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• Attempt the following easy tasks

this is a simple testing task

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• Cost and profit functions

Calculate the marginal and average cost for a given cost function. Find the corresponding startup/shutdown price.
Maximize the profit function at a given price.

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• Algebra: Solving quadratics by factorising

Some quadratics are to be solved by factorising

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• Algebra: Solving quadratics by completing the square

A few quadratic equations are given, to be solved by completing the square. The number of solutions is randomised.

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• Equation of a line from a graph

Tests the ability to find the gradient and intercept of a straight line graph.

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• Differential Elements

Given a random spandrel, find the expressions for the differential elements of area and the coordinates of its centroid needed to determine the location of the centroid by integration.

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• SageMath Cell

Uses an extension to embed SageMath cells into content areas.

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• MATH6058 Factorising Quadratic Equations with $x^2$ Coefficients of 1

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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• MATH6058 Algebraic fractions: operations involving algebraic fractions

Add, subtract, multiply and divide algebraic fractions.

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• Blathnaid's copy of Simplify logarithms

Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$

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