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Skill map
Mathematical Methods
Matrices and plane transformations
Chapter 7
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RESTS ON
Multiplication and division
CH 2
Signed numbers
CH 2
Decimal place value
FOUNDATIONS
Solve two-step linear equations by inverse operations in reverse order
CH 1
Solve a one-step linear equation
FOUNDATIONS
Simplify a fraction
CH 2
Solve equations with unknowns on both sides by collecting them onto one side
CH 1
Check a claimed solution or point by substituting into the original equation
CH 1
Identify the intercept and slope in y = a + bx, including its edge shapes
CH 1
Transformed graphs and matrices
Plane transformations and matrices
Composing plane transformations
Identify a translation, reflection, dilation or simple affine combination from its coordinate rule, matrix-and-vector data or mapped point pairs
Determine the rule of an image relation by expressing the pre-image coordinates in terms of image coordinates and substituting exactly
Determine or verify a point fixed by a stated affine transformation, subject to the stated domain
Substitute known values into a formula and evaluate it correctly
Interpret f, f(x), image, preimage, rule, domain and co-domain; evaluate a function at a stated exact input and solve a simple equation of the form f(x)=c
Multiply and divide fractions
Write a pair of linear equations as a matrix equation
Solve a matrix equation by left-multiplying by the inverse
Apply the 2 × 2 inverse rule
Solve a pair of simultaneous linear equations for the shared (x, y)
Recognise from equal slopes that a system has no solution or every point
Read the point of intersection of two graphed lines
Apply an affine map in the exact form p′ = M p + t to a point and reverse it when the inverse map is supplied or constructible
Apply or recover a translation vector and distinguish the direction from pre-image to image
Apply and recognise reflections in either coordinate axis, in the line y = x, and in a line parallel to a coordinate axis
Apply and recognise one-axis and two-axis dilations about the origin, using both VCAA descriptions “parallel to an axis” and “from an axis”
Transform every column of a coordinate matrix while preserving vertex labels and order
Represent a finite labelled set of plane points with each point as a column, and recover labelled points from that representation
Multiply matrices by pairing rows with columns and summing the products
Add or subtract matrices entry by corresponding entry
State the order of a matrix as rows × columns
Address an element by row and column subscripts, in both directions
Classify row, column, square, symmetric and zero matrices
Decide whether a sum or difference of matrices is defined
Use the zero matrix's behaviour under addition and subtraction
Multiply every entry of a matrix by a scalar
Evaluate a combination of scalar multiples of two matrices
Test whether a matrix product is defined from the inner numbers
State a matrix product's order from the outer numbers
Recognise that matrix multiplication is not commutative
Use the identity matrix and its unchanged products
Calculate the determinant of a 2 × 2 matrix
Recognise that a matrix with determinant zero has no inverse
Define the inverse as the matrix that multiplies to the identity
Read coordinates off a graphed line respecting its axis scales
Replace two successive affine maps by the exact composite matrix and translation vector
Apply transformations in the stated chronological order and recognise that reversing the order can change the image
Raise a square matrix to a power by repeated multiplication