Maths Quest 10+10A for the Australian Curriculum

Maths Quest 10+10A Australian Curriculum Work Program

Chapter 1 Indices

Content strand: Number and algebra

Sub-strand: Patterns and algebra

Australian Curriculum Content Strands

• Simplify algebraic products and quotients using index laws. – understanding that the use of index notation is an efficient way of representing numbers and symbols and has many applications, particularly in

science – connecting different strategies for simplifying expressions with indices to illustrate the meaning of negative indices, expanding and simplifying results – moving fluently between representations of numeric and algebraic terms with negative indices, and applying understanding of negative indices to

calculations – applying knowledge of index laws to algebraic terms, and simplifying algebraic expressions using both positive and negative integral indices

Section

Chapter opening • What do you know?

(page 1)

Hungry brain activity Surds and fractional indices doc-5167

Readiness Test Chapter 1

Are you ready? (page 2) • SkillSHEET 1.1 doc-5168 • SkillSHEET 1.2 doc-5169 • SkillSHEET 1.3 doc-5170 • SkillSHEET 1.4 doc-5171 • SkillSHEET 1.5 doc-5172 • SkillSHEET 1.6 doc-5173

• SkillSHEET 1.7 doc-5174 • SkillSHEET 1.8 doc-5175

1A Review of Index laws (page 3) Exercise 1A (page 5) Reflection (page 7)

1-A-1 Reviewing index operations doc-4948 (page 5) 1-A-2 Practising the index laws doc-4949 (page 5) 1-A-3 Applying the index laws doc-4950 (page 5)

IP Activities – answers Homework Book answers

Progress Test 1A Homework

1B Negative indices (page 7) Exercise 1B (page 10) Reflection (page 12)

1-B-1 Negative indices doc-4951 (page 10) 1-B-2 Harder negative indices doc-4952 (page 10) 1-B-3 Tricky negative indices doc-4953 (page 10) • Interactivity

Negative indices int-2777


Progress Test 1B Homework

1C Fractional indices (page 12) Exercise 1C (page 14) Reflection (page 16)

1-C-1 Fractional indices doc-4954 (page 14) 1- C-2 Harder fractional indices doc-4955 (page 14) 1- C-3 Tricky fractional indices doc-4956 (page 14) • SkillSHEET 1.9 doc-5176 • SkillSHEET 1.10 doc-5177 • SkillSHEET 1.11doc-5178 • SkillSHEET 1.12 doc-5179 • WorkSHEET 1.1 doc-5180

IP Activities – answers Homework Book answers WorkSHEET 1.1 Answers

Progress Test 1C Homework

1D Combining index laws (page 17) Exercise 1D (page 20)

1-D-1 Review of indices doc-4957 (page 20) 1-D-2 Indices practice doc-4958 (page 20) 1-D-3 Tricky indices doc-4959 (page 20) • WorkSHEET 1.2 doc-5181


Progress Test 1D Homework

Reflection (page 22)

Closing pages • Summary (page 23) • Mapping your

understanding (page 23) • Chapter review (page 24)

Interactivities • Test yourself int-2828 • Word search int-2826 • Crossword int-2827

Chapter 1 Test A & solutions Chapter 1 Test B & solutions

Achievement Practice test Chapter 1 Achievement Test Chapter 1 (Teacher Set)

Chapter 2 Linear algebra




• Apply the four operations to simple algebraic fractions with numerical denominators – solving a wide range of linear equations, including those involving one or two simple algebraic fractions, and checking solutions by substitution

• Solve linear equations involving simple algebraic fractions – solving a wide range of linear equations, including those involving one or two simple algebraic fractions, and checking solutions by substitution – representing word problems, including those involving fractions, as equations and solving them to answer the question

Section


(page 27)

Hungry brain activity Fraction frenzy doc-5182



2A Substitution (page 29) Exercise 2A (page 31)

2-A-1 Substitution doc-4960 (page 31) 2-A-2 Harder substitution doc-4961 (page 31) 2-A-3 Tricky substitution doc-4962 (page 31)


Progress Test 2A

Reflection (page 33) • SkillSHEET 2.7 doc-5189 Homework

2B Adding and subtracting algebraic fractions (page 33) Exercise 2B (page 36) Reflection (page 37)

2-B-1 Introducing algebraic fractions doc-4963 (page 36) 2-B-2 Working with algebraic fractions doc-4864 (page 36) 2-B-3 Advanced algebraic fractions doc-4965 (page 36) • SkillSHEET 2.8 doc-5190



2C Multiplying and dividing algebraic fractions (page 37) Exercise 2C (page 39) Reflection (page 40)

2-C-1 Learning operations with algebraic fractions doc-4966 (page 39) 2-C-2 Operations with algebraic fractions doc-4967 (page 39) 2-C-3 Advanced operations with algebraic fractions doc-4968 (page 39) • SkillSHEET 2.9 doc-5191 • SkillSHEET 2.10 doc-5192 • WorkSHEET 2.1 doc-5193



2D Solving linear equations (page 40) Exercise 2D (page 43) Reflection (page 44)

2-D-1 Simple puzzling equations doc-4969 (page 43) 2-D-2 Puzzling equations doc-4970 (page 43) 2-D-3 Advanced puzzling equations doc-4971 (page 43)



2E Solving equations with algebraic fractions and multiple brackets (page 45) Exercise 2E (page 48)

2-E-1 Algebraic equations with fractions doc-4972 (page 48) 2-E-2 Harder algebraic equations with fractions doc-4973 (page 48) 2-E-3 Tricky algebraic equations with fractions doc-4974 (page 48)


Progress Test 2E Homework


• WorkSHEET 2.2 doc-5194 • Interactivity

Solving equations int-2778

WorkSHEET 2.2 Answers

Closing pages • Summary (page 50) • Mapping your

understanding (page 51) • Chapter review (page 52)




Chapter 3 Coordinate geometry


Sub-strand: Linear and non-linear relationships


• Solve problems involving linear equations, including those derived from formulas – solving equations that are the result of substitution into common formulas from mathematics and elsewhere, including those that involve

rearrangement – checking the solution by substitution into the equation

• Solve problems involving parallel and perpendicular lines – Developing fluency with the geometric calculations which connect the graphical and analytical representations of parallel and perpendicular lines,

using geometric software to carry out investigations with parallel and perpendicular lines

Section


(page 55)

Hungry brain activity Cartesian island doc-5195



3A Sketching linear graphs (page 57)

3-A-1 Sketching linear graphs doc-4975 (page 62)


Exercise 3A (page 62) Reflection (page 63)

3-A-2 Graphs of linear equations doc-4976 (page 62) 3-A-3 More graphs of linear equations doc-4977 (page 62) • SkillSHEET 3.7 doc-5202 • SkillSHEET 3.5 doc-5200 • SkillSHEET 3.8 doc-5203


3B Determining linear equations (page 64) Exercise 3B (page 67) Reflection (page 68)

3-B-1 Determining linear equations doc-4978 (page 67) 3-B-2 Linear equations doc-4979 (page 67) 3-B-3 More complex linear equations doc-4980 (page 67) • SkillSHEET 3.1 doc-5196 • SkillSHEET 3.9 doc-5204 • WorkSHEET 3.1 doc-5205



3C The distance between two points on a straight line (page 68) Exercise 3C (page 70) Reflection (page 71)

3-C-1 Finding the distance between two points on a straight line doc-4981 (page 70) 3-C-2 Calculations of distance between two points doc-4982 (page 70) 3-C-3 Applications of distance between two points doc-4983 (page 70) • Spreadsheet 021

Distance between two points doc-5206



3D The midpoint of a line segment (page 71) Exercise 3D (page 73)

3-D-1 Finding the midpoint of a line segment doc-4984 (page 73) 3-D-2 Calculations − Midpoint of a segment


Progress Test 3D


doc-4985 (page 73) 3-D-3 Applications − Midpoint of a segment doc-4986 (page 73) • Spreadsheet 075

Midpoint of a segment doc-5207 • WorkSHEET 3.2 doc-5208


Homework

3E Parallel and perpendicular lines (page 74) Exercise 3E (page 79) Reflection (page 82)

3-E-1 Parallel and perpendicular lines doc-4987 (page 79) 3 E-2 More difficult parallel and perpendicular lines doc-4988 (page 79) 3-E-3 Complex parallel and perpendicular lines doc-4989 (page 79) • Spreadsheet 085

Perpendicular checker doc-5209 • Spreadsheet 029

Equation of a straight line doc-5210 • Interactivity

Parallel and perpendicular lines int-2779



Closing pages • Summary (page 83) • Mapping your understanding

(page 84) • Chapter review (page 85)



Achievement Practice test Chapter 3 Achievement Test Chapter 3

(Teacher Set)

Chapter 4 Simultaneous linear equations and inequations




• Solve linear inequalities and graph their solutions on a number line – representing word problems with simple linear inequalities and solving them to answer questions

• Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology – using simple algebraic techniques to solve pairs of linear simultaneous equations – generalising pairs of equations from word problems and choosing an appropriate strategy for solving them simultaneously

Section


(page 89)

Hungry brain activity How are you feeling today? doc-5211


Are you ready? (page 90) • SkillSHEET 4.1 doc-5212 • SkillSHEET 4.2 doc-5213 • SkillSHEET 4.3 doc-5214 • SkillSHEET 4.4 doc-5215 • SkillSHEET 4.5 doc-5216 • SkillSHEET 4.6 doc-5217 • SkillSHEET 4.7 doc-5218

4A Graphical solution of simultaneous linear equations

4-A-1 Investigating graphs of simultaneous equations doc-4990 (page 94)


(page 91) Exercise 4A (page 94) Reflection (page 96)

4-A-2 Graphing simultaneous equations doc-4991 (page 94) 4-A-3 Further graphing of simultaneous equations doc-4992 (page 95) • SkillSHEET 4.6 doc- 5217


4B Solving simultaneous linear equations using substitution (page 96) Exercise 4B (page 98) Reflection (page 99)

4-B-1 Learning substitution doc-4993 (page 98) 4-B-2 Practising substitution doc-4994 (page 98) 4-B-3 Tricky substitution doc-4995 (page 98)



4C Solving simultaneous linear equations using elimination (page 99) Exercise 4C (page 101) Reflection (page 103)

4-C-1 Elimination practice doc-4996 (page 101) 4-C-2 Let's eliminate doc-4997 (page 102) 4-C-3 More elimination doc-4998 (page 103) • WorkSHEET 4.1 doc-5220 • Interactivity

Simultaneous linear equations int-2780



4D Problem solving using simultaneous linear equations (page 103) Exercise 4D (page 105) Reflection (page 106)

4-D-1 Problem solving doc-4999 (page 105) 4-D-2 Harder problem solving doc-5000 (page 105) 4-D-3 Tricky problem solving doc-5001 (page 105) • WorkSHEET 4.2 doc-5221



4E Solving linear inequations (page 106) Exercise 4E (page 108) Reflection (page 110)

4-E-1 Puzzling inequations 1 doc-5002 (page 108) 4-E-2 Puzzling inequations 2 doc-5003 (page 108) 4-E-3 Puzzling inequations 3 doc-5004 (page 109) • SkillSHEET 4.7 doc-5218 • SkillSHEET 4.8 doc-5219



4F Sketching linear inequations (page 110) Exercise 4F (page 113) Reflection (page 116)

4-F-1 Understanding linear inequations doc-5005 (page 113) 4-F-2 Graphing linear inequations doc-5006 (page 114) 4-F-3 Interpreting linear inequation graphs doc-5007 (page 114)


Progress Test 4F Homework

4G Solving simultaneous linear inequations (page 116) Exercise 4G (page 118) Reflection (page 122)

4-G-1 Introducing simultaneous linear inequations doc-5008 (page 118) 4-G-2 Practising simultaneous linear inequations doc-5009 (page 118) 4-G-3 Further simultaneous linear inequations doc-5010 (page 118) • WorkSHEET 4.3 doc-5222


Progress Test 4G Homework






Chapter 5 Trigonometry

Content strand: Measurement and geometry

Sub-strand: Pythagoras and trigonometry


• Solve right-angled triangle problems including those involving direction and angles of elevation and depression – applying Pythagoras’s Theorem and trigonometry to problems in surveying and design

For 10A

• Apply Pythagoras’ theorem and trigonometry to solving three-dimensional problems in right-angled triangles – investigating the applications of Pythagoras’s theorem in authentic problems

Section


(page 131)

Hungry brain activity Exploring triangles doc-5223


Are you ready? (page 132) • SkillSHEET 5.1 doc-5224 • SkillSHEET 5.2 doc-5225 • SkillSHEET 5.3 doc-5226 • SkillSHEET 5.5 doc-5227 • SkillSHEET 5.6 doc-5228

5A Pythagoras’ theorem (page 133)

5-A-1 Review of Pythagoras' theorem doc-5011 (page 137) 5-A-2 Practising Pythagoras' theorem



doc-5012 (page 137) 5-A-3 More of Pythagoras' theorem doc-5013 (page 137) • SkillSHEET 5.1 doc-5224


5B Pythagoras’ theorem in three dimensions (page 140) Exercise 5B (page 143) Reflection (page 145)

5-B -1 Pythagoras in 3-dimensions doc-5014 (page 143) 5-B-2 Pythagoras in 3-D figures doc-5015 (page 143) 5-B-3 Investigating triangles in 3-D figures doc-5016 (page 143) • SkillSHEET 5.4 doc-5229 • WorkSHEET 5.1 doc-5230



5C Trigonometric ratios (page 145) Exercise 5C (page 149) Reflection (page 151)

5-C-1 Review of trigonometry doc-5017 (page 149) 5-C-2 Using trigonometry doc-5018 (page 149) 5-C-3 Applying trigonometry doc-5019 (page 149) • SkillSHEET 5.3 doc-5226 • SkillSHEET 5.7 doc-5231



5D Using trigonometry to calculate side lengths (page 151) Exercise 5D (page 154) Reflection (page 155)

5-D-1 Calculating side lengths using trigonometry doc-5020 (page 154) 5-D-2 Applying trigonometry to simple figures doc-5021 (page 154) 5-D-3 Practical applications of trigonometry doc-5022 (page 154)



• Interactivity

Using trigonometry int-1146

5E Using trigonometry to calculate angle size (page 156) Exercise 5E (page 158) Reflection (page 160)

5-E-1 Review of angle calculations doc-5023 (page 158) 5-E-2 Calculating angles using trigonometry doc-5024 (page 158) 5-E-3 Applying trigonometry to angle calculations doc-5025 (page 159) • SkillSHEET 5.8 doc-5232 • WorkSHEET 5.2 doc-5233



5F Angles of elevation and depression (page 161) Exercise 5F (page 163) Reflection (page 165)

5-F-1 Identifying elevation and depression doc-5026 (page 163) 5-F-2 Calculating elevation and depression doc-5027 (page 163) 5-F-3 Applications of elevation and depression doc-5028 (page 163) • SkillSHEET 5.6 doc-5228 • WorkSHEET 5.3 doc-5234



5G Bearings and compass directions (page165 ) Exercise 5G (page 169) Reflection (page 171)

5-G-1 Bearings doc-5029 (page 170) 5-G-2 Calculations involving bearings doc-5030 (page 170) 5-G-3 Applications involving bearings doc-5031 (page 170)



5H Applications (page 172)

5-H-1 Trigonometry applications 1 doc-5032 (page 173) 5-H-2 Trigonometry applications 2


Exercise 5H (page 173) Reflection (page 176)

doc-5033 (page 173) 5-H-3 Trigonometry applications 3 doc-5034 (page 173) • Interactivity

Applying trigonometry to drafting problems int-2781

Progress Test 5H Homework






Chapter 6 Surface area and volume


Sub-strand: Using units of measurement


• Solve problems involving surface area and volume for a range of prisms, cylinders and composite solids – building on understanding of surface areas and volumes of prisms and cylinders, to include pyramids, cones and spheres

For 10A

• Solve problems involving surface area and volume of right pyramids, right cones, spheres and related composite solids – using formulas to solve problems – using authentic situations to apply knowledge and understanding of surface area and volume

Section


(page 183)

Hungry brain activity The Soma cube doc-5235



6A Area (page 185)

6-A-1 Review of area doc-5035 (page 189)



6-A-2 Area problems doc-5036 (page 189) 6-A-3 Tricky area problems doc-5037 (page 189) • SkillSHEET 6.1 doc-5236 • SkillSHEET 6.2 doc-5237 • eLesson

Heron’s formula eles-0177 • WorkSHEET 6.1 doc-5241



6B Total surface area (page 193) Exercise 6B (page 199) Reflection (page 202)

6-B-1 Introducing surface area doc-5038 (page 199) 6-B-2 Surface area problems doc-5039 (page 199) 6-B-3 Tricky surface area problems doc-5040 (page 199) • SkillSHEET 6.3 doc-5238 • Interactivity

TSA-sphere int-2782 • WorkSHEET 6.2 doc-5242



6C Volume (page 203) Exercise 6C (page 208) Reflection (page 212)

6-C-1 Review of volume and capacity doc-5041 (page 208) 6-C-2 Volume and capacity problems doc-5042 (page 208) 6-C-3 Tricky volume and capacity problems doc-5043 (page 208)



• SkillSHEET 6.4 doc-5239 • SkillSHEET 6.5 doc-5240 • WorkSHEET 6.3 doc-6753







Chapter 7 Quadratic expressions




• Factorise algebraic expressions by taking out a common algebraic factor. – factorising a range of expressions by taking out a common factor, including those where the common factor is an algebraic expression.

• Expand binomial products and factorise monic quadratic expressions using a variety of strategies – identifying and using common factors, including binomial terms, to factorise algebraic expressions using the technique of grouping in pairs to

factorise algebraic expressions with four terms – using expansion patterns for the special binomial products (a + b)(a − b) and (a ± b)2 inversely to factorise quadratics – using the area model inversely to factorise quadratic expressions of the form ax2 + bx + c, where a= ±1 – exploring the method of completing the square to factorise quadratic expressions and solve quadratic equations

• Substitute values into formulas to determine an unknown – representing word problems with simple linear equations and solving them to answer questions

Section


(page 219)

Hungry brain activity Modelling plant growth doc-5243



• SkillSHEET 7.8 doc-5249

7A Expanding algebraic expressions (page 221) Exercise 7A (page 225) Reflection (page 227)

7-A-1 Review of expansion doc-5044 (page 225) 7-A-2 Expanding algebraic expressions doc-5045 (page 225) 7-A-3 Expanding more complex algebraic expressions doc-5046 (page 225) • SkillSHEET 7.1 doc-5244 • SkillSHEET 7.2 doc-5245



7B Factorising expressions with three terms (page 227) Exercise 7B (page 229) Reflection (page231 )

7-B-1 Introducing quadratic factorisation doc-5050 (page 229) 7-B-2 Practising quadratic factorisation doc-5051 (page 229) 7-B-3 Tricky quadratic factorisation doc-5052 (page 229) • SkillSHEET 7.5 doc-5250 • WorkSHEET 7.1 doc-5251



7C Factorising expressions with two or four terms (page 231) Exercise 7C (page 234) Reflection (page 236)

7-C-1 Factorising expressions with two or four terms doc-5047 (page 234) 7-C-2 More factorising expressions with two or four terms doc-5048 (page 234) 7-C-3 Advanced factorising expressions with two or four terms doc-5049 (page 234) • SkillSHEET 7.3 doc-5246 • SkillSHEET 7.4 doc-5247



7D Factorising by completing the square (page 236) Exercise 7D (page 239) Reflection (page 240)

7-D-1 Introducing completing the square doc-5053 (page 239) 7-D-2 Practising completing the square doc-5054 (page 239) 7-D-3 Completing the square doc-5055 (page 239) • Interactivity

Completing the square int-2783



7E Mixed factorisation (page 240) Exercise 7E (page 240) Reflection (page 241)

7-E-1 Mixed factorisation doc-5056 (page 240) 7-E-2 Harder mixed factorisation doc-5057 (page 240) 7-E-3 Advanced mixed factorisation doc-5058 (page 240) • SkillSHEET 7.6 doc-5252 • SkillSHEET 7.7 doc-5248 • WorkSHEET 7.2 doc-5254








Chapter 8 Quadratic equations




• Solve simple quadratic equations using a range of strategies – developing an understanding that many relationships are non-linear and that these can also be represented graphically and algebraically – identifying the connection between algebraic and graphical solutions of equations (for example understanding that the x-intercepts are the solutions of

f(x) = 0) exploring the method of completing the square to factorise quadratic expressions and solve quadratic equations

For 10A

• Factorise monic and non-monic quadratic expressions and solve a wide range of quadratic equations derived from a variety of contexts – developing fluency with algebraic techniques associated with quadratics to facilitate describing relationships and solving problems

Section

Chapter opening What do you know?

(page 247)

Hungry brain activity The Null Factor Law doc-5255



8A Solving quadratic equations (page 249)

8-A-1 Solving simple quadratics doc-5059 (page 253)



8-A-2 Solving quadratic equations doc-5060 (page 253) 8-A-3 Solving more complex quadratics doc-5061 (page 253) • WorkSHEET 8.1 doc-5261



8B The quadratic formula (page 255) Exercise 8B (page 257) Reflection (page 258)

8-B-1 Introducing the quadratic formula doc-5062 (page 257) 8-B-2 Practice using the quadratic formula doc-5063 (page 257) 8-B-3 Using the quadratic formula doc-5064 (page 257) • SkillSHEET 8.6 doc-5262 • SkillSHEET 8.7 doc-5263



8C Solving quadratic equations by inspecting graphs (page 258) Exercise 8C (page 261) Reflection (page 263)

8-C-1 Finding solutions to quadratic equations by inspecting graphs doc-5065 (page 261) 8-C-2 Solving quadratic equations by inspecting graphs doc-5066 (page 261) 8-C-3 Harder solutions to quadratic equations by inspecting graphs doc-5067 (page 261)



8D Finding solutions to quadratic equations by interpolation and using the discriminant (page 263) Exercise 8D (page 267) Reflection (page 268)

8-D-1 Finding solutions to quadratic equations by interpolation doc-5068 (page 267) 8-D-2 Harder solutions to quadratic equations by interpolation doc-5069 (page 267) 8-D-3 Difficult solutions to quadratic equations by interpolation doc-5070 (page 267)



• Interactivity

Solving by interpolation int-1147 • WorkSHEET 8.2 doc-6264


8E Solving a quadratic equation and a linear equation simultaneously (page 269) Exercise 8E (page 272) Reflection (page 273)

8-E-1 Introduction to quadratic and linear solutions doc-5071 (page 272) 8-E-2 Practising quadratic and linear solutions doc-5072 (page 272) 8-E-3 Tricky quadratic and linear solutions doc-5073 (page 272) • Interactivity

Simultaneous quadratic equations int-2784



Closing pages Summary (page 274) Mapping your understanding

(page 275) Chapter review (page 276)




Chapter 9 Functions




• Explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials using digital technology as appropriate – identifying, matching and describing algebraic and graphical representations of parabolas, rectangular hyperbolas, exponential functions and circles,

including those that have undergone a single transformation – sketching the graphical representations of parabolas, exponential functions and circles

Section


(page 279)

Hungry brain activity Cartoon cartesians doc-5265



9A Plotting parabolas (page 281) Exercise 9A (page 284)

9-A-1 Review of plotting parabolas doc-5074 (page 284) 9-A-2 Plotting parabolas doc-5075 (page 284)


Progress Test 9A

Reflection (page 286) 9-A-3 Trends in plotted parabolas doc-5076 (page 285) • SkillSHEET 9.1 doc-5266 • SkillSHEET 9.2 doc-5267

Homework

9B Sketching parabolas using the basic graph of y = x2 (page 287) Exercise 9B (page 291) Reflection (page 292)

9-B-1 Review of sketching parabolas doc-5077 (page 291) 9-B-2 Sketching basic parabolas doc-5078 (page 291) 9-B-3 Trends in sketching basic parabolas doc-5079 (page 291) • Interactivities

Dilation of y = x2 int-1148 Vertical translation of y = x2 + c int-1192 Horizontal translation of y = (x − h)2 int-1193 • WorkSHEET 9.1 doc-5272



9C Sketching parabolas in turning point form (page 292) Exercise 9C (page 296) Reflection (page 298)

9-C-1 Reviewing turning point form doc-5080 (page 296) 9-C-2 Turning point form doc-5081 (page 296) 9-C-3 Interpreting turning point from trends doc-5082 (page 296)



9D Sketching parabolas of the form y = ax2 + bx + c (page 298)

9-D-1 Understanding parabola sketching doc-5083 (page 302) 9-D-2 Parabola sketching


Exercise 9D (page 302) Reflection (page 306)

doc-5084 (page 302) 9-D-3 Sketching tricky parabolas doc-5085 (page 302) • SkillSHEET 9.3 doc-5268 • SkillSHEET 9.4 doc-5269 • SkillSHEET 9.5 doc-5270 • SkillSHEET 9.6 doc-5271 • Interactivity

Sketching parabolas int-2785 • WorkSHEET 9.2 doc-5273



9E Exponential functions and their graphs (page 306) Exercise 9E (page 309) Reflection (page 312)

9-E-1 Exploring exponential graphs doc-5086 (page 309) 9-E-2 Features of exponential graphs doc-5087 (page 309) 9-E-3 Tricky exponential graphs doc-5088 (page 309) • SkillSHEET 9.7 doc-5274 • Interactivity

Exponential graphs int-1149



9F The hyperbola (page 312) Exercise 9F (page 314) Reflection (page 315)

9-F-1 Hyperbola graphs doc-5089 (page 314) 9-F-2 Exploring the hyperbola doc-5090 (page 314) 9-F-3 More hyperbola graphs doc-5091 (page 314)



9G The circle (page 315)

9-G-1 Circle graphs doc-5092 (page 317)


Exercise 9G (page 317) Reflection (page 318)

9-G-2 Exploring the circle doc-5093 (page 317) 9-G-3 More circle graphs doc-5094 (page 317)







Chapter 10 Deductive geometry


Sub-strand: Geometric reasoning


• Formulate proofs involving congruent triangles and angle properties – proving that a quadrilateral with equal-length diagonals bisecting at right angles is a square

• Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes – presenting formal geometric arguments to develop skills in mathematical reasoning and presenting reasoned arguments (proofs) – using mathematical language and notation, based on congruence and similarity – applying an understanding of relationships to deduce properties of geometric figures (for example the base angles of an isosceles triangle are equal) – distinguishing between a practical demonstration and a proof (for example demonstrating triangles are congruent by placing them on top of each other,

as compared to using congruence tests to establish that triangles are congruent)

Section


(page 325)

Hungry brain activity Cubism doc-5275


Are you ready? (page 326) • SkillSHEET 10.1 doc-5276 • SkillSHEET 10.2 doc-5277 • SkillSHEET 10.3 doc-5278 • SkillSHEET 10.4 doc-5279

10A Congruence review (page 327)

10-A-1 Review of congruent shapes doc-5095 (page 329)



10-A-2 Practice with congruent figures doc-5096 (page 329) 10-A-3 Tricky congruent figures doc-5097 (page 330) • SkillSHEET 10.1 doc-5276 • SkillSHEET 10.2 doc-5277 • SkillSHEET 10.5 doc-5280


10B Similarity review (page 332) Exercise 10B (page 335) Reflection (page 336)

10-B-1 Review of similar shapes doc-5098 (page 335) 10-B-2 Similarity practice doc-5099 (page 335) 10-B-3 Tricky similarity problems doc-5100 (page 335) • SkillSHEET 10.3 doc-5278 • SkillSHEET 10.6 doc-5281 • WorkSHEET 10.1 doc-5282



10C Congruence and proof (page 336) Exercise 10C (page 338) Reflection (page 339)

10-C-1 Congruent triangles doc-5101 (page 338) 10-C-2 Matching congruent triangles doc-5102 (page 338) 10-C-3 Harder congruent triangles doc-5103 (page 338)



10D Quadrilaterals: definitions and properties (page 340) Exercise 10D (page 341) Reflection (page 343)

10-D-1 Quadrilaterals doc-5104 (page 341) 10-D-2 Harder quadrilaterals doc-5105 (page 342) 10-D-3 Tricky quadrilaterals doc-5106 (page 342)



• SkillSHEET 10.4 doc-5279 • Interactivity

Quadrilateral definitions int-2786 • WorkSHEET 10.2 doc-5283


10E Quadrilaterals and proof (page 344) Exercise 10E (page 345) Reflection (page 346)

10-E-1 Quadrilateral proofs doc-5107 (page 345) 10-E-2 Harder quadrilateral proofs doc-5108 (page 345) 10-E-3 Tricky quadrilateral proofs doc-5109 (page 345) • WorkSHEET 10.3 doc-5284








Chapter 11 Problem solving I

Pages 355 to 378

130 problems of varying levels of difficulty

This chapter expands on the strategies introduced for problem solving in the previous three texts (Maths Quest 7, 8 and 9 for the Australian curriculum).

As mentioned in those previous texts, the main processes which can be used to solve problems are:

• Read the question at least twice, underlining all the important facts.

• Identify the solution required.

• Solve the problem using an appropriate strategy.

• Communicate the solution using appropriate language and mathematical terms.

• Support the solution with mathematical reasoning.

• Reflect on the solution. Does it answer the question? Does it make sense? Could a better method have been used?

Strategies which can be used to solve the problem include:

• Create a table.

• Draw a diagram.

• Look for a pattern.

• Work backwards from the answer.

• Eliminate possible solutions which do not match the given information.

• Look at a simplified version of the same problem.

• Guess and check.

• Use technology as this can greatly reduce calculations with unwieldy numbers.

• Simulate the problem.

The problems in this chapter can be classified into 3 levels: Level 1, Level 2 and Level 3. It must be recognised that the classification of these problems is a subjective matter, and the expertise and exposure of students to problem solving greatly influences their ability to solve these problems.

Level 1 Level 2 Level 3

These include questions: 5, 6, 9, 10, 13, 18, 22, 38, 49, 52, 57, 58, 61, 63, 70, 72, 78, 80, 83, 84, 88, 89, 92, 96, 106, 110, 112, 114, 115, 119, 124, 128

These include questions: 1, 2, 4, 8, 12, 14, 15, 16, 17, 19, 24, 25, 27, 29, 30, 32, 33, 34, 35, 36, 37, 40, 41, 43, 45, 46, 47, 48, 50, 51, 53, 56, 59, 60, 62, 64, 65, 66, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 81, 82, 85, 86, 94, 95, 97, 99, 101, 102, 104, 107, 108, 113, 116, 118, 120, 121, 125, 126, 129

These include questions: 3, 7, 11, 20, 21, 23, 26, 28, 31, 39, 42, 44, 54, 55, 87, 90, 91, 93, 98, 100, 103, 105, 109, 111, 117, 122, 123, 127, 130

Chapter 12 Probability

Content strand: Statistics and probability

Sub-strand: Chance


• Describe the results of two- and three-step chance experiments, both with and without replacements, assign probabilities to outcomes and determine probabilities of events. Investigate the concept of independence – recognising and identifying that some sets of chance events are dependent on a previous result and others are not, that this distinction is important

when calculating probabilities, and that events are independent if P(A) x P(B) = P(A and B) – distinguishing that event A is mathematically dependent on event B if the occurrence of event B affects the chance of the occurrence of event A (for

example, selecting a ball from a bag where one ball has already been taken and not replaced) • Use the language of ‘if ....then’, ‘given’, ‘of’, ‘knowing that’ to investigate conditional statements and identify common mistakes in interpreting such

language – evaluating media reports that refer to data from a range of contexts, where the evaluation allows students to demonstrate their statistical literacy

Section


(page 379)

Hungry brain activity Independent and mutually exclusive events doc-5285



12A Review of probability (page 381)

12-A-1 Review of probability doc-5110 (page 392)



12-A-2 General probability problems doc-5111 (page 392) 12-A-3 Tricky probability problems doc-5112 (page 392) • SkillSHEET 12.1 doc-5286 • SkillSHEET 12.2 doc-5287 • SkillSHEET 12.6 doc-5291 • SkillSHEET 12.7 doc-5292 • SkillSHEET 12.8 doc-5293 • Interactivity

Random number generator int-0089


12B Complementary and mutually exclusive events (page 396) Exercise 12B (page 400) Reflection (page 403)

12-B-1 Complementary and mutually exclusive events doc-5113 (page 401) 12-B-2 Harder complementary and mutually exclusive events doc-5114 (page 401) 12-B-3 Tricky complementary and mutually exclusive events doc-5115 (page 401) • SkillSHEET 12.3 doc-5288 • SkillSHEET 12.4 doc-5289 • SkillSHEET 12.9 doc-5294 • WorkSHEET 12.1 doc-5295



12C Two-way tables and tree diagrams (page 403) Exercise 12C (page 410)

12-C-1 Review of two-way tables and tree diagrams doc-5116 (page 410) 12-C-2 Practice with two-way tables and tree diagrams doc-5117 (page 410) 12-C-3 Tricky two-way tables and tree


Progress Test 12C


diagrams doc-5118 (page 410) • SkillSHEET 12.5 doc-5290 • eLesson

Games at Wimbledon eles-1032 • WorkSHEET 12.2 doc-5296


Homework

12D Independent and dependent events (page 413) Exercise 12D (page 415) Reflection (page 417)

12-D-1 Simple independent and dependent events doc-5119 (page 415) 12-D-2 Independent and dependent events doc-5120 (page 415) 12-D-3 Tricky independent and dependent events doc-5121 (page 415) • Interactivities

A pack of cards int-2787 Random numbers int-0085



12E Conditional probability (page 417) Exercise 12E (page 419) Reflection (page 420)

12-E-1 Introducing conditional probability doc-5122 (page 419) 12-E-2 Practice with conditional probability doc-5123 (page 419) 12-E-3 Tricky conditional probability problems doc-5124 (page 419)



12F Subjective probability (page 420) Exercise 12F (page 421) Reflection (page 422)

12-F-1 Subjective probability doc-5125 (page 421) 12-F-2 Harder subjective probability doc-5126 (page 421) 12-F-3 In-depth subjective probability doc-5127 (page 421)



• WorkSHEET 12.3 doc-5297 WorkSHEET 12.3 Answers






Chapter 13 Univariate data


Sub-strand: Data representation and interpretation


• Determine quartiles and interquartile range – finding the five-number summary (minimum and maximum values, median and upper and lower quartiles) and using its graphical representation, the

box plot, as tools for both numerically and visually comparing the centre and spread of data sets • Construct and interpret box plots and use them to compare data sets

– understanding that box plots are an efficient and common way of representing and summarising data and can facilitate comparisons between data sets – using parallel box plots to compare data about the distribution of Aboriginal and Torres Strait Islander people by age with that of the Australian

population as a whole • Compare shapes of box plots to corresponding histograms and dot plots

– Investigating data in different ways to make comparisons and draw conclusions

For 10A

• Calculate and interpret the mean and standard deviation of data and use these to compare data sets – evaluating the appropriateness of sampling methods and sample size in reports where statements about a population are based on a sample

Section


(page 429)

Hungry brain activity Displaying distributions doc5298-


Are you ready? (page 430) • SkillSHEET 13.1 doc-5299 • SkillSHEET 13.2 doc-5300

• SkillSHEET 13.3 doc-5301 • SkillSHEET 13.4 doc-5302 • SkillSHEET 13.5 doc-5303 • SkillSHEET 13.6 doc-5304

13A Measures of central tendency (page 431) Exercise 13A (page 435) Reflection (page 439)

13-A-1 Mean, median and mode doc-5128 (page 435) 13-A-2 Practice with mean, median and mode doc-5129 (page 435) 13-A-3 Mean, median and mode in depth doc-5130 (page 435) • SkillSHEET 13.1 doc-5299 • SkillSHEET 13.2 doc-5300 • SkillSHEET 13.3 doc-5301 • SkillSHEET 13.4 doc-5302 • SkillSHEET 13.5 doc-5303 • SkillSHEET 13.6 doc-5304



13B Measures of spread (page 439) Exercise 13B (page 442) Reflection (page 444)

13-B-1 Range and quartiles doc-5131 (page 442) 13-B-2 Practice with range and quartiles doc-5132 (page 442) 13-B-3 Range and quartiles in depth doc-5133 (page 442) • WorkSHEET 13.1 doc-5311



13C Box-and-whisker plots (page 444) Exercise 13C (page 447) Reflection (page 449)

13-C-1 Constructing boxplots doc-5134 (page 447) 13-C-2 Boxplots and outliers doc-5135 (page 447) 13-C-3 Boxplots with decimals doc-5136 (page 447)



13D The standard deviation 13-D-1 Standard deviation IP Activities – answers

(suitable for 10A) (page 449) Exercise 13D (page 451) Reflection (page 453)

doc-5137 (page 451) 13-D-2 Practice with standard deviation doc-5138 (page 451) 13-D-3 Standard deviation in depth doc-5139 (page 451) • WorkSHEET 13.2 doc-5318

Homework Book answers WorkSHEET 13.2 Answers


13E Comparing data sets (page 454) Exercise 13E (page 455) Reflection (page 459)

13-E-1 Comparing data 1 doc-5140 (page 455) 13-E-2 Comparing data 2 doc-5141 (page 455) 13-E-3 Comparing data 3 doc-5142 (page 455) • Interactivity

Parallel boxplots int-2788



13F Skewness (page 459) Exercise 13F (page 461) Reflection (page 463)

13-F-1 Skewed data doc-5143 (page 461) 13-F-2 More skewed data doc-5144 (page 461) 13-F-3 Tricky skewed data doc-5145 (page 461) • WorkSHEET 13.3 doc-5325







Achievement Practice test Chapter 13 Achievement Test

Chapter 13 (Teacher Set)

Chapter 14 Bivariate data




• Use scatter plots to investigate and comment on relationships between two continuous variables – using authentic data to construct scatter plots, make comparisons and draw conclusions

• Investigate and describe bivariate numerical data where the independent variable is time – constructing and interpreting data displays representing bivariate data over time – investigating biodiversity changes in Australia since white settlement

Section


(page 471)

Hungry brain activity Scatter plots doc-5326


Are you ready? (page 472) • SkillSHEET 14.1 doc-5327 • SkillSHEET 14.2 doc-5328 • SkillSHEET 14.3 doc-5329 • SkillSHEET 14.4 doc-5330 • SkillSHEET 14.5 doc-5331 • SkillSHEET 14.6 doc-5332 • SkillSHEET 14.7 doc-5333

14A Identifying related pairs of variables (page 474)

14-A-1 Pairs of variables doc-5146 (page 476)



14-A-2 More pairs of variables doc-5147 (page 476) 14-A-3 Advanced pairs of variables doc-5148 (page 476)


14B Graphing bivariate data (page 477) Exercise 14B (page 481) Reflection (page 483)

14-B-1 Scatterplots doc-5149 (page 481) 14-B-2 More scatterplots doc-5150(page 481) 14-B-3 Advanced scatterplots doc-5151 (page 481) • WorkSHEET 14.1 doc-5334



14C Scatterplots (page 483) Exercise 14C (page 488) Reflection (page 490)

14-C-1 Types of relationships doc-5152 (page 488) 14-C-2 More relationships doc-5153 (page 488) 14-C-3 Advanced relationships doc-5154 (page 488) • Interactivity

Scatterplots int-2789 • WorkSHEET 14.2 doc-5335







Achievement Practice test Chapter 14 Achievement Test Chapter 14

(Teacher Set)

Chapter 15 Statistics in the media




• Evaluate statistical reports in the media and other places by linking claims to displays, statistics and representative data – investigating real-life examples that demonstrate that predicted outcomes can be accompanied by unpredicted effects, and understanding the causes for

this (for example, Chinese one-child policy becoming the ‘one-male’ policy) – evaluating statistical reports comparing the life expectancy of Aboriginal and Torres Strait Islander people with that of the Australian population as a

whole

For 10A

• Investigate reports of studies in digital media and elsewhere for information on the planning and implementation of such studies, and the reporting of variability – evaluating media reports that refer to data from a range of contexts – evaluating whether graphs in a report could mislead, and whether graphs and numerical information support the claims – evaluating the appropriateness of sampling methods and sample size in reports where statements about a population are based on a sample

Section


(page 497)

Hungry brain activity Hot ‘n cold coffee doc-5336


Are you ready? (page 498) • SkillSHEET 15.1 doc-5337 • SkillSHEET 15.2 doc-5338 • SkillSHEET 15.3 doc-5339 • SkillSHEET 15.4 doc-5340


15A Populations and samples (page 499) Exercise 15A (page 502) Reflection (page 503)

15-A-1 Populations and samples doc-5155 (page 502) 15-A-2 More populations and samples doc-5156 (page 502) 15-A-3 In depth populations and samples doc-5157 (page 502) • WorkSHEET 15.1 doc-5342



15B Primary and secondary data (page 503) Exercise 15B (page 508) Reflection (page 510)

15-B-1 Data collection doc-5158 (page 509) 15-B-2 Further data collection doc-5159 (page 509) 15-B-3 Advanced data collection doc-5160 (page 509)



15C Evaluating inquiry methods and statistical reports (page 511) Exercise 15C (page 518) Reflection (page 521)

15-C-1 Collecting and analysing data doc-5161 (page 518) 15-C-2 More collecting and analysing data doc-5162 (page 518) 15-C-3 Detailed collecting and analysing data doc-5163 (page 518) • Interactivity

Compare statistical reports int-2790



15D Statistical investigations (page 521) Exercise 15D (page 525) Reflection (page 526)

15-D-1 Analysing reports doc-5164 (page 525) 15-D-2 Analysing reports in depth doc-5165 (page 525) 15-D-3 Analysing reports in greater depth doc-5166 (page 525) • WorkSHEET 15.2 doc-5343



Chapter 16 Financial maths


Sub-strand: Money and financial mathematics


• Connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies. – working with authentic information, data and interest rates to calculate compound interest and solve related problems

Section


(page 537)

Hungry brain activity What does it take to be a millionaire doc-5344



16A Purchasing goods (page 539) Exercise 16A (page 540) Reflection (page 542)

16-A-1 Simple interest doc-5167 (page 541) 16-A-2 Harder simple interest doc-5168 (page 541) 16-A-3 Tricky simple interest doc-5169 (page 541)




16B Buying on terms (page 542) Exercise 16B (page 543) Reflection (page 545)

16-B-1 Buying on terms doc-4170 (page 544) 16-B-2 Buying on difficult terms doc-5171 (page 544) 16-B-3 Buying on tricky terms doc-5172 (page 544) • SkillSHEET 16.3 doc-5347 • WorkSHEET 16.1 doc-5350



16C Successive discounts (page 546) Exercise 16C (page 547) Reflection (page 548)

16-C-1 Successive discounts doc-5173 (page 547) 16-C-2 Difficult successive discounts doc-5174 (page 547) 16-C-3 Tricky successive discounts doc-5175 (page 547) • SkillSHEET 16.4 doc-5348 • SkillSHEET 16.5 doc-5349 • SkillSHEET 16.6 doc-5351



16D Compound interest (page 549) Exercise 16D (page 551) Reflection (page 553)

16-D-1 Compound interest puzzle 1 doc-5176 (page 551) 16-D-2 Compound interest puzzle 2 doc-5177 (page 551) 16-D-3 Compound interest puzzle 3 doc-5178 (page 551) • Interactivity

Compound interest int-2791




16E Depreciation (page 553) Exercise 16E (page 554) Reflection (page 556)

16-E-1 Depreciation doc-5179 (page 554) 16-E-2 Harder depreciation doc-5180 (page 554) 16-E-3 Tricky depreciation doc-5181 (page 555) • eLesson

What is depreciation? eles-0182 • Interactivity

Different rates of depreciation int-1155



16F Loan repayments (page 556) Exercise 16F (page 558) Reflection (page 559)

16-F-1 Repaying a loan doc-5182 (page 558) 16-F-2 Harder loan repayments doc-5183 (page 558) 16-F-3 Difficult loan repayments doc-5184 (page 558) • WorkSHEET 16.3 doc-5353








Chapter 17 Problem solving II

Pages 565 to 588

130 problems of varying levels of difficulty

This second problem solving chapter continues to expand on the strategies practised in Chapter 11 (Problem solving I). As a refresher, you are reminded of the following points.

The main processes which can be used to solve problems are:

• Read the question at least twice, underlining all the important facts.

• Identify the solution required.

• Solve the problem using an appropriate strategy.

• Communicate the solution using appropriate language and mathematical terms.

• Support the solution with mathematical reasoning.

• Reflect on the solution. Does it answer the question? Does it make sense? Could a better method have been used?

Strategies which can be used to solve the problem include:

• Create a table.

• Draw a diagram.

• Look for a pattern.

• Work backwards from the answer.

• Eliminate possible solutions which do not match the given information.

• Look at a simplified version of the same problem.

• Guess and check.

• Use technology as this can greatly reduce calculations with unwieldy numbers.

• Simulate the problem.

The problems in this chapter can be classified into 3 levels of difficulty: Level 1, Level 2 and Level 3. It must be recognised that the classification of these problems is a subjective matter, and the expertise and exposure of students to problem solving greatly influences their ability to solve these problems.

Level 1 Level 2 Level 3

These include questions: 1, 2, 3, 4, 6, 10, 12, 15, 18, 32, 39, 42, 47, 48, 51, 53, 54, 56, 58, 60, 63, 64, 65, 69, 70, 73, 81, 82, 84, 85, 87, 92, 120.

These include questions: 5, 7, 8, 9, 11, 13, 14, 16, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 33, 34, 37, 38, 40, 43, 44, 45, 46, 49, 50, 55, 57, 59, 61, 62, 67, 68, 71, 72, 74, 76, 77, 78, 80, 83, 86, 88, 96, 97, 101, 103, 104, 105, 107, 110, 112, 114, 117, 121, 122, 123, 125, 126.

These include questions: 17, 27, 35, 36, 41, 52, 66, 75, 79, 89, 90, 91, 94, 95, 98, 99, 100, 102, 106, 108, 109, 111, 113, 115, 116, 118, 119, 124, 127, 128, 129, 130.

Chapter 18 Real numbers


Sub-strand: Real numbers


For 10A

• Define rational and irrational numbers and perform operations with surds and fractional indices – understanding that the real number system includes irrational numbers and that certain subsets of the real number system have particular properties – applying the index laws to numeric and algebraic expressions and evaluating or simplifying them as required

• Use the definition of a logarithm to establish and apply the laws of logarithms – investigating the relationship between exponential and logarithmic expressions – investigating the use of logarithmic scale

Section


(page 589)



18A Number classification review • Interactivity

(page 591) Exercise 18A (page 594) Reflection (page 595)

Classifying numbers int-2792


18B Surds (page 595) Exercise 18B (page 597) Reflection (page 598)



18C Operations with surds (page 599) Exercise 18C (page 607) Reflection (page 609)

• SkillSHEET 18.2 doc-5355 • SkillSHEET 18.3 doc-5356 • SkillSHEET 18.4 doc-5357 • SkillSHEET 18.7 doc-5360 • SkillSHEET 18.8 doc-5361 • SkillSHEET 18.9 doc-5362 • WorkSHEET 18.1 doc-5363



18D Fractional indices (page 609) Exercise 18D (page 612) Reflection (page 614)



18E Negative indices (page 614) Exercise 18E (page 616) Reflection (page 617)



18F Logarithms (page 617) Exercise 18F (page 618) Reflection (page 619)


18G Logarithm laws (page 619) Exercise 18G (page 622) Reflection (page 624)


18H Solving equations (page 624) Exercise 18H (page 628) Reflection (page 629)


Progress Test 18H Homework






Chapter 19 Polynomials




For 10A

• Investigate the concept of a polynomial and apply the factor and remainder theorems to solve problems – investigating the relationship between algebraic long division and the factor and remainder theorems

Section


(page 635)



19A Polynomials (page 637) Exercise 19A (page 638) Reflection (page 639)


19B Adding, subtracting and multiplying polynomials (page 639) Exercise 19B (page 640) Reflection (page 641)



19C Long division of polynomials (page 641) Exercise 19C (page 646) Reflection (page 646)

• Interactivity Long division of polynomials

int-2793


19D Polynomial values (page 647) Exercise 19D (page 648) Reflection (page 649)

• SkillSHEET 19.2 doc-5367 • WorkSHEET 19.1 doc-5375



19E The remainder and factor theorems (page 649) Exercise 19E (page 650) Reflection (page 651)


19F Factorising polynomials (page 651) Exercise 19F (page 654) Reflection (page 655)



19G Solving polynomial equations (page 655) Exercise 19G (page 657) Reflection (page 658)

• SkillSHEET 19.4 doc-5369 • SkillSHEET 19.5 doc-5370 • WorkSHEET 19.2 doc-5376



Closing pages • Summary (page 659)

Interactivities • Test yourself int-2876

Chapter 19 Test A & solutions

• Mapping your understanding (page 660)

• Chapter review (page 661)

• Word search int-2874 • Crossword int-2875

Chapter 19 Test B & solutions


Chapter 20 Functions and relations


Sub-strand: Linear and non-linear relations


For 10A

• Solve simple exponential equations – investigating exponential equations derived from authentic mathematical models based on population growth

• Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations – using a range of strategies to investigate the effect of multiplying by a constant term, including negative numbers – connecting the graphical and algebraic representations and describing the transformation

• Apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation – investigating the features of graphs of polynomials using digital technology

Section


(page 663)




20A Functions and relations (page 665) Exercise 20A (page 669) Reflection (page 671)

• WorkSHEET 20.1 doc-5385



20B Exponential functions (page 671) Exercise 20B (page 675) Reflection (page 678)

• SkillSHEET 20.8 doc-5386 • SkillSHEET 20.9 doc-5387 • eLesson

Exponential growth eles-0176 • WorkSHEET 20.2 doc-5388



20C Cubic functions (page 679) Exercise 20C (page 682) Reflection (page 683)


20D Quartic functions (page 683) Exercise 20D (page 685) Reflection (page 686)



20E Transformations (page 686) Exercise 20E (page 692) Reflection (page 693)

• Interactivity Polynomial transformations int-2794



(page 695)



Achievement

• Chapter review (page 696) Practice test Chapter 20 Achievement Test Chapter 20 (Teacher Set)

Chapter 21 Circle geometry


Sub-strand: Geometric reasoning


For 10A

• Prove and apply angle and chord properties of circles – applying properties of circles to develop formal proofs

Section


(page 699)



21A Angles in a circle (page 701) Exercise 21A (page 706) Reflection (page 708)

• SkillSHEET 21.1 doc-5390 • SkillSHEET 21.2 doc-5391 • SkillSHEET 21.3 doc-5392 • SkillSHEET 21.4 doc-5393 • SkillSHEET 21.5 doc-5394


• Interactivity

Angles in a circle int-2795 • WorkSHEET 21.1 doc-5395


21B Intersecting chords, secants and tangents (page 708) Exercise 21B (page 713) Reflection (page 715)


21C Cyclic quadrilaterals (page 715) Exercise 21C (page 717) Reflection (page 718)

• SkillSHEET 21.6 doc-5396 • WorkSHEET 21.2 doc-5397



21D Tangents, secants and chords (page 718) Exercise 21D (page 720) Reflection (page 723)







Chapter 22 Trigonometry II


Sub-strand: Pythagoras and trigonometry


For 10A

• Establish the sine, cosine and area rules for any triangle and solve related problems – applying knowledge of sine, cosine and area rules to authentic problems such as those involving surveying and design

• Use the unit circle to define trigonometric functions, and graph them with and without the use of digital technologies – establishing the symmetrical properties of trigonometric functions – investigating angles of any magnitude

• Solve simple trigonometric equations – understanding that trigonometric functions are periodic and that this can be used to describe motion – using the notion of periodicity and symmetry to consider an infinite number of solutions

Section


(page 731)



22A The sine rule (page 733) Exercise 22A (page 739) Reflection (page 740)



22B The cosine rule (page 741) Exercise 22B (page 744) Reflection (page 744)


22C Area of triangles (page 745) Exercise 22C (page 747) Reflection (page 749)




22D The unit circle (page 749) Exercise 22D (page 752) Reflection (page 754)


22E Trigonometric functions (page 755) Exercise 22E (page 757) Reflection (page 759)

• Interactivity Trigonometric functions int-2796


22F Solving trigonometric equations (page 759) Exercise 22F (page 761) Reflection (page 761)


Closing pages • Summary (page 762)

Interactivities • Test yourself int-2885

Chapter 22 Test A & solutions

• Mapping your understanding (page 763

• Chapter review (page 764)

• Word search int-2883 • Crossword int-2884

Chapter 22 Test B & solutions


Chapter 23 Interpreting data




For 10A

• Use information technologies to investigate bivariate numerical data sets. Where appropriate use a straight line to describe the relationship allowing for variation – investigating different techniques for finding a ‘line of best fit’

Section


(page 767)



23A Bivariate data (page 769) Exercise 23A (page 773)


Reflection (page 776) Progress Test 23A Homework

23B Lines of best fit (page 776) Exercise 23B (page 784) Reflection (page 786)

• SkillSHEET 23.5 doc-5409 • Interactivity

Extrapolation int-1154 • WorkSHEET 23.1 doc-5412



23C Time series (page 786) Exercise 23C (page 790) Reflection (page 793)

• eLesson Fluctuations and cycles eles-0181









Maths Quest 10+10A for the Australian Curriculum

Documents

Transcript of Maths Quest 10+10A for the Australian Curriculum