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Quadratic factorisation that does not rely upon pattern matching.

One could also use the pattern matching syntax to check automatically; this is programatically harder.

An application of quadratic functions based on the Gladesville Bridge in Sydney, Australia. Student is given an equation representing the arch of the bridge and asked to find the height of the arch and the width of the river. Requires and understanding of the quadratic function and where and how to apply correct formulae.

An application of quadratic functions based on the Gateshead Bridge in the UK city of Newcastle. Student is given an equation representing the arch of the bridge and asked to find the height of the arch and the width of the river. Requires and understanding of the quadratic function and where and how to apply correct formulae.

Student is given a rational function, h(x), with randomised coefficients, and a linear function, k(x), also with randomised coeffieients and asked to find:

1. h(k(x)) or k(h(x)) (randomly selected) for a randomised value of x
2. The domain of h(x) - multiple choice part
3. A general expresion for k(h(x)) or h(k(x)) - opposite combination to first part.

Variables are constrained so that h(x) is not a degenerate form and that when evaluating h(x) denomiator is not 0.

This question gives the student the formula for the charge on a capacitor as a function of time then asks them to find the value of k, the exponential constant given other values and hence write out the formula for the given case. A custom function (in Extensions & scripts) extracts the student's formula and plots it on a JSXGraph object in the question. The student is then asked to evaluate the function at a given point using the plot or other methods. The value of the capacitor (Q_0), time (t) and charge at time t are randomised as is the value at which the formula is to be evaluated.

Students need to prove a given trig identity, Written as a scan solution and upload question, no randomisation.

Students need to prove a given trig identity, Written as a scan solution and upload question, no randomisation.

Students need to prove a given trig identity, Written as a scan solution and upload question, no randomisation.

Inputting algebraic expressions into Numbas.

Students are presented with an AI generated solution to rerrange the quadratic equation where the AI has made errors, they are asked to rewrite the solution correctly. No variables but this is version 5 of 5 versions of the question. This version uses a much more mangled AI generated solution that the other 4 versions and does not ask for the line with the first error, just for the student to rewrite the solution correctly.

Students are presented with an AI generated solution to rerrange the quadratic equation where the AI has made errors, they are asked to identify on which line the first error occurs, then rewrite the solution correctly. No variables but this is version 4 of 5 versions of the question.

Students are presented with an AI generated solution to rerrange the quadratic equation where the AI has made errors, they are asked to identify on which line the first error occurs, then rewrite the solution correctly. No variables but this is version 2 of 5 versions of the question.

Students are presented with an AI generated solution to rerrange the quadratic equation where the AI has made errors, they are asked to identify on which line the first error occurs, then rewrite the solution correctly. No variables but this is 1 of 5 versions of the question.

This question asks students to find the distance from an aircraft to a given marker. Angle of depression of 2 markers from the aircraft are given and the distance between the markers on the ground (all randomised). Students need to use the sine rule to find the answer. The workding of the question makes googling the answer difficult.

Exercises for HELM Book 2.5.3.

Exercises for HELM Book 2.5.1

Student is asked to find the distance from a given point, A, to a house, given the distance between A and another point B, and the angles at A and B. Requires use of the sine rule. Distance and angles are randomised.

Students need to solve a quadratic equation and recognise that only the positive root has physical significance. Roots are randomised with one always negative and one positive. Equation can be factorised fairly easily or the quadratic formula can be used to find the solution. Advice gives solution by factorisation.

Simultaneous equation problem as circuit analysis to find unknown currents. Students need to solve the equations and type in the solutions for each variable. Advice is given in terms of solution by elimination.

Question requires students to determine if the smallest angle of a triangle is smaller than a given value. Answer is Yes/No but students need to use cosine rule to find the smallest angle and to know that smallest angle is oppositeshortest side (otherwise they will need to find all angles of the triangle). Designed for a test where students upload handwritten working for each question as a check against guessing. Also designed to make it difficult for students to google or use AI to find the answer.

Question requires students to determine if the largest angle of a triangle is smaller than a given value. Answer is Yes/No but students need to use cosine rule to find the largest angle and to know that largest angle is opposite longest side (otherwise they will need to find all angles of the triangle). Designed for a test where students upload handwritten working for each question as a check against guessing. Also designed to make it difficult for students to google or use AI to find the answer.

Students are asked to solve two simulatineous linear equations in an application of mixing two liquids to arrive at a given final volume and concentration. Students are expected to write up working for their solution and upload it seperately. Final volume, final concentration and concentrations of each solution are randomised.

This question is an application of a quadratic equation. Student is given dimensions of a rectangular area, and an area of pavers that are available. They are asked to calculate the width of a border that can be paved around the given rectangle (assuming border is the same width on all 4 sides). The equation for the area of the border is given in terms of the unknown border width. Students need to recognise that only one solution of the quadratic gives a physically possible solution.

The dimensions of the rectangle, available area of tiles and type of space are randomised. Numeric variables are constructed so that resulting quadratic equation has one positive and one negative root.

Edit the Python code to make a 3D plot of a surface defined parametrically.

Plot the Fourier series coefficients for a piece-wise linear function.  Write a Python script to reproduce the same figure.

Some examples of interactive plots illustrating mathematical concepts, supported by Python exercises.

Partial differentiation question with customised feedback to catch some common errors.

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