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
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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
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
Content strand: Number and algebra
Sub-strand: Patterns and algebra
Australian Curriculum Content Strands
• 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
Interactivities • Test yourself int-2831 • Word search int-2829 • Crossword int-2830
Chapter 2 Test A & solutions Chapter 2 Test B & solutions
Achievement Practice test Chapter 2 Achievement Test Chapter 2 (Teacher Set)
Chapter 3 Coordinate geometry
Content strand: Number and algebra
Sub-strand: Linear and non-linear relationships
Australian Curriculum Content Strands
• 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
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
IP Activities – answers Homework Book answers WorkSHEET 3.1 Answers
Progress Test 3B Homework
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
IP Activities – answers Homework Book answers
Progress Test 3C Homework
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
IP Activities – answers Homework Book answers
Progress Test 3D
Reflection (page 74)
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
WorkSHEET 3.2 Answers
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
IP Activities – answers Homework Book answers
Progress Test 3E Homework
Closing pages • Summary (page 83) • Mapping your understanding
(page 84) • Chapter review (page 85)
Interactivities • Test yourself int-2834 • Word search int-2832 • Crossword int-2833
Chapter 3 Test A & solutions Chapter 3 Test B & solutions
Achievement Practice test Chapter 3 Achievement Test Chapter 3
(Teacher Set)
Chapter 4 Simultaneous linear equations and inequations
Content strand: Number and algebra
Sub-strand: Linear and non-linear relationships
Australian Curriculum Content Strands
• 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
Chapter opening • What do you know?
(page 89)
Hungry brain activity How are you feeling today? doc-5211
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
IP Activities – answers Homework Book answers WorkSHEET 4.3 Answers
Progress Test 4G Homework
Closing pages • Summary (page 123) • Mapping your understanding
(page 124) • Chapter review (page 125)
Interactivities • Test yourself int-2837 • Word search int-2835 • Crossword int-2836
Chapter 4 Test A & solutions Chapter 4 Test B & solutions
Achievement Practice test Chapter 4 Achievement Test Chapter 4 (Teacher Set)
Chapter 5 Trigonometry
Content strand: Measurement and geometry
Sub-strand: Pythagoras and trigonometry
Australian Curriculum Content Strands
• 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
Applying trigonometry to drafting problems int-2781
Progress Test 5H Homework
Closing pages • Summary (page 177) • Mapping your understanding
(page 178) • Chapter review (page 179)
Interactivities • Test yourself int-2840 • Word search int-2838 • Crossword int-2839
Chapter 5 Test A & solutions Chapter 5 Test B & solutions
Achievement Practice test Chapter 5 Achievement Test Chapter 5 (Teacher Set)
Chapter 6 Surface area and volume
Content strand: Measurement and geometry
Sub-strand: Using units of measurement
Australian Curriculum Content Strands
• 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
Closing pages • Summary (page 213) • Mapping your understanding
(page 213) • Chapter review (page 214)
Interactivities • Test yourself int-2843 • Word search int-2841 • Crossword int-2842
Chapter 6 Test A & solutions Chapter 6 Test B & solutions
Achievement Practice test Chapter 6 Achievement Test Chapter 6 (Teacher Set)
Chapter 7 Quadratic expressions
Content strand: Number and algebra
Sub-strand: Patterns and algebra
Australian Curriculum Content Strands
• 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
IP Activities – answers Homework Book answers WorkSHEET 7.1 Answers
Progress Test 7B Homework
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
IP Activities – answers Homework Book answers
Progress Test 7C Homework
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
IP Activities – answers Homework Book answers
Progress Test 7D Homework
7E Mixed factorisation (page 240) Exercise 7E (page 240) Reflection (page 241)
IP Activities – answers Homework Book answers WorkSHEET 7.2 Answers
Progress Test 7E Homework
Closing pages • Summary (page 242) • Mapping your understanding
(page 243) • Chapter review (page 244)
Interactivities • Test yourself int-2846 • Word search int-2844 • Crossword int-2845
Chapter 7 Test A & solutions Chapter 7 Test B & solutions
Achievement Practice test Chapter 7 Achievement Test Chapter 7 (Teacher Set)
Chapter 8 Quadratic equations
Content strand: Number and algebra
Sub-strand: Linear and non-linear relationships
Australian Curriculum Content Strands
• 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
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
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)
IP Activities – answers Homework Book answers
Progress Test 8C Homework
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)
IP Activities – answers Homework Book answers
Progress Test 8D Homework
• Interactivity
Solving by interpolation int-1147 • WorkSHEET 8.2 doc-6264
WorkSHEET 8.2 Answers
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
IP Activities – answers Homework Book answers
Progress Test 8E Homework
Closing pages Summary (page 274) Mapping your understanding
(page 275) Chapter review (page 276)
Interactivities • Test yourself int-2849 • Word search int-2847 • Crossword int-2848
Chapter 8 Test A & solutions Chapter 8 Test B & solutions
Achievement Practice test Chapter 8 Achievement Test Chapter 8 (Teacher Set)
Chapter 9 Functions
Content strand: Number and algebra
Sub-strand: Linear and non-linear relationships
Australian Curriculum Content Strands
• 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
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
IP Activities – answers Homework Book answers WorkSHEET 9.1 Answers
Progress Test 9B Homework
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)
IP Activities – answers Homework Book answers
Progress Test 9C Homework
9D Sketching parabolas of the form y = ax2 + bx + c (page 298)
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)
IP Activities – answers Homework Book answers
Progress Test 9F Homework
9G The circle (page 315)
9-G-1 Circle graphs doc-5092 (page 317)
IP Activities – answers Homework Book answers
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)
Progress Test 9G Homework
Closing pages • Summary (page 319) • Mapping your understanding
(page 320) • Chapter review (page 321)
Interactivities • Test yourself int-2852 • Word search int-2850 • Crossword int-2851
Chapter 9 Test A & solutions Chapter 9 Test B & solutions
Achievement Practice test Chapter 9 Achievement Test Chapter 9 (Teacher Set)
Chapter 10 Deductive geometry
Content strand: Measurement and geometry
Sub-strand: Geometric reasoning
Australian Curriculum Content Strands
• 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)
IP Activities – answers Homework Book answers WorkSHEET 10.3 Answers
Progress Test 10E Homework
Closing pages • Summary (page 347) • Mapping your understanding
(page 348) • Chapter review (page 349)
Interactivities • Test yourself int-2855 • Word search int-2853 • Crossword int-2854
Chapter 10 Test A & solutions Chapter 10 Test B & solutions
Achievement Practice test Chapter 10 Achievement Test Chapter 10 (Teacher Set)
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.
• 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
Chapter opening • What do you know?
(page 379)
Hungry brain activity Independent and mutually exclusive events doc-5285
IP Activities – answers Homework Book answers WorkSHEET 12.1 Answers
Progress Test 12B Homework
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
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
IP Activities – answers Homework Book answers
Progress Test 12D Homework
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)
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)
IP Activities – answers Homework Book answers
Progress Test 12F Homework
• WorkSHEET 12.3 doc-5297 WorkSHEET 12.3 Answers
Closing pages • Summary (page 423) • Mapping your understanding
(page 424) • Chapter review (page 425)
Interactivities • Test yourself int-2858 • Word search int-2856 • Crossword int-2857
Chapter 12 Test A & solutions Chapter 12 Test B & solutions
Achievement Practice test Chapter 12 Achievement Test Chapter 12 (Teacher Set)
Chapter 13 Univariate data
Content strand: Statistics and probability
Sub-strand: Data representation and interpretation
Australian Curriculum Content Strands
• 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
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
IP Activities – answers Homework Book answers WorkSHEET 13.1 Answers
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
Progress Test 13D Homework
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
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
IP Activities – answers Homework Book answers WorkSHEET 13.3 Answers
Progress Test 13F Homework
Closing pages • Summary (page 464) • Mapping your understanding
(page 465) • Chapter review (page 466)
Interactivities • Test yourself int-2861 • Word search int-2859 • Crossword int-2860
Chapter 13 Test A & solutions Chapter 13 Test B & solutions
Achievement Practice test Chapter 13 Achievement Test
Chapter 13 (Teacher Set)
Chapter 14 Bivariate data
Content strand: Statistics and probability
Sub-strand: Data representation and interpretation
Australian Curriculum Content Strands
• 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
IP Activities – answers Homework Book answers WorkSHEET 14.2 Answers
Progress Test 14C Homework
Closing pages • Summary (page 491) • Mapping your understanding
(page 491) • Chapter review (page 492)
Interactivities • Test yourself int-2864 • Word search int-2862 • Crossword int-2863
Chapter 14 Test A & solutions Chapter 14 Test B & solutions
Achievement Practice test Chapter 14 Achievement Test Chapter 14
(Teacher Set)
Chapter 15 Statistics in the media
Content strand: Statistics and probability
Sub-strand: Data representation and interpretation
Australian Curriculum Content Strands
• 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
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
IP Activities – answers Homework Book answers WorkSHEET 15.2 Answers
Progress Test 15D Homework
Closing pages • Summary (page 527) • Mapping your understanding
(page 528) • Chapter review (page 529)
Interactivities • Test yourself int-2867 • Word search int-2865 • Crossword int-2866
Chapter 15 Test A & solutions Chapter 15 Test B & solutions
Achievement Practice test Chapter 15 Achievement Test Chapter 15 (Teacher Set)
Chapter 16 Financial maths
Content strand: Number and algebra
Sub-strand: Money and financial mathematics
Australian Curriculum Content Strands
• 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
Chapter opening • What do you know?
(page 537)
Hungry brain activity What does it take to be a millionaire doc-5344
IP Activities – answers Homework Book answers WorkSHEET 16.3 Answers
Progress Test 16F Homework
Closing pages • Summary (page 560) • Mapping your understanding
(page 561) • Chapter review (page 562)
Interactivities • Test yourself int-2870 • Word search int-2868 • Crossword int-2869
Chapter 16 Test A & solutions Chapter 16 Test B & solutions
Achievement Practice test Chapter 16 Achievement Test Chapter 16 (Teacher Set)
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.
• 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
Closing pages • Summary (page 630) • Mapping your understanding
(page 631) • Chapter review (page 632)
Interactivities • Test yourself int-2873 • Word search int-2871 • Crossword int-2872
Chapter 18 Test A & solutions Chapter 18 Test B & solutions
Achievement Practice test Chapter 18 Achievement Test Chapter 18 (Teacher Set)
Chapter 19 Polynomials
Content strand: Number and algebra
Sub-strand: Patterns and algebra
Australian Curriculum Content Strands
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
Achievement Practice test Chapter 19 Achievement Test Chapter 19 (Teacher Set)
Chapter 20 Functions and relations
Content strand: Number and algebra
Sub-strand: Linear and non-linear relations
Australian Curriculum Content Strands
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
Closing pages • Summary (page 724) • Mapping your understanding
(page 725) • Chapter review (page 726)
Interactivities • Test yourself int-2882 • Word search int-2880 • Crossword int-2881
Chapter 21 Test A & solutions Chapter 21 Test B & solutions
Achievement Practice test Chapter 21 Achievement Test Chapter 21 (Teacher Set)
Chapter 22 Trigonometry II
Content strand: Measurement and geometry
Sub-strand: Pythagoras and trigonometry
Australian Curriculum Content Strands
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
Achievement Practice test Chapter 22 Achievement Test Chapter 22 (Teacher Set)
Chapter 23 Interpreting data
Content strand: Statistics and probability
Sub-strand: Data representation and interpretation
Australian Curriculum Content Strands
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’