Why us?AboutParent PlusSign in / Create account

Year 11: Mathematics Methods ATAR

Listed Mathematics syllabus content points at Year 11 Β· Units 1 and 2, in the words of the School Curriculum and Standards Authority (SCSA), Western Australia, with the practice on this site that covers it. Checked against the source on 4 September 2026.

For teaching from 2026. Mathematical notation is flattened out of the syllabus PDF, so fractions and indices read on one line here. The wording is the syllabus's own.

  • 93syllabus content points
  • 118skills mapped
  • 99%have practice

Coverage is the percentage of listed syllabus content points with at least one linked practice skill; it does not measure how fully every part of an entry is practised. A skill can practise more than one syllabus content point, so some appear more than once below.

Topic 1.1: Counting and probability

  1. 1.1.1understand the notion of a combination as a set of π‘Ÿ objects taken from a set of 𝑛 distinct objects

  2. 1.1.2use the notation ( 𝑛 π‘Ÿ ) and the formula ( 𝑛 π‘Ÿ ) = 𝑛! π‘Ÿ!(π‘›βˆ’π‘Ÿ)! for the number of combinations of π‘Ÿ objects taken from a set of 𝑛 distinct objects

  3. 1.1.3investigate Pascal’s triangle and its properties to link ( 𝑛 π‘Ÿ ) to the binomial coefficients of the expansion of (π‘₯ + 𝑦)𝑛 for small positive integers 𝑛

  4. 1.1.4review the concepts and language of outcomes, sample spaces, and events, as sets of outcomes

  5. 1.1.5use set language and notation for events, including: a. 𝐴̅ (or 𝐴′ ) for the complement of an event 𝐴 b. 𝐴 ∩ 𝐡 and 𝐴 βˆͺ 𝐡 for the intersection and union of events 𝐴 and 𝐡 respectively c. 𝐴 ∩ 𝐡 ∩ 𝐢 and 𝐴 βˆͺ 𝐡 βˆͺ 𝐢 for the intersection and union respectively of the three events 𝐴, 𝐡 and 𝐢 d. recognise mutually exclusive events

  6. 1.1.6use everyday occurrences to illustrate set descriptions and representations of events and set operations

  7. 1.1.7review probability as a measure of β€˜the likelihood of occurrence’ of an event

  8. 1.1.8review the probability scale: 0 ≀ 𝑃(𝐴) ≀ 1 for each event 𝐴, with 𝑃(𝐴) = 0 if 𝐴 is an impossibility and 𝑃(𝐴) = 1 if 𝐴 is a certainty

  9. 1.1.9review the rules: 𝑃(A Μ…) = 1 βˆ’ 𝑃(𝐴) and 𝑃(𝐴 βˆͺ 𝐡) = 𝑃(𝐴) + 𝑃(𝐡) βˆ’ 𝑃(𝐴 ∩ 𝐡)

  10. 1.1.10use relative frequencies obtained from data as estimates of probabilities

  11. 1.1.11understand the notion of a conditional probability and recognise and use language that indicates conditionality

  12. 1.1.12use the notation 𝑃(𝐴|𝐡) and the formula 𝑃(𝐴 ∩ 𝐡) = 𝑃(𝐴|𝐡)𝑃(𝐡)

  13. 1.1.13understand the notion of independence of an event A from an event B, where 𝑃(𝐴|𝐡) = 𝑃(𝐴)

  14. 1.1.14establish and use the formula 𝑃(𝐴 ∩ 𝐡) = 𝑃(𝐴)𝑃(𝐡) for independent events 𝐴 and 𝐡, and recognise the symmetry of independence

  15. 1.1.15use relative frequencies obtained from data as estimates of conditional probabilities and as indications of possible independence of events

Topic 1.2: Functions and graphs

  1. 1.2.1recognise features of the graph of 𝑦 = π‘šπ‘₯ + 𝑐, including its linear nature, its intercepts and its slope or gradient

  2. 1.2.2determine the equation of a straight line given sufficient information, including for parallel and perpendicular lines

  3. 1.2.3examine examples of quadratically related variables

  4. 1.2.4recognise features of the graphs of 𝑦 = π‘₯2 , 𝑦 = π‘Ž(π‘₯ βˆ’ 𝑏)2 + 𝑐, and 𝑦 = π‘Ž(π‘₯ βˆ’ 𝑏)(π‘₯ βˆ’ 𝑐), including their parabolic nature, turning points, axes of symmetry and intercepts

  5. 1.2.5solve quadratic equations, including the use of quadratic formula and completing the square

  6. 1.2.6determine the equation of a quadratic given sufficient information

  7. 1.2.7determine turning points and zeros of quadratics and understand the role of the discriminant

  8. 1.2.8recognise features of the graph of the general quadratic 𝑦 = π‘Žπ‘₯^2 + 𝑏π‘₯ + 𝑐

  9. 1.2.9examine the concept of inverse proportion

  10. 1.2.10recognise features and determine equations of the graphs of 𝑦 = π‘₯ and 𝑦 = π‘Ž π‘₯βˆ’π‘ , including their hyperbolic shapes and their asymptotes.

  11. 1.2.11recognise features of the graphs of 𝑦 = π‘₯^𝑛 for 𝑛 ∈ 𝑡, 𝑛 = βˆ’1 and 𝑛 = Β½, including shape, and behaviour as π‘₯ β†’ ∞ and π‘₯ β†’ βˆ’βˆž

  12. 1.2.12identify the coefficients and the degree of a polynomial

  13. 1.2.13expand factors to obtain quadratic and cubic polynomials

  14. 1.2.14recognise features and determine equations of the graphs of 𝑦 = π‘₯3 , 𝑦 = π‘Ž(π‘₯ βˆ’ 𝑏)3 + 𝑐 and 𝑦 = π‘˜(π‘₯ βˆ’ π‘Ž)(π‘₯ βˆ’ 𝑏)(π‘₯ βˆ’ 𝑐), including shape, intercepts and behaviour as π‘₯ β†’ ∞ and π‘₯ β†’ βˆ’βˆž

  15. 1.2.15factorise cubic polynomials in cases where all roots are given or easily obtained from the graph

  16. 1.2.16solve cubic equations using technology, and algebraically in cases where all roots are given or easily obtained from the graph

  17. 1.2.17recognise features and determine equations of the graphs of π‘₯2 + 𝑦2 = π‘Ÿ2 and (π‘₯ βˆ’ π‘Ž)2 + (𝑦 βˆ’ 𝑏)2 = π‘Ÿ2 , including their circular shapes, their centres and their radii

  18. 1.2.18recognise features of the graph of 𝑦2 = π‘₯, including its parabolic shape and its axis of symmetry

  19. 1.2.19understand the concept of a function as a mapping between sets and as a rule or a formula that defines one variable quantity in terms of another

  20. 1.2.20use function notation; determine domain and range; recognise independent and dependent variables

  21. 1.2.21understand the concept of the graph of a function

  22. 1.2.22examine translations and the graphs of 𝑦 = 𝑓(π‘₯) + π‘Ž and 𝑦 = 𝑓(π‘₯ βˆ’ 𝑏)

  23. 1.2.23examine dilations and the graphs of 𝑦 = 𝑐𝑓(π‘₯) and 𝑦 = 𝑓(𝑑π‘₯)

  24. 1.2.24recognise the distinction between functions and relations and apply the vertical line test

Topic 1.3: Trigonometric functions

  1. 1.3.1review sine, cosine and tangent as ratios of side lengths in right-angled triangles

  2. 1.3.2understand the unit circle definition of cos πœƒ, sin πœƒ and tan πœƒ and periodicity using degrees

  3. 1.3.3examine the relationship between the angle of inclination of a line and the gradient of that line

  4. 1.3.4establish and use the cosine and sine rules, including consideration of the ambiguous case and the formula π΄π‘Ÿπ‘’π‘Ž = (1/2)𝑏𝑐 sin 𝐴 for the area of a triangle

  5. 1.3.5define and use radian measure and understand its relationship with degree measure

  6. 1.3.6use radian measure to calculate lengths of arcs and areas of sectors and segments in a circle

  7. 1.3.7understand the unit circle definition of sinπœƒ, cosπœƒ and tan πœƒ and periodicity using radians

  8. 1.3.8recognise the exact values of sinπœƒ, cosπœƒ and tan πœƒ at integer multiples of πœ‹ and πœ‹

  9. 1.3.9recognise the graphs of 𝑦 = sinπ‘₯, 𝑦 = cos π‘₯ , and 𝑦 = tan π‘₯ on extended domains

  10. 1.3.10examine amplitude changes and the graphs of 𝑦 = π‘Ž sin π‘₯ and 𝑦 = π‘Ž cos π‘₯

  11. 1.3.11examine period changes and the graphs of 𝑦 = sin 𝑏π‘₯, 𝑦 = cos 𝑏π‘₯ and 𝑦 = tan 𝑏π‘₯

  12. 1.3.12examine phase changes and the graphs of 𝑦 = sin(π‘₯ βˆ’ 𝑐), 𝑦 = cos(π‘₯ βˆ’ 𝑐) and 𝑦 = tan (π‘₯ βˆ’ 𝑐)

  13. 1.3.13examine the relationships sin(π‘₯ + πœ‹ ) = cos π‘₯ and cos (π‘₯ βˆ’ πœ‹ ) = sinπ‘₯

  14. 1.3.14prove and apply the angle sum and difference identities

  15. 1.3.15identify contexts suitable for modelling by trigonometric functions and use them to solve practical problems

  16. 1.3.16solve equations involving trigonometric functions using technology, and algebraically in simple cases

Topic 2.1: Exponential functions

  1. 2.1.1review indices (including fractional and negative indices) and the index laws

  2. 2.1.2use radicals and convert to and from fractional indices

  3. 2.1.3understand and use scientific notation and significant figures

  4. 2.1.4establish and use the algebraic properties of exponential functions

  5. 2.1.5recognise the qualitative features of the graph of 𝑦 = π‘Ž^π‘₯ (π‘Ž > 0), including asymptotes, and of its translations (𝑦 = π‘Ž^π‘₯ + 𝑏 and 𝑦 = π‘Ž^(π‘₯βˆ’π‘))

  6. 2.1.6identify contexts suitable for modelling by exponential functions and use them to solve practical problems

  7. 2.1.7solve equations involving exponential functions using technology, and algebraically in simple cases

Topic 2.2: Arithmetic and geometric sequences and series

  1. 2.2.1recognise and use the recursive definition of an arithmetic sequence: 𝑑_(𝑛+1) = 𝑑_𝑛 + 𝑑

  2. 2.2.2develop and use the formula 𝑑_𝑛 = 𝑑_1 + (𝑛 βˆ’ 1)𝑑 for the general term of an arithmetic sequence and recognise its linear nature

  3. 2.2.3use arithmetic sequences in contexts involving discrete linear growth or decay, such as simple interest

  4. 2.2.4establish and use the formula for the sum of the first 𝑛 terms of an arithmetic sequence

  5. 2.2.5recognise and use the recursive definition of a geometric sequence: 𝑑_(𝑛+1) = 𝑑_𝑛 π‘Ÿ

  6. 2.2.6develop and use the formula 𝑑_𝑛 = 𝑑_1 π‘Ÿ^(π‘›βˆ’1) for the general term of a geometric sequence and recognise its exponential nature

  7. 2.2.7understand the limiting behaviour as 𝑛 β†’ ∞ of the terms 𝑑_𝑛 in a geometric sequence and its dependence on the value of the common ratio π‘Ÿ

  8. 2.2.8establish and use the formula 𝑆_𝑛 = 𝑑_1(π‘Ÿ^𝑛 βˆ’ 1)/(π‘Ÿ βˆ’ 1) for the sum of the first 𝑛 terms of a geometric sequence

  9. 2.2.9use geometric sequences in contexts involving geometric growth or decay, such as compound interest

Topic 2.3: Introduction to differential calculus

  1. 2.3.1interpret the difference quotient 𝑓(π‘₯+β„Ž)βˆ’π‘“(π‘₯) β„Ž as the average rate of change of a function 𝑓

  2. 2.3.2use the Leibniz notation 𝛿π‘₯ and 𝛿𝑦 for changes or increments in the variables π‘₯ and 𝑦

    No practice for this one yet.

  3. 2.3.3use the notation 𝛿𝑦 𝛿π‘₯ for the difference quotient 𝑓(π‘₯+β„Ž)βˆ’π‘“(π‘₯) β„Ž where 𝑦 = 𝑓(π‘₯)

  4. 2.3.4interpret the ratios 𝑓(π‘₯+β„Ž)βˆ’π‘“(π‘₯) β„Ž and 𝛿𝑦 𝛿π‘₯ as the slope or gradient of a chord or secant of the graph of 𝑦 = 𝑓(π‘₯)

  5. 2.3.5examine the behaviour of the difference quotient 𝑓(π‘₯+β„Ž)βˆ’π‘“(π‘₯) β„Ž as β„Ž β†’ 0 as an informal introduction to the concept of a limit

  6. 2.3.6define the derivative 𝑓′(π‘₯) as lim β„Žβ†’0 𝑓(π‘₯+β„Ž)βˆ’π‘“(π‘₯) β„Ž

  7. 2.3.7use the Leibniz notation for the derivative: 𝑑𝑦/𝑑π‘₯ = lim_(𝛿π‘₯β†’0) 𝛿𝑦/𝛿π‘₯ and the correspondence 𝑑𝑦/𝑑π‘₯ = 𝑓′(π‘₯) where 𝑦 = 𝑓(π‘₯)

  8. 2.3.8interpret the derivative as the instantaneous rate of change

  9. 2.3.9interpret the derivative as the slope or gradient of a tangent line of the graph of 𝑦 = 𝑓(π‘₯)

  10. 2.3.10estimate numerically the value of a derivative for simple power functions

  11. 2.3.11examine examples of variable rates of change of non-linear functions

  12. 2.3.12establish the formula 𝑑/𝑑π‘₯ (π‘₯^𝑛) = 𝑛π‘₯^(π‘›βˆ’1) for non-negative integers 𝑛 by expanding (π‘₯ + β„Ž)^𝑛 or by factorising (π‘₯ + β„Ž)^𝑛 βˆ’ π‘₯^𝑛

  13. 2.3.13understand the concept of the derivative as a function

  14. 2.3.14identify and use linearity properties of the derivative

  15. 2.3.15calculate derivatives of polynomial functions

  16. 2.3.16determine instantaneous rates of change

  17. 2.3.17determine the slope of a tangent and the equation of the tangent

  18. 2.3.18construct and interpret position-time graphs with velocity as the slope of the tangent

  19. 2.3.19recognise velocity as the first derivative of displacement with respect to time

  20. 2.3.20sketch curves associated with simple polynomials, determine stationary points, and local and global maxima and minima, and examine behaviour as π‘₯ β†’ ∞ and π‘₯ β†’ βˆ’βˆž

  21. 2.3.21solve optimisation problems arising in a variety of contexts involving polynomials on finite interval domains

  22. 2.3.22calculate anti-derivatives of polynomial functions

Other Year 11 skills

Year 11 skills not currently linked to an entry on this page. These may include revision, extension practice, or skills still awaiting a curriculum mapping.

Copyright Β© 2023-2026 Mathpractice.xyz and Oloum.xyz (ABN: 39 786 035 724). All rights reserved.