A quadratic equation (equivalent to $(x+a)^2-b$) is given and sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

A (quadratic) function is skethed sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

Differentiate $f(x) = ax^m$.

This question tests the student's knowledge of the remainder theorem and the ways in which it can be applied.

This question tests the student's ability to find remainders using the remainder theorem. 

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Quiz to assess matrix addition, subtraction, multiplication and multiplication by scalar, determinants and inverses, solving a system of simultaneous equations.

Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

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Identify when the student gives an expected incorrect answer, and give appropriate feedback as well as partial marks.

Some questions which use JSXGraph to create interactive graphics.

Find the first three terms in the binomial series expansion having a non-Natural exponent

Find the first 3 terms of Binomial series having a Natural exponent

Binomial series for Natural exponent

Find the binomial expansion of the following:

Ratio, working hours

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$X$ is a continuous uniform random variable defined on $[a,\;b]$. Find the PDF and CDF of $X$ and find  $P(X \ge c)$.

Solving a second-order constant coefficient ODE. Uses the differentiation extension: https://github.com/Tandethsquire/Differentiation, and the Differential Equation custom part type, to differentiate a student answer and ensure it satisfies the equation.

A sample of what can be done with the differentiation extension, and the corresponding custom part type.

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A small sequence of questions on calculating percentage increases and decreases. Moving from percentages of 100, to percentages of some random whole number, and onto calculating percentage changes in applied financial situations.

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$\frac{3}{4}$

This question tests the students ability to calculate the area of different 2D shapes given the units and measurements required. The formulae for the areas are available if required but students are encouraged to try to remember them themselves.

The shapes are: a rectangle, a parallelogram, a right-angled triangle, and a trapezium.

Author of gif: Picknick
https://commons.wikimedia.org/wiki/File:Parallelogram_area_animated.gif
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.

Substitute values into formulae for the area or volume of various geometric objects.

Ratio of sides of rectangles

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