St Stephens' SchoolYear 10 Mathematics Program

Primary resource: Essential Mathematics 10 for the Australian CurriculumOther resources: Text books available on LearningField (e.g. MathsQuest 10, Oxford Insights) Online homework: MangaHigh.com

Semester 1

Week Content: Solving Linear Equations Australian Curriculum ResourcesTerm 4

- 2015 Maths 1 & 2

1 Solve one-step and multi-step linear equations. Solve problems involving linear equations,

including those derived from formulasACMNA235

2

Graph linear equations on a set of axes Determine the gradient of a line between two points Determine the x-intercept and y-intercept of a straight

line graph Determine the equation of a line given 2 points or one

point and the gradient

Substitute values into formulas to determine an unknownACMNA234

3 Solve linear inequalities and plot them on a number

line.Solve linear inequalities and graph their solutions on a number lineACMNA236

4 Solve simultaneous equations algebraically - substitution and elimination methods

Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology ACMNA237

5 Solve simultaneous equations graphically

6 Solve problems using parallel and perpendicular lines Solve problems involving parallel and

perpendicular linesACMNA238

7

Algebraic fractions Linear equations with algebraic fractions

Apply four operations to simple algebraic fractions with numerical denominatorsACMNA232

Solve linear equations involving simple algebraic fractionsACMNA240

Test 1: Linear equations and solving

A B C D EFormulates a pair of simultaneous linear equations from a word problem and determines the simultaneous solution in a variety of ways. Rearranges linear rules given in a variety of forms to justify the presence, or not, of a geometric relationship. Solves problems involving perpendicular lines. Formulates and solves a linear equation or inequality involving fractions from a complex word problem, verifies the solution/s and illustrates the solutions of inequalities with a suitable graph.

Graphs a pair of linear relations given in a variety of ways, writes the simultaneous solution and justifies algebraically. Rearranges linear rules into forms to make conclusions about the geometric relationship. Solves problems involving parallel lines. Uses algebraic techniques to solve a pair of simultaneous linear equations. Solves problems involving linear equations and inequalities involving fractions. Illustrates the solution of inequalities graphically.

Graphs a pair of simple linearrelations and writes thesimultaneous solution. Identifiesthe relationship between linesas being parallel orperpendicular by referring to thegradients. Solves problemsinvolving linear equations orinequalities.

Writes the simultaneous solution when given a graph of a pair of linear relations.

Solves linear equations involving one variable.

Simplifies sums and differencesof algebraic fractions withunrelated denominators.

Simplifies sums and differences of algebraic fractions with related denominators. Substitutes into formulas, identifying the form of the resulting equation, and selects the appropriate method of solution.

Simplifies sums and differencesof algebraic fractions with likedenominators. Substitutes intoformulas and solves theresulting linear equation.

Substitutes values into formulas to determine an unknown.

Substitutes values into simple formulas.

Week Content: Area and Volume Australian Curriculum Resources

Maths 2 Maths 1

8 - 9

Convert units of length/area/volume

Perimeter of composite shapes

Pythagoras’ theorem Area of shapes Area of composite

shapes Use net to find SA of

prisms and cylinders Surface area of

composite solids Convert units of

volume and capacity Find volumes of

prisms Find volumes of

cylinders Find volumes of

composite shapes

Draw a net for a solid Use net to find SA of a cone and a

pyramid Determine the slant height of a

cone Determine the height of a cone Determine the surface area of a

composite solid Determine the volume of a pyramid Determine the volume of a cone Investigate the volume of an oblique cone and pyramid

Determine the surface area of a sphere

Determine the volume of a sphere Determine the radius of a sphere Determine the surface area of

composite shapes involving spheres

Determine the volume of composite shapes involving spheres

Solve problems involving surface area and volume for a range of prisms, cylinders and composite solidsACMMG242

Solve problems involving surface area and volume for right pyramids, right cones, spheres and related composite solidsACMNG271

A B C D EDraws a diagram to represent information extracted from a multi-step word problem. Solves problems by applying the appropriate surface area and volume formulas for objects, including inverse use of formulas and rates.

Draws a diagram to represent information extracted from a word problem. Solves problems involving composite solids by applying the appropriate surface area and volume formulas.

Uses the appropriate formulas to calculate the surface area and volume of objects comprising of prisms.

Calculates the surface area and volume of a simple right prism.

Attempts to calculate the surface area and volume of a simple right prism, but confuses concepts and makes consistent errors.

Week Content: Algebra Australian Curriculum ResourcesTerm 1 -

2016 Maths 2 Maths 1

1 – 2

Index Laws 1 – 4

Multiplying algebraic expressions (Law 1)

Dividing algebraic expressions (Law 2)

Zero index (Law 3) Raising powers to a

power (Law 4)

Rational and irrational numbers

Surds and fractional indices

Logarithms

Simplify algebraic products and quotients using index lawsACMNA231

Define rational and irrational numbers and perform operations with surds and fractional indicesACMNA264

Define rational and irrational numbers and perform operations with surds and fractional indicesACMNA264

Use the definition of a logarithm to establish and apply the laws of logarithmsACMNA265

Solve simple exponential equationsACMNA270

3

4

Expanding and factorising Apply the distributive law to the expansion of algebraic expressions, and collect like terms where appropriateACMNA213

Factorise algebraic expressions by taking out a common algebraic factorACMNA230

5

Algebraic fractions Apply four operations to simple algebraic fractions with numerical denominators

ACMNA232

Test 2: Measurement and Algebra

A B C D ESimplifies sums and differences of algebraic fractions with unrelated denominators. Applies index laws to simplify complex algebraic products and quotients involving integral indices. Substitutes into formulas and solves the resulting quadratic equation in a variety of ways, identifying that some solutions may be inappropriate.

Expands and simplifies the sumsand differences of binomialexpressions involving fractions.Applies factorisation multipletimes to expressions includingnon-monic quadratic trinomials.Applies multi-step factorisation,at least three times, to simplifyproducts and quotients ofalgebraic fractions.

Simplifies sums and differences of algebraic fractions with related denominators. Substitutes into formulas, identifying the form of the resulting equation, and selects the appropriate method of solution. Applies index laws to simplify algebraic products and quotients involving integral indices.

Expands and simplifies the sums and differences of binomial expressions. Factorises two-step algebraic expressions involving common factors, quadratic binomials and monic trinomials. Applies one-step factorisation to simplify algebraic products and quotients.

Simplifies sums and differences of algebraic fractions with like denominators. Substitutes into formulas and solves the resulting linear equation. Applies index laws to simplify algebraic products and quotients involving non-negative integral indices.

Expands and simplifies, wherenecessary, binomial expressions.Factorises monic quadraticexpressions such as commonfactors, binomials, trinomialsand quadnomials.

Substitutes values into formulas to determine an unknown. Applies index laws to simplify numerical expressions with positive integral powers, but makes frequent errors when applying index laws to algebraic expressions.

Factorises a onestep algebraic expression involving a numerical common factor.

Substitutes values into simple formulas. Shows the meaning of a number written with a power, and evaluates it.

Week Content: Finance Australian Curriculum Resources

Maths 1&2

6 Use the simple

interest formula Use the compound

interest formula Depresiation Worded probelms

Use numbers/excel to draw interest tables

Find interest on speadsheets

Use spreadsheets to solve worded problems

Use the classpad draw interest tables

Find interest on classpad Use classpad to solve

worded problems

Connect the compound interest formula to repeated applications of simple interest using appropriate digital technologiesACMNA249

Substitute values into formulas to determine an unknownACMNA234

7

Investigation 1: Finance (hand out week 6, due end week 7)

A B C D EExtracts relevant information from word problems and applies repeated interest calculations for the comparison of loans and investments. Provides valid justification for the recommendations made. Uses inverse calculations to solve for the rate with compound interest, showing full working.

Extracts multiple pieces of information from text and tables to make ongoing interest calculations for loans and investments. Uses inverse calculations to solve for the principal in compound interest.

Applies formulas for simple and compound interest. Identifies compound interest as repeated applications of simple interest.

Applies simple interest to allcalculations.

Attempts to apply simple interest, but makes frequent errors.

Week Content: Chance Australian Curriculum Resources

Maths 1&2

8

Chance/probability Replacement and non-replacement problems Tree diagrams Dependent vs independent events

Assign probabilities to outcomes and determine probabilities of eventsACMSP246

Describe the results of two- and three-step chance experiments, both with and without replacementsACMSP246

9

Two way tables Venn diagrams

Investigate the concept of independenceACMSP246

Use the language of ‘if ... then’, ‘given’, ‘of’, ‘knowing that’ to investigate conditional statements and identify common mistakes in interpreting such languageACMSP247

A B C D ELists outcomes for multi-step chance experiments, with and without replacement, including the use of probability trees, assigns probabilities to the outcomes and determines probabilities of compound events, with conditions. Identifies events that are independent.

Lists outcomes for multi-step chance experiments, with and without replacement, assigns probabilities to the outcomes and determines probabilities of compound events. Draws twoway tables and Venn diagrams, and determines probabilities of compound events.

Lists outcomes for multi-step chance experiments and assigns probabilities.

Lists outcomes for two-step chance experiments and determines associated probabilities.

With assistance, lists outcomes for one- and two-step chance experiments, and determines associated probabilities.

Semester 1/2

Week Content: Quadratics Australian Curriculum ResourcesTerm 2 -

2016 Maths 2 Maths 1

10

Expanding binomials

Trinomials Solve quadratic

equations

sketch a graph from a polynomial

describe freatures of polynomial graphs

Expand binomial products and factorise monic quadratic expressions using a variety of strategies

ACMNA233

Term 3 –

2016

1

Exam revision

Exam 1

2

Expanding binomials

Trinomials Solve quadratic

equations

sketch a graph from a polynomial

describe freatures of polynomial graphs

Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriateACMNA213

Apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equationACMNA268

3Solve simple quadratic equations using a range of strategiesACMNA241

Investigate the concept of a polynomial

and apply the factor and remainder theorems to solve problemsACMNA266

4

Test 3: Factorising and Quadratics

A B C D EExpands and simplifies the sums and differences of binomial expressions involving fractions. Applies factorisation multiple times to expressions including non-monic quadratic trinomials. Applies multi-step factorisation, at least three times, to simplify products and quotients of algebraic fractions. Formulates a quadratic equation by extracting relevant information from a complex word problem. Rearranges the equation into a form for ease of computation and solves it through a variety of techniques, including graphical. Applies the quadratic formula, showing full working, to obtain the simplified irrational solution/s.

Expands and simplifies the sums and differences of binomial expressions. Factorises two-step algebraic expressions involving common factors, quadratic binomials and monic trinomials. Applies one-step factorisation to simplify algebraic products and quotients. Solves a quadratic equation algebraically and justifies the solution/s using a variety of techniques.

Expands and simplifies, where necessary, binomial expressions. Factorises monic quadratic expressions such as common factors, binomials, trinomials and quadnomials. Solves a simple quadratic equation algebraically and links the solution to the - intercepts on the matching graph. Applies the four operations to simple algebraic fractions. Simplifies algebraic fractions expressed in factored form.

Solves a quadratic equation graphically and when given in factored form. Factorises a onestep algebraic expression involving a numerical common factor.

Solves linear equations with up to three steps only.

Week Content: Statistics Australian Curriculum Resources

Maths 2 Maths 15 Determine quartiles Use Classpad to draw Determine quartiles and interquartile

and IQR Use above to draw Box

and whisker plots Find and plot outliers

using formula Compare parallel B&W

plots Match B&W to

histograms and dot plots

5 point summaries

B&W plots Standard deviation

rangeACMSP248

Construct and interpret box plots and use them to compare data setsACMSP249

Compare shapes of box plots to corresponding histograms and dot plotsACMSP250

Calculate and interpret the mean and standard deviation of data and use these to compare data setsACMSP278

6

Investigate and describe bivariate numerical data where the independent variable is timeACMSP252

7

Discuss bivariate data as comparison between two variables

Describe scatterplots in terms of correlation

Identify outliers Find line of best fit

(pictorially and algebraically)

Interpolate and extrapolate points on line

Plot bivariate data using a classpad

Find line of best fit using a classpad

Use scatter plots to investigate and comment on relationships between two numerical variablesACMSP251

Evaluate statistical reports in the media and other places by linking claims to displays, statistics and representative dataACMSP253

Use information technologies (classpad) to investigate bivariate numerical data sets. Where appropriate use a straight line to describe the relationship allowing for variationACMSP279

8

9

Investigation 2: Statistics

CAMP: Week 10

A B C D EMatches box plots to corresponding histograms and dot plots, and provides an explanation using concise statistical reasoning. Applies algebraic techniques to calculate the equation of the trend line for bivariate and time-series data. Uses the equation to make predictions, identifying factors that influence the reliability of predictions and gives reasons why predictions and actual values may vary. Uses explicit statistical language when writing statistical reports, making links/references to resources relevant to the report.

Uses the quartiles, together with minimum, median and maximum data values, to draw box plots of data from primary and secondary sources, identifying possible outliers. Compares data presented on parallel box plots, using correct statistical language. Investigates and describes relationships between variables for bivariate and time-series data relating to economic, social and environmental issues. Draws trend lines, comments on predictions and gives possible reasons why predictions and actual values may vary.

Calculates quartiles and interquartile range for collected or given authentic data. Compares data sets by referring to the shape of the display. Describes the trend and patterns for bivariate data where the independent variable is time. Describes the statistical relationship between two continuous variables. Evaluates statistical reports.

Calculates quartiles and interquartile range for a small sample of ordered data. Completes or draws a scatter plot for bivariate or time-series data. Writes statistical reports using vague language.

Completes a scatter plot and calculates the mean and median for each variable.

Term 3 – 2016 Week 1: Student Free

Week Content: Trigonometry Australian Curriculum Resources

Maths 2 Maths 1

2 - 3

Sine, cos and tan ratios Solve for unknown

sides in right triangles (in worded questions)

Trigonometric inverses (asin, acos, atan)

Find unknown angles from sides in right triangles

Visualise and draw a right triangles

Understand and apply ‘elevation’ and ‘depression’ wrt angles

State directions in bearings

Find true bearings Draw triangles from

bearings

Draw 3D problems in terms of 2D triangles

Relate answers from 2D diagram to 3D question

Find areas using the sine rule

Solve right-angled triangle problems including those involving direction and angles of elevation and depressionACMMG245

Pythagoras theorem and trigonometry to solve three dimensional problems in

right angled trianglesACMNG276

4 Draw the unit circle Define sine,cos and tan

for all angles in the unit circle

Find supplementary angles for each trig ratio

Describe relationship between angles/ quadrants and trig ratios

Find exact values for sin,cos,tan using pythagoras

Relate the unit circle to the sine/cosine graphs

Identify graphs of

Use the unit circle to define trigonometric functions and graph them with and without digital technologiesACMNG274

Establish the sine, cosine and area rules for any triangle and solve related problemsACMNG273

trigonometric functions State its properties

(amplitude/symmetry etc)

Find unknown sides and angles of any triangle using cosine and sine rule

Discuss the ambiguous case of sine rule

Test 4: Statistics and Trigonometry

A B C D EChooses to use algebra in solving a problem requiring the use of Pythagoras’ Theorem to find the missing lengths of the side/s. Diagrammatically represents a complex word problem, including the application of direction and elevation. Follows multiple steps to solve the problem, e.g. applies rates, Pythagoras’ Theorem and trigonometry.

Diagrammatically represents a word problem involving elevations. Follows multiple steps to solve the problem, e.g. applies Pythagoras’ Theorem and trigonometry

Selects and uses the correct trigonometric ratio to calculate unknown angles.

Uses trigonometric ratios to find unknown sides in right-angled triangles.

Identifies some trigonometric ratios.

Week Content: Geometric Reasoning Australian Curriculum Resources

Maths 2 Maths 1

5 Congruency Similarity

Properties of circles

Formulate proofs involving congruent triangles and angle properties

ACMMG243

Prove and apply angle & chord properties of circlesACMNG272

6

Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes

ACMMG244

7 Revision

Exam 2

A B C D EJustifies similarity of triangles after drawing a diagram to represent a familiar two dimensional situation, such as trees and shadows, and applies ratios to deduce the unknown.Draws a diagram for given information, proves congruency or similarity and deduces further properties of geometric figures.

Draws a diagram to represent a familiar two-dimensional situation, such as trees and shadows, and applies ratios to deduce the unknown. Draws a diagram for given information and proves congruency or similarity of triangles.

.Uses angle and triangle properties to prove congruency or similarity of triangles using given diagrams. Applies ratios and geometric reasoning to deduce missing values in given diagrams.

Uses ratios to deduce unknowns when given a pair of similar triangles. Applies congruency to triangles to determine unknown values.

Identifies pairs of similar triangles. Identifies pairs of congruent triangles.

Week Content: Co-ordinate geometry Australian Curriculum Resources

Maths 2 Maths 1

9 - 10 matching graphs to

equations

parabolas hyperbolas circles

Explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials using digital technologies as appropriate

ACMNA239

Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformationsACMNA267

A B C D EMakes connections between transformed relations and writes the rule for the given graph.

Makes connections between the algebraic and graphical forms of quadratic, circular and exponential relations, distinguishing between rules for relations of the same kind. Sketches relations, applying transformations.

Makes connections between the algebraic and graphical representations of relations such as quadratic, circular and exponential.

Makes connections between the algebraic and graphical representation of linear and quadratic relations.

Makes connections between the algebraic and graphical representation of linear relations only.

Assessments Date Weighting

Investigations

Investigation 1: Finance Term 1 Week 7 10%

Investigation 2: Statistics Term 2 Week 9 10%

Tests

Test 1: Linear Equations Term 4 Week 8 10%

Test 2: Measurement and algebra Term 1 Week 5 10%

Test 3: Factorising and quadratics Term 2 Week 6 10%

Test 4: Statistics and trigonometry Term 3 Week 5 10%

Exam S1 Term 2, week 2 20%

Exam S2 Term 3 Week 8 20%