whisker plots |Data analysis |Box-and-whisker plots |

| |Ch5 Applications of trigonometry | | | |

|154 |5.1 Right-angled trigonometry |5.0A Side lengths using any ratio |Trigonometry: Introduction |Side lengths using any ratio |

|154 |5.1 Right-angled trigonometry |5.0B Calculating angles |Trigonometry: Introduction |Calculating angles |

|158 |5.2 Bearings |5.1 What are bearings? |Trigonometry: Minutes & bearings |What are bearings? |

|158 |5.2 Bearings |5.2 Using bearings |Trigonometry: Minutes & bearings |Using bearings |

|163 |5.3 Trigonometry with obtuse angles |5.3 Related angles |Trig beyond right triangles |Related ratios |

|166 |5.4 Sine rule |5.5 Sine rule |Trigonometry beyond right triangles |Sine rule |

|172 |5.5 Area of a triangle |5.4 Area using trig |Trigonometry beyond right triangles |Area using trig |

|175 |5.6 Cosine rule |5.6 Cosine rule |Trigonometry beyond right triangles |Cosine rule |

| |Ch6 Multi-stage events | | | |

|195 |6.1 Tree diagrams |6.1 Theoretical probability |Chance |Theoretical probability |

|195 |6.1 Tree diagrams |6.2 Calculating probability |Probability |Calculating probability |

| |Ch7 Annuities & loan repayments | | | |

|228 |7.1 Future value of an annuity |Go to Ch 1 Lesson 1.5 Loans | | |

| |Ch9 Modelling linear & non-lin. rels. | | | |

|271 |9.1 Linear functions |9.0 Gradient-intercept graphs |Number plane: Straight lines |Gradient-intercept graphs |

|275 |9.2 Intersecting graphs |9.0A Intersecting lines |The number plane |Intersecting lines |

|279 |9.3 Quadratic functions |9.1 Plotting curves |Number plane: Curves |Plotting curves |

|279 |9.3 Quadratic functions |9.2 Parabolas |Number plane: Curves |Parabolas |

|284 |9.4 Cubic, exponential & hyperbolic funct. |9.3 Hyperbolas |Number plane: Curves |Hyperbolas |

|299 |9.7 Modelling |9.4 Graphs with curve |Bivariate data |Graphs with curve |

|TEXTBOOK |LESSON NUMBER & NAME |Original HOTmaths topic/lesson |

|Page |Chapter/sections |IN HOTMATHS MENU |Topic |Lesson |

| |Ch10 Spherical geometry | | | |

|307 |10.1 Arc length of a circle |10.1 Perimeters & arcs |Perimeter & area |Perimeters & arcs |

|324 |10.5 Time differences and local time |10.2 Time zones |Time |Time zones |

|329 |10.6 Time zones |10.2 Time zones |Time |Time zones |

| |Ch11 Applications of probability | | | |

|339 |11.1 Expected outcomes |Go to Ch 6 Lesson 6.1 Theoretical probability | | |

|339 |11.1 Expected outcomes |Go to Ch 6 Lesson 6.2 Calculating probability | | |

| |Ch12 Depreciation | | | |

|363 |12.1 Modelling depreciation |12.1 Depreciation |Buying, borrowing, investing |Depreciation |

|Cambridge HSC General Mathematics | |

|HOTmaths integrated program summary | |

|TEXTBOOK |LESSON NUMBER & NAME |Notes for students |

|Page |Chapter/sections |IN HOTMATHS MENU | |

| |Ch1 Credit and borrowing | | |

|1 |1.1 Flat-rate loans |1.1 Buying on credit | |

|1 |1.1 Flat-rate loans |1.2 Simple interest | |

|1 |1.1 Flat-rate loans |1.5 Loans | |

|8 |1.2 Home loan repayments |1.5 Loans (see above) | |

|14 |1.3 Comparing loans |1.3 Compound interest | |

|14 |1.3 Comparing loans |1.4 Compound interest formula | |

| |Ch2 Further apps of area & volume | | |

|33 |2.1 Area of circles, annuluses and sectors |2.1 Areas of parts of a circle | |

|42 |2.3 Area of composite shapes |2.1A Formula for area of a triangle | |

|52 |2.5 Surface area of cylinders and spheres |2.2 Surface areas of cylinders | |

|52 |2.5 Surface area of cylinders and spheres |2.3 Surface areas of spheres | |

| |Ch3 Algebraic skills & techniques | | |

|71 |3.1 Substitution & evaluation |3.0 Substitution | |

|75 |3.2 Adding & Subtracting like terms |3.1 Add & subtract algebraic fractions | |

|75 |3.2 Adding & Subtracting like terms |3.2 Multiply & divide algebraic fractions | |

|75 |3.2 Adding & Subtracting like terms |3.3 Expanding & simplifying | |

|78 |3.3 Multiplying & dividing of algebraic terms |3.2 Multiply & divide algebraic fractions | |

|78 |3.3 Multiplying & dividing of algebraic terms |3.4 Factorising | |

|78 |3.3 Multiplying & dividing of algebraic terms |3.5 Extending algebraic fraction | |

|84 |3.4 Equations |3.6 Using algebra | |

|84 |3.4 Equations |3.7 Solving linear equations | |

|84 |3.4 Equations |3.8 Equations with brackets | |

|84 |3.4 Equations |3.9 Equations with fractions | |

|84 |3.4 Equations |3.10 Problems & formulas | |

|101 |3.7 Scientific notation |3.11 Scientific notation | |

|TEXTBOOK |LESSON NO./NAME ON HOTMATHS |Notes for students |

|Page |Chapter/sections |Lesson name in menu | |

| |Ch4 Interpreting sets of data | | |

|109 |4.1 Mean |4.1 Exploring the mean | |

|109 |4.1 Mean |4.3 Centres for grouped data | |

|116 |4.2 Median |4.2 The mode, median & range | |

|116 |4.2 Median, |4.3 Centres for grouped data | |

|120 |4.3 Measures of spread |4.2 The mode, median & range | |

|120 |4.3 Measures of spread |4.3 Centres for grouped data | |

|122 |4.3 Measures of spread |4.5 Standard deviation & distribution | |

|132 |4,5 Double stem-and-leaf plots |4.6 Stem-and-leaf plots | |

|135 |4.4 Double box-and-whisker plots |4.4 Box-and-whisker plots | |

| |Ch5 Applications of trigonometry | | |

|154 |5.1 Right-angled trigonometry |5.0A Side lengths using any ratio | |

|154 |5.1 Right-angled trigonometry |5.0B Calculating angles | |

|158 |5.2 Bearings |5.1 What are bearings? | |

|158 |5.2 Bearings |5.2 Using bearings | |

|163 |5.3 Trigonometry with obtuse angles |5.3 Related angles | |

|166 |5.4 Sine rule |5.5 Sine rule | |

|172 |5.5 Area of a triangle |5.4 Area using trig | |

|175 |5.6 Cosine rule |5.6 Cosine rule | |

| |Ch6 Multi-stage events | | |

|195 |6.1 Tree diagrams |6.1 Theoretical probability | |

|195 |6.1 Tree diagrams |6.2 Calculating probability | |

| |Ch7 Annuities & loan repayments | | |

|228 |7.1 Future value of an annuity |Go to Ch 1 Lesson 1.5 Loans | |

| |Ch9 Modelling linear & non-lin. rels. | | |

|271 |9.1 Linear functions |9.0 Gradient-intercept graphs | |

|275 |9.2 Intersecting graphs |9.0A Intersecting lines | |

|279 |9.3 Quadratic functions |9.1 Plotting curves | |

|279 |9.3 Quadratic functions |9.2 Parabolas | |

|284 |9.4 Cubic, exponential & hyperbolic funct. |9.3 Hyperbolas | |

|299 |9.7 Modelling |9.4 Graphs with curve | |

|TEXTBOOK |LESSON NO./NAME ON HOTMATHS |Notes for students |

|Page |Chapter/sections |Lesson name in menu | |

| |Ch10 Spherical geometry | | |

|307 |10.1 Arc length of a circle |10.1 Perimeters & arcs | |

|324 |10.5 Time differences and local time |10.2 Time zones | |

|329 |10.6 Time zones |10.2 Time zones | |

| |Ch11 Applications of probability | | |

|339 |11.1 Expected outcomes |Go to Ch 6 Lesson 6.1 Theoretical probability | |

|339 |11.1 Expected outcomes |Go to Ch 6 Lesson 6.2 Calculating probability | |

| |Ch12 Depreciation | | |

|363 |12.1 Modelling depreciation |12.1 Depreciation | |

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