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Your search for "compare data with predictions and use as evidence in developing explanations" returned 53 result(s)

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ACMSM005

determine and use the formulas for finding the number of elements in the union of two and the union of three sets.

ACMSM052

define and use addition and subtraction of matrices, scalar multiplication, matrix multiplication, multiplicative identity and inverse

ACMSM082

define and use multiplication, division, and powers of complex numbers in polar form and the geometric interpretation of these

ACMSM098

use and apply the notation \(\left|x\right|\) for the absolute value for the real number \(x\) and the graph of \(y=\left|x\right|\)

ACMSM104

use vector equations of curves in two or three dimensions involving a parameter, and determine a ‘corresponding’ Cartesian equation in the two-dimensional case

ACMSM109

recognise the general form of a system of linear equations in several variables, and use elementary techniques of elimination to solve a system of linear equations

ACMSM118

establish and use the formula \(\int\frac1xdx=\ln{\;\vert x\;\vert}+c\) for x ≠ 0

ACMSM128

use implicit differentiation to determine the gradient of curves whose equations are given in implicit form

ACMSM142

use simulation to illustrate variations in confidence intervals between samples and to show that most but not all confidence intervals contain \(\mu\)

ACMSM117

use substitution \(u = g(x)\) to integrate expressions of the form \(f\left(g\left(x\right)\right)g'\left(x\right)\)

ACMSM080

use the modulus \(\left|z\right|\) of a complex number z and the argument \(Arg\;(z)\) of a non-zero complex number \(z\) and prove basic identities involving modulus and argument

define and use basic linear transformations: dilations of the form \((\mathrm x,\mathrm y)\longrightarrow({\mathrm\lambda}_1\mathrm x,{\mathrm\lambda}_2\mathrm y)\) , rotations about the origin and reflection in a line which passes through the origin, …

ACMSM136

consider and solve problems involving motion in a straight line with both constant and non-constant acceleration, including simple harmonic motion and the use of expressions \(\frac{dv}{dt}\), \(v\frac{dv}{dx}\) and \(\frac{d(\frac12v^2)}{dx}\) for a …