Year 9 Term 1 Weeks 1-2

Algebraic Tech 3 Factorising

Syllabus Reference Outcome

MA4-8NA, MA5.2-6NA Generalises number properties to operate with algebraic expressions. Simplifies algebraic fractions, and expands and factorises quadratic expressions. Graded Examples

(Link to powers 3)

• Factorise algebraic expressions by taking out a common algebraic factor

• Factorise algebraic expressions by determining common factors

Eg. 3𝑥2 − 6𝑥 14𝑎𝑏 ÷ 12𝑎2 21𝑥𝑦 − 3𝑥 + 9𝑥2 15𝑝2𝑞3 − 12𝑝𝑞4

• Recognise that expressions such as 24𝑥2𝑦 + 16𝑥𝑦2 = 4𝑥𝑦(6𝑥 + 4𝑦) are partially factorised and that further factorisation is necessary.

E

D

C

B

A

Year 9 Term 1 Weeks 3-5

Area and Perimeter Composite Shapes

Syllabus Reference Outcome

MA5.1-8MG, MA4-12MG Calculates the areas of composite shapes, and the surface areas of rectangular and triangular prisms. Calculate the perimeters of plane shapes and the circumferences of circles. Graded Examples

Area and Perimeter of composite figures including:

• Quadrants • Sectors • Kites • Rhombus • Trapezium

Problems to include use of Pythagoras’ Theorem Area of an Annulus A variety of measurement units NOTE: abbreviation m2 is read as “square metres” NOT “metres squared”

E

Area and Perimeter of Rectangles and/or Triangles.

D

Area and perimeter of quadrants, sectors, kites, rhombuses, trapezium.

C

Area and Perimeter of Composite figures. Area of an annulus. B

Area and perimeter of an annulus broken into a “sector”.

A

Year 9 Term 1 Weeks 6-7 Data 3

Syllabus Reference Outcome

Graded Examples

E

D

C

B

A

Year 9 Term 1 Weeks 8-9 Ratios/Sim Figures 1

Syllabus Reference Outcome

Graded Examples

Be careful of how fractions are used

E

D

C

B

A

Year 9 Term 1 Weeks 10-11 Surface Area 1

Syllabus Reference Outcome

Previous topics: Area & perim of composite shapes, Pythag 2, Circle Area, Circle perim.

Graded Examples

1. Nets

2. Prisms Find SA from given sides, find sides from given SA Use Pythagoras

3. Cylinders Closed / open 𝑆𝐴 = 2𝜋𝑟2ℎ + 2𝜋𝑟ℎ, 𝑆𝐴 = 𝜋𝑟2ℎ + 2𝜋𝑟ℎ, 𝑆𝐴 = +2𝜋𝑟ℎ,

4. Easy pyramids

E

D

C

B

A

Year 9 Term 1 Weeks 1-2 Algebraic Solving 3-step

Syllabus Reference Outcome

Graded Examples

E

D

C

B

A

Year 9 Term 1 Weeks 5-6 Powers 3

Syllabus Reference Outcome

ACMNA150, ACMNA212, ACMNA213 Graded Examples

Use the notation for square root √ and cube root √3 Determine through numerical examples that: (𝑎𝑏)2 = 𝑎2𝑏2, eg (2 × 3)2 = 22 × 32 √𝑎𝑏 = √𝑎 × √𝑏 eg. √9 × 4 = √9 × √4 Use the index laws previously established for numbers to develop the index laws in algebraic form. Eg. 22 × 23 = 22+3 = 25 𝑎𝑚 × 𝑎𝑛 = 𝑎𝑚+𝑛 25 ÷ 22 = 25−2 = 23 𝑎𝑚 ÷ 𝑎𝑛 = 𝑎𝑚−𝑛 (22)3 = 22×3 = 26 (𝑎𝑚)𝑛 = 𝑎𝑚𝑛 Explain why a particular algebraic sentence is incorrect. Eg. explain why 𝑎3 × 𝑎2 = 𝑎6 is incorrect Establish that 𝑎0 = 1 using the index laws, explain why 𝑥0 = 1 Eg. 𝑎3 ÷ 𝑎3 = 𝑎3−3 = 𝑎0 And 𝑎3 ÷ 𝑎3 = 1 ∴ 𝑎0 = 1 Simplify expressions which use the zero index Eg. 5𝑥0 + 3 = 8 Simplify expressions that involve the product and quotient of simple algebraic terms containing indices. Eg. (3𝑥2)3 = 27𝑥6 2𝑥2 × 3𝑥3 = 6𝑥5 15𝑎6 ÷ 3𝑎2 = 5𝑎4 15𝑎6 ÷ 3𝑎2 = 5𝑎4 3𝑎2

15𝑎6=

15𝑎4

Compare expressions such as 3𝑎2 × 5𝑎 and 3𝑎2 + 5𝑎 by substituting values for 𝑎 Establish the meaning of negative indices - by patterns

33 32 31 30 3−1 3−2 27 9 3 1 1

3

132

=19

Evaluate numerical expressions with a negative index by first rewriting with a positive index Eg. 3−4 = 1

34= 1

81

Expand algebraic expressions, including those involving negatives and indices Eg. −3𝑥2(5𝑥2 + 2𝑥4𝑦) Expand algebraic expressions by removing grouping symbols and

E

D

C

B

A

collecting like terms where applicable. Eg. 2𝑦(𝑦 − 5) + 4(𝑦 − 5) 4𝑥(3𝑥 + 2) − (𝑥 − 1) Use index notation and the index laws to establish that

𝑎−1 =1𝑎

, 𝑎2 =1𝑎2

𝑎−3 =1𝑎3

Explain the difference between similar pairs of algebraic expressions Eg. are 𝑥−2𝑎𝑛𝑑 − 2𝑥 equivalent expressions? Translate expressions with negative indices to expressions with positive indices and vice versa Apply the index laws to simplify algebraic expressions involving negative indices Eg. 4𝑏−5 × 8𝑏−3

9𝑥−4 ÷ 3𝑥−3 State whether particular equivalences are true or false and give reasons Eg. explain why each of the following are true or false:

5𝑥0 = 1 9𝑥5 ÷ 3𝑥5 = 3𝑥 𝑎5 ÷ 𝑎7 = 𝑎2

2𝑐−4 =1

2𝑐4

Determine and justify whether a simplified expression is correct by substituting numbers for pronumerals Evaluate a numerical fraction raised to the power of -1, leading to

�𝑎𝑏�−1

= 𝑏𝑎

Translate numbers to index form (integer indices only) • Pronumerals • Numbers & pronumerals (combination of laws) •

Problems can include multiple pronumerals eg. 3𝑥2𝑦 × 2𝑥𝑦 = -Just pronumerals -pronumerals mixed with numbers

Year 9 Term 2 Weeks 5-6

Graphing Equations (Gradient / Y-intercept)

Syllabus Reference Outcome

Previous Topic: Graphing equations – table of values Graded Examples

1. What is a gradient?

Ways to express gradient (%, ratio, fraction, angle)

2. Calculate visually as 𝑟𝑖𝑠𝑒𝑟𝑢𝑛

Draw right angled triangles on graph of equation

3. Identify the gradient and the y-intercept on a straight line graph & in an equation

4. Describe, interpret and sketch 𝑦 = 𝑚𝑥 + 𝑏 Recognise 𝑦 = 𝑚𝑥 + 𝑏 as a straight line Graph <-> equation Effect of changing gradient and/or y-intercept on a line (sliders in Geogebra)

5. Identify parallel and perpendicular lines

𝑚 = 𝑚, 𝑚 = −𝑚

Vocab: Gradient Rise Run Y-intercept 𝑚 𝑏 Parallel Perpendicular Plot vs sketch

E

D

C

B

A

Year 9 Term 2 Weeks 8-9 Algebraic Fractions

Syllabus Reference MA5.2-6NA

Graded Examples/Responses

Outcome Simplifies algebraic fractions, and expands and factorises quadratic expressions

• Review operations with fractions • Review simplifying fractions • Simplify algebraic fractions • Operating with algebraic fractions

Using understanding from powers 3 (index laws) Simplify algebraic fractions, including those with indices,

Eg. 10𝑎4

5𝑎2 9𝑎

2𝑏3𝑎𝑏

3𝑎𝑏9𝑎2𝑏

Simplify expressions that involve algebraic fractions, including those with algebraic

E

D

C

B

A

denominators and/or indices eg 2𝑎𝑏3

× 62𝑏

3𝑥2

8𝑦5÷

15𝑥2

4𝑦

𝑎2𝑏4

6×

9𝑎2𝑏2

3𝑥−

12𝑥

Year 9 Term 3 Weeks 1-2

Algebraic Solving (pronumerals both sides)

Syllabus Reference Outcome

MA4-10NA, MA5.2-8NA Uses algebraic techniques to solve simple linear equations. Graded Examples

Review Solving equations (up to 3 step) • Solve linear equations that contain pronumerals on both

sides of the equal sign. Equations may have non-integer solutions.

• Solve linear equations that involve algebraic fractions

• Check solutions to equations by substituting. Examples 2𝑥 = 𝑥 + 5 3𝑥 = 5𝑥 𝑥3 +

𝑥2 = 5

3𝑥5 =

2𝑥9

2𝑥 + 5

3 =𝑥 − 1

4

3(𝑥 + 1) = 2𝑥 (2𝑥 − 5)

3 −𝑥 + 7

5 = 2

E

D

C

B

A

Year 9 Term 3 Weeks 3-4 Volume 2

Syllabus Reference Outcome

MA5.2-12MG Applies formulas to calculate the volumes of composite solids composed of right prisms and cylinders Graded Examples

Prisms & Cylinders

• volumes of composite right prisms with uniform cross section

eg • practical problems related to the volumes and capacities of composite

right prisms • volumes and capacities of various everyday containers, eg. water

tanks or cartons used by removalists • Compare the surface area of prisms with the same volume

Composite Solids

• Dissect into two or more simpler solids to find their volumes

• practical problems related to the volumes and capacities of prisms,

cylinders, right pyramids, right cones and spheres and related composite solids

Pyramids and Cones

• develop and use the formula to find the volumes of right pyramids and right cones

• Volume of pyramid/cone = 13𝐴ℎ where 𝐴 is the base area and ℎ is the

perpendicular height • recognise and use the fact that a pyramid/cone has one-third the

volume of a prism/cylinder with the same base and the same perpendicular height

• deduce that the volume of a cone is given by 𝑉 = 13𝜋𝑟2ℎ

• find the volumes of composite solids that include right pyramids, right cones and hemispheres,

eg find the volume of a cylinder with a cone on top • apply Pythagoras' theorem as needed to calculate the volumes of

pyramids and cones •

Sphere

• use the formula to find the volumes of spheres • Volume of sphere=4

3𝜋𝑟3 where r is the length of the radius

Life Skills Outcome: selects and uses units to estimate and measure volume and capacity

• use informal units to estimate and measure capacity, eg count the number of times a glass can be filled and emptied into a jug

E

D

C

B

A

• use informal units to estimate and measure volume, eg count the number of same-sized marbles required to fill a box, ensuring there are no large spaces

• compare and order the volumes of two or more models by counting the number of blocks used in each model

• recognise the appropriate unit, and its abbreviation, for measuring capacity, eg millilitre (mL), litre (L)

• select and use the appropriate unit and device for measuring volume and capacity, eg a medicine glass for medicine, measuring cups for recipes

• recognise the relationship between commonly used units for measuring volume and capacity, eg 1 L = 1000 mL

• estimate the capacities of everyday objects and check using a measuring device, eg estimate the capacity of a bucket and check using a measuring jug

• identify the concept of volume/capacity in a problem • select and use appropriate strategies, and make calculations, to solve a

problem • convert measurements of volume/capacity in larger units to

measurements in smaller units, eg 3 L = 3000 mL

Year 9 Term 3 Weeks 5-6 Algebra Rearranging

Syllabus Reference Outcome

Graded Examples

Rearrange general form of equation to gradient intercept

3𝑥

= 5

E

D

C

B

A

Year 9 Term 4 Weeks 1-2 Trig 1

Syllabus References Current topic: Stage 5.1 (ACMMG223), (ACMMG224), (ACMMG245) Next Topics: Year 10 Trig 2 – Finding angles, bearings and picture problems Outcomes 1. Correctly label sides relative to angles (letters and names – opp, adj, hyp) 2. Define and use the 3 trig ratios to find missing sides on RA triangles 3. Use trig ratios to solve problems involving elevation and depression

CONTENT…

1. What is Trigonometry? Which occupations use it most? What is it used for?

Revise correct labelling of sides and angles a, b, c and A, B, C (sides opposite angles)

2. Identify adjacent, opposite and hypotenuse sides (relative to given angle) Investigate ratios of sides in similar RA triangles.

3. Define the 3 trig ratios (sine, cosine, tangent)

Use the calculator with trig ratios (sin, cos, tan only not sin-1)

4. Correct setting out of Finding a Missing Side problems (missing side on top only eg 𝑠𝑖𝑛30 = 𝑥6)

- Angles given in degrees only not degrees and minutes

5. Missing side on bottom of ratio problems eg 𝑠𝑖𝑛30 = 6𝑥

Ext: use Pythagoras to calculate the missing side, compare answers to trig ratio answers Ext: investigate 𝑠𝑖𝑛𝜃

𝑐𝑜𝑠𝜃, exact ratios and complimentary ratios (sin & cos) details in Trig 3

6. Use a clinometer to measure angles of elevation and depression

7. Calculate distances using elevation and depression problems

Diagrams provided! Vocab: Trigonometry – triangle measurement Cosine – the compliment of sine Elevation – the angle from the horizontal looking upwards Depression – the angle from the horizontal looking downwards

1. Use your calculator to find the following (correct to 2 decimal places)

a) Sin 30o = ______________ d) 3 Sin 20o = ______________

b) Cos 30o = ______________ e) 6cos30°

= ______________

c) Tan 30o = ______________ f) Tan 14.1o = ______________

2. Label the sides as opposite to 𝜃(O), adjacent to 𝜃 (A) or hypotenuse (H).

3. For the triangle shown, state the length of the side which corresponds to:

a) the side opposite angle 𝜃 _____________

b) the side adjacent to angle 𝛼. _____________

4. Complete the words for each mathematical formulae used in Trigonometry.

S__________ of the angle = _________________

C__________ of the angle = _________________

T__________ of the angle = _________________

5. Label the sides of the triangles below, then, put the correct numbers into the formulae.

Sin _____ = Tan _____ =

Some Old Horse Caught Another Horse Taking Oats Away

Some Old Hippy Came Around Here Tripping on Acid

Some Old Hags Can't Always Hide Their Old Age

Some Out-Houses Can Actually Have Totally Odourless Aromas

Some Old Horses Can Always Hear Their Owner Approach

Some Old Hippie Came a Hopping through Our Apartment

O

H

A

H

O

A

Name: _______________ Class: __________

6. Circle the ratio you would you use to find the length of 𝑥 in each triangle?

7. Rearrange and calculate the value of 𝑥 (to 2 decimal places)

a) sin 50° = 𝑥4 𝑥 =_________________ (rearrange)

𝑥 =_________ (answer)

b) tan 81° = 3𝑥 𝑥 =_________________ (rearrange)

𝑥 =_________ (answer)

8. Use Trigonometry to find the value of 𝑥 in these 3 triangles.

Steps to finding a missing side.

1. Label the sides (O, H, A) 2. Choose the rule (Sine, Cos, Tan) 3. Write out the rule 4. Fill in the numbers 5. Rearrange the rule 6. Solve

a) Sine

b) Cosine

c) Tangent

a) Sine

b) Cosine

c) Tangent

____________________________________

____________________________________

____________________________________

____________________________________

____________________________________

____________________________________

____________________________________

____________________________________

____________________________________

____________________________________

____________________________________

____________________________________

9. A helicopter is hovering at an altitude of 250 metres, and the angle of elevation from the helipad to the helicopter is 35°. Find the horizontal distance of the helicopter from the helipad, to the nearest centimetre.

1. The angle of depression from the top of a 25 metre high viewing tower to a crocodile on the ground is 62°. Find the direct distance from the top of the tower to the crocodile, to the nearest cm.

Choose ONE of the following questions to answer – show all working out

2. Find the length of AB in one of these diagrams:

3. Draw a diagram and calculate the height of the taller building to the nearest metre. The distance between two buildings is 24.5 metres. The angle of elevation from the base of the shorter building to the top of the taller building is 85° and the height of the shorter building is 40 m.

Choose ONE of the following questions to answer – show all working out

1. Find the Perimeter of this triangle (to 1 decimal place).

2. Find the value of 𝑥 (to 1 decimal place).

3. Two unidentified flying discs are detected by a receiver. The angle of elevation from the receiver to each disc is 39.48°. The discs are hovering at a direct distance of 826 m and 1.296 km from the receiver. Find the difference in height between the two unidentified flying discs to the nearest metre.

Year 9 Term 4 Weeks 4-5

Inequations (solving and graphing)

Syllabus Reference Outcome

Previous topics: 3 step equations, substitution, pronumerals on both sides, algebraic fractions NA236 Graded Examples

1. Reading the symbols

Words for the symbols, <, >, ≤, ≥, =, ≠ With numbers 5 > 4, with numbers and operators 4 + 3 > 6 demonstrate infinite solutions 𝑥 > 2, 𝑥 ≤ −7

2. Graph & check with substitution

𝑥 > 2, 𝑥 ≤ 7, 𝑥 <25

, 𝑥 ≥ 347

, 𝑥 < 0.3

Sets: −2 < 𝑥 ≤ 3, 𝑥 < 2 𝑎𝑛𝑑 𝑥 ≥ 3

3. Solve, graph and check with substitution 1 step + and – eg 𝑥 + 5 < 8, − 12 + 𝑚 < −7 1 step x and ÷ eg 5𝑥 ≥ 15, 𝑥

3≥ 4

Change the sign rule when x or ÷ by negative eg 5 < 8 → −5 > −8, 𝑖𝑓 − 𝑥 > 1 𝑡ℎ𝑒𝑛 𝑥 < −1 2 step no sign change eg 3𝑚 − 7 < 11, 2𝑥

5≤ 8

2 step sign change eg 4 − 3𝑥 > −8 Answers in fract/dec form 3 step eg 2𝑥+6

7< 4, 4(𝑥 + 2) < 12

Include algebraic fractions eg 2𝑥 + 13

> 𝑥4

Pronumerals both sides eg 2𝑥 + 9 ≤ 6𝑥 − 1 1 + 𝑥

2<𝑥 − 1

3

Integers which satisfy 2 equations eg 2𝑥 + 1 ≤ 5 𝑎𝑛𝑑 5 − 2𝑥 ≤ 5

4. Word problems

Ext: Graphing regions on number plane Ext: solve 1 ≤ 𝑥 − 2 ≤ 7, − 2.5 < 5 − 2𝑥 ≤ 3 Vocab: Inequality Greater than Less than Equation Solve Pronumeral Integer Solution Graph on a number line Substitute

E True or false 5 > 4 4 + 3 > 6 Write “four is less than six” in symbols.

D Give some solutions for 𝑥 > 2 𝑥 ≤ −7 If x is a number greater than negative three, what are three possible numbers x could stand for?

C Solve & graph up to 3 step equations Incl sign changes & algebraic fractions Solve and graph with pronumerals both sides B

Solve 1+𝑥2

< 𝑥−13

Integers which satisfy 2 equations eg 2𝑥 + 1 ≤ 5 𝑎𝑛𝑑 5 − 2𝑥 ≤ 5

A

Inequations Test Name................................ Class.................

E GRADE

1. Answer true or false for the following statements a. 5>3

b. 2+4≤ 7

c. Five is less than x.,is written as 5>x 2. State the meaning of the following symbols

a. > ....................................

b. ≤ ....................................

3. Write “x is less than four” using symbols ........................................... 4. If x is greater than 4, what are 2 possible values for x ? ............ ........... 5. Graph on a number line, where x >2

D GRADE

6. Solve then Graph on a number line , the solution to 𝑥 + 2 > 5

7. What solution is the number line below showing

8. Show on a number line,the following inequalities 𝑥 < 1 𝑎𝑛𝑑 𝑥 ≥ 3

9. Solve and graph 2𝑥 ≥ 5

C GRADE

10. Solve & graph the following inequalities a. 2𝑥 + 1 < 7

b. 3𝑥 − 4 ≥ −4

c. 1+𝑥2≤ 2

d. Write as an inequality “𝑡ℎ𝑒 𝑠𝑢𝑚 𝑜𝑓 3𝑥 𝑎𝑛𝑑 7 𝑖𝑠 𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛 𝑡ℎ𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 2𝑥 𝑎𝑛𝑑 4"

B GRADE

11. Solve and graph the following a. 2 − 3𝑥 < 8

b. 3𝑥 − (−1) < 4 − 2𝑥

c. −1 < 𝑥 − 2 ≤ 4

d. 4−3𝑥−2

≥ 3 (do not graph)

A GRADE

12. Solve the following inequalities

a.2𝑥+13

> 𝑥4

b. 3𝑥−2

< 12

c. Graph on an x-y number plane, the following region(shade in the correct space)

2𝑥 − 𝑦 ≤ 4

Year 9 Term 4 Weeks 1-3

Probability 3 (Multi-stage Events)

Syllabus References Current topic: Stage (ACMSP225), (ACMSP292) Next Topics: Year 10 Prob 4 – Outcomes 1. Venn diagrams (up to 3 attributes) – and, or, not 2. 2 Way Tables 3. Systematic Methods of listing outcomes for Multi-stage Events

CONTENT…

NOTE: (Connections Maths 10 5.3/5.2/5.1 is a good resource for Venn Diagrams and Two-Way tables) 1. Venn Diagrams – up to 3 attributes

Ext: Set notation

2. 2 Way Tables Interpret, complete, convert between 2 way tables and Venn diagrams(not in syllabus)

3. Compound Events – 2 or 3 step Experiments

With/without replacement, relative frequency (and/or events)

4. Systematic methods to list outcomes Tree diagrams, arrays, tables, lists

5. Theoretical Probability calculations from diagrams No fractions or probs used on diagrams

E Grade

Pr(𝑇𝑇) =12

Year 9 Term 4

Weeks 4-5 Data 4

Syllabus Reference MA5.2-15SP

Outcome Uses quartiles and box plots to compare sets of data, and evaluates sources of data Graded Examples/Responses

• Determine the upper and lower extremes, median, and

upper and lower quartiles for sets of numerical data (five-number summary) o Describe the proportion of data values contained

between various quartiles, e.g. 75% of data values lie between the lower quartile and the upper extreme

• Determine the interquartile range for sets of data o Recognise that the interquartile range is a measure of

spread of the middle 50% of the data • Compare the relative merits of the range and the

interquartile range as measures of spread o Explain whether the range or interquartile range is a

better measure of spread for particular sets of data

• Construct and interpret box plots and use them to compare data sets o using the median, upper and lower quartiles, upper and

lower extremes of a set of data o comparison of two or more sets of data using parallel

box plots on the same scale e.g. describe differences in spread using

interquartile range, and suggest reasons for such differences

• Compare shapes of box plots to corresponding histograms

and dot plots o Determine quartiles from data displayed in histograms

and dot plots, and use these to draw a box plot to represent the same set of data Compare the relative merits of a box plot with its

corresponding histogram or dot plot o Identify skewed and symmetrical sets of data displayed

in histograms and dot plots, and describe the shape/features of the corresponding box plot for such sets of data

E

Determines the upper and lower extremes of a set of data.

D

Given a five-number summary constructs a box plot. Determines the median of a set of data. Determines the range of a set of data. C

Determines five-number summary from a set of data and constructs a box plot. Determines the interquartile range of a set of data. B

A

Year 9 Term 4 Weeks 6-7 Scientific Notation

Syllabus Reference Outcome

MA5.1-9MG interprets very small and very large units of measurement, uses scientific notation, and rounds to significant figures Graded Examples

Express numbers in scientific notation • recognise the need for a notation to express very large or very small numbers • express numbers in scientific notation explain the difference between numerical expressions

such as 2 × 104 and 24 • enter and read scientific notation on a calculator • use index laws to make order of magnitude checks for numbers in scientific notation, eg (3.12 × 104) × (4.2 × 106) ≈ 12 × 1010 = 1.2 × 1011 • convert numbers expressed in scientific notation to decimal form • order numbers expressed in scientific notation • solve problems involving scientific notation communicate and interpret technical information using

scientific notation

E

D

C

B

A

Year 9 Term 4 Weeks 8-9 Simultaneous Equations

Syllabus Reference Outcome

Solves linear simultaneous equations, using analytical and graphical techniques MA5.2-8NA Graded Examples

1. What are simultaneous equations?

Recognise that 𝑚 + 3𝑏 = 5 has infinite solutions Lead towards solving 𝑚 + 3𝑏 = 5 and 2𝑚 − 𝑏 = 4 at the same time.

2. Graphical Method of solving 2 linear equations (**Revise gradient-intercept method first**) Sketch lines given 2 or more points Sketch lines given equation in intercept & general form Find the point of intersection

3. Solve linear simultaneous equations using algebraic methods

Substitution

4. Solve word problems that involve sim eqns

E Look at 2 lines on a graph and identify the point at which they intersect.

D Sketch 2 linear equations and identify the point at which they intersect. Solve thru substitution: 𝑦 = 2 𝑥 + 𝑦 = 7

C Solve thru substitution: 𝑦 = 2𝑥 + 3 𝑦 = 6𝑥 − 7

𝑦 = 3𝑥 + 1 2𝑦 + 3𝑥 = 10

B Solve thru substitution: 3𝑥 + 6𝑦 = 10 2𝑥 + 𝑦 = 5

A Solve algebraically: 2𝑥 + 5𝑦 = 10 3𝑥 − 2𝑦 = −6

Language- Solution, Substitution, Intersection, Equation, Algebraic, Graphic

Year 9 Term 4 Weeks 10 Taxable Income

Syllabus Reference Outcome

Previous topic: Money 1 (earning an income), Percentages 2 / Money 2 (GST, simple interest)

Graded Examples

1. Who pays Tax? Why do we pay Tax? How do we pay Tax? GST, BAS, Tax returns, Financial Year

2. Calculating Taxable income Deductions, gross & net income, rebates and levies incl. Medicare, Family Tax Benefit etc.

3. Calculating Tax Payable Refunds, liability, PAYG, tax rates, forms

http://www.ato.gov.au/Rates/Individual-income-tax-rates/ Vocab: PAYG Refund Liability GST Gross Net Deduction BAS Financial year Rebate Levy Tax return

E

D

C

B

A