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Skills available for Australia year 12 maths curriculum

Objectives are in black and IXL maths skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practise that skill.

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11-12.1.1 Combinatorics

11-12.1.2 Vectors in the plane

11-12.1.3 Geometry

  • 11-12. The nature of proof:

  • 11-12. Circle properties and their proofs including the following theorems:

  • 11-12. Geometric proofs using vectors in the plane including:

    • 11-12.ACMSM039 The diagonals of a parallelogram meet at right angles if and only if it is a rhombus

    • 11-12.ACMSM040 Midpoints of the sides of a quadrilateral join to form a parallelogram

    • 11-12.ACMSM041 The sum of the squares of the lengths of the diagonals of a parallelogram is equal to the sum of the squares of the lengths of the sides.

11-12.2.1 Trigonometry

11-12.2.2 Matrices

11-12.2.3 Real and complex numbers

11-12.3.1 Complex numbers

11-12.3.2 Functions and sketching graphs

11-12.3.3 Vectors in three dimensions

11-12.4.1 Integration and applications of integration

  • 11-12. Integration techniques:

    • 11-12.ACMSM116 integrate using the trigonometric identities sin²x = ½(1–cos 2x), cos²x = ½(1+cos2x) and 1+ tan²x = sec²x

    • 11-12.ACMSM117 use substitution u = g(x) to integrate expressions of the form f(g(x))g'(x)

    • 11-12.ACMSM118 establish and use the formula ∫1/x dx = ln |x|+ c, for x ≠ 0

    • 11-12.ACMSM119 find and use the inverse trigonometric functions: arcsine, arccosine and arctangent

    • 11-12.ACMSM120 find and use the derivative of the inverse trigonometric functions: arcsine, arccosine and arctangent

    • 11-12.ACMSM121 integrate expressions of the form ±1/√a² –x² and a/(a² + x²)

    • 11-12.ACMSM122 use partial fractions where necessary for integration in simple cases

    • 11-12.ACMSM123 integrate by parts.

  • 11-12. Applications of integral calculus:

    • 11-12.ACMSM124 calculate areas between curves determined by functions

    • 11-12.ACMSM125 determine volumes of solids of revolution about either axis

    • 11-12.ACMSM126 use numerical integration using technology

    • 11-12.ACMSM127 use and apply the probability density function, f(t) = λe to the –λt power for t ≥ 0, of the exponential random variable with parameter λ > 0, and use the exponential random variables and associated probabilities and quantiles to model data and solve practical problems.

11-12.4.2 Rates of change and differential equations

  • 11-12. Rates of change and differential equations

    • 11-12.ACMSM128 use implicit differentiation to determine the gradient of curves whose equations are given in implicit form

    • 11-12.ACMSM129 Related rates as instances of the chain rule: dy/dx = dy/du × du/dx

    • 11-12.ACMSM130 solve simple first-order differential equations of the form dy/dx = f(x), differential equations of the form dy/dx = g(y) and, in general, differential equations of the form dy/dx = f(x)g(y) using separation of variables

    • 11-12.ACMSM131 examine slope (direction or gradient) fields of a first order differential equation

    • 11-12.ACMSM132 formulate differential equations including the logistic equation that will arise in, for example, chemistry, biology and economics, in situations where rates are involved

  • 11-12. Modelling motion:

    • 11-12.ACMSM133 examine momentum, force, resultant force, action and reaction

    • 11-12.ACMSM134 consider constant and non-constant force

    • 11-12.ACMSM135 understand motion of a body under concurrent forces

    • 11-12.ACMSM136 consider and solve problems involving motion in a straight line with both constant and nonconstant acceleration, including simple harmonic motion and the use of expressions dv/dt,v(dv/dx) and (d(½v²)/dx for acceleration.

11-12.4.3 Statistical inference

  • 11-12. Sample means:

    • 11-12.ACMSM137 examine the concept of the sample mean X as a random variable whose value varies between samples where X is a random variable with mean μ and the standard deviation σ

    • 11-12.ACMSM138 simulate repeated random sampling, from a variety of distributions and a range of sample sizes, to illustrate properties of the distribution of X across samples of a fixed size n, including its mean μ, its standard deviation σ/√n(where μ and σ are the mean and standard deviation of X), and its approximate normality if n is large

    • 11-12.ACMSM139 simulate repeated random sampling, from a variety of distributions and a range of sample sizes, to illustrate the approximate standard normality of X–μ/s √n for large samples (n ≥ 30), where s is the sample standard deviation.

  • 11-12. Confidence intervals for means:

    • 11-12.ACMSM140 understand the concept of an interval estimate for a parameter associated with a random variable

    • 11-12.ACMSM141 examine the approximate confidence interval (X – zs/√n, X + zs/√n), as an interval estimate for μ, the population mean, where z is the appropriate quantile for the standard normal distribution

    • 11-12.ACMSM142 use simulation to illustrate variations in confidence intervals between samples and to show that most but not all confidence intervals contain μ

    • 11-12.ACMSM143 use x and s to estimate μ and σ, to obtain approximate intervals covering desired proportions of values of a normal random variable and compare with an approximate confidence interval for μ

    • 11-12.ACMSM144 collect data and construct an approximate confidence interval to estimate a mean and to report on survey procedures and data quality.