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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 individual computers at home or in class:- Revise prior knowledge.
- Do a HOTmaths lesson as homework to prepare for a lesson using the textbook.
- Test prior knowledge with a TOPIC QUIZ or a test from the TEST GENERATOR (new in 2011) as homework or classwork.
- Do SCORCHER quizzes
- Try the alternative approach of an interactive WIDGET or WALKTHROUGH when having difficulty grasping a concept or learning a skill.
- Use theDICTIONARY to test and reinforce understanding of mathematical terminology and use the links provided to see mathematical terms in use.
- Display an interactive WIDGET in class to illustrate a concept.
- After going through a widget, print out multiple copies of an accompanying HOTsheetto work through
- Display an interactive WALKTHROUGH example for the class to suggest answers for the embedded questions.
- Use the TEST GENERATOR (new in 2011) to print out a test of prior knowledge to do on paper
- Display and discuss the HOTmaths lesson notes.
- Set foundation-level students to work as a group revisiting previous work (including previous years) while the rest of the class tackles 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:
The exact design and appearance of the menus and lessons may change.
Check periodically for updates to this program at:
or
2How 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.
1In the textbook, note the HOTmaths icon indicating there 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 /2Log on to HOTmaths and choose Cambridge HSC General Maths
and the chapter (topic).
/
3Choose the HOTmaths lesson number
indicated by the icon. /
4The matching HOTmaths lesson will open under the textbook headings:
Cambridge University Press General Maths / HOTmaths Integrated program Issue: 11 February 2011
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Notes
1HOTmaths 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.
2HOTmaths 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.
3Frequent 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 University Press General Maths / HOTmaths Integrated program Issue: 11 February 2011
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Cambridge HSC General MathematicsHOTmaths integrated program summary / The following table summarises the location of linked HOTmaths content in the textbook, the name of the lesson to use in the 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
Cambridge University Press General Maths / HOTmaths Integrated program Issue: 11 February 2011