Used for LANTITE preparation (Australia). NA = Number & Algebra strand. SP = Statistics & Probability strand. Students read a percentage from the chart, and calculate that percentage of the number of children (randomly generated).

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

The student is presented with a scenario then asked to select a sample size to investigate and the number of bins for a histogram of the data. Theoretical distributions of normal, uniform and lognormal distributions can be overlayed on the histogram. Student is asked to identify the most likely distribution and the mean of this distribution (within a +/-10% margin of error).

Find the derivative of a function of the form $y=ax^b$ using a table of derivatives.

3 Repeated integrals of the form $\int_a^b\;\int_c^{f(x)}g(x,y)\;dy \;dx$ where $g(x,y)$ is a polynomial in $x,\;y$ and $f(x)$ is a degree 0, 1 or 2 polynomial in $x$.

Calculate a repeated integral of the form $\displaystyle I=\int_0^1\;\int_0^{x^{m-1}}mf(x^m+a)dy \;dx$

The $y$ integral is trivial, and the $x$ integral is of the form $g'(x)f'(g(x))$, so it straightforwardly integrates to $f(g(x))$.

Cálculo de forma normal reducida por filas.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

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Retrieval practivce after pre-class activities

Given th original formula the student enters the transformed formula

Given the graph the student enters the  formula

Ready to use

Given th original formula the student enters the transformed formula

Ready to use

Given th original formula the student enters the transformed formula

Ready to use

Given the original formula the student enters the transformed formula

Ready to use

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Given the original formula the student enters the transformed formula

Ready to use

Given the original formula the student enters the transformed formula.

READY TO USE

Solving a differential equation of the form $\frac{dy}{dx}=\frac{ax^n}{y}$ using separation of variables.

Solving a differential equation of the form $\frac{dy}{dx}=axy^2$ using separation of variables.

Solving a differential equation of the form $\frac{dy}{dx}=axy$ using separation of variables.

Calculating the integral of a function of the form $4ax(ax^2+b)^n$ using integration by substitution.

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Integrating a function of the form $\frac{a}{x}$ using a table of integrals / anti-derivatives.

Given a discrete random variable (as a formula) calculate:
E(X), Var, std dev, cumulative distribution and probabilties.