Factorising further basic quadratics into linear factors.

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A collection of questions to show off at a workshop for the North East and Yorkshire sigma hub, June 2016.

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This question allows you to practice working out a fraction of an amount.

It is designed for you to complete without a calculator.

Given ratio of ingredients in a preparation, and amounts of each ingredient, work out how much of the preparation you can make.

Based on question 5 from section 3 of the maths-aid workbook on numerical reasoning.

Working with powers

Working with powers

Working with powers

Add, subtract, multiply and divide algebraic fractions.

Add, subtract, multiply and divide algebraic fractions.

Simplifying algebraic expressions

Simplifying algebraic expressions

Use the quotient rule to differentiate various functions.

Use the product rule to differentiate various functions.

Use the chain rule to differentiate various functions.

Find an integral by choosing a suitable substitution.

Add, subtract, multiply and divide numerical fractions.

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Tiny demo question for the polynomials extension.

It's important to wrap the student's answer in polynomial() in the marking script, otherwise the marking doesn't work.

Using differentiation to find the tangent and normal to a line at a given point

Questions about complex arithmetic; argument and modulus of complex numbers; complex roots of polynomials; de Moivre's theorem.

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Find (hyperbolic substitution):
$\displaystyle \int_{b}^{2b} \left(\frac{1}{\sqrt{a^2x^2-b^2}}\right)\;dx$