Students are supposed to use Excel (or similar) to find the answers (e.g., enter coordinates of two points then plot and add trendline).

Uses an embedded Geogebra graph of a line $y=mx+c$ with random coefficients set by NUMBAS.

This uses an embedded Geogebra graph of a line $y=mx+c$ with random coefficients set by NUMBAS.

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.

Given the gradient of a slope and the coefficient of friction for a mass resting on it, use the equations of motion to calculate how it moves.

Includes a GeoGebra rendering of the model.

Students need to find solution to simultaneous linear equations with randomised coefficients.

Question asks student to find zeros of a quadratic equation - disguised as finding time for particle to reach a given position. In this version students are expected to write up their working and submit it seperately to the Numbas question. Students are expcted to recognise that only the positive solution has physical significance. Coefficients of the quadratic are randomly chosen within linits which give one positive and one negative root.

This uses an embedded Geogebra graph of a polar function with random coefficients set by NUMBAS.

Simultaneous equations question. values for the coefficients are generated to be small numbers, random values are generated for the weights and the resultant energies are calculated for the question. Student needs to solve equations to find coefficients. Advice gives solution using method of elimination.

A two part question. Students are first given the formula for the time for a ball to come to rest after being dropped on a block. Part a) asks the students to rearrange the formula to make e, the coefficient of restitution, the subject of the formula. Part b) gives students realistic values for variables in the formula and asks them to calculate the coefficient of restitution using the formula derived in part a). 

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

The student must solve a pair of simultaneous equations in $x$ and $y$.

The variables are generated backwards: first $x$ and $y$ are picked, then values for the coefficients of the equations are chosen satisfying those values.

Rearrange an equation for a variable e in k.1/(1-e) and then evaluate for e, given values for the variables.

This uses an embedded Geogebra graph of a sine curve $y=a\sin (bx+c)+d$  with random coefficients set by NUMBAS.

This uses an embedded Geogebra graph of a sine curve $y=a\sin (bx+c)+d$  with random coefficients set by NUMBAS.

This uses an embedded Geogebra SHM graph with coefficients set by NUMBAS.

This uses an embedded Geogebra SHM graph with coefficients set by NUMBAS.

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

This uses an embedded Geogebra graph of amodulus function with random coefficients set by NUMBAS.

This uses an embedded Geogebra graph of a modulus function with random coefficients set by NUMBAS.

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

This uses an embedded Geogebra graph of a polar function with random coefficients set by NUMBAS.

Determine frictional force acting on a block on an incline.  Coefficients of friction, weight and a horizontal force are given

Basic Algebra question, expand one set of brackets, coefficients may be positive or negative, pronumerals randomised.

Statistical notation including mean, standard deviation, probability, correlation coefficient, chi-square and others.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Solving a pair of simultaneous equations of the form $y=mx+c_1$ and $y=ax^2+kx+c_2$ to find the possible values for the unknown coefficient $k$, when given the values of $m$, $a$, $c_1$ and $c_2$.

Solving a quadratic equation via factorisation (or otherwise) with the $x^2$-term having a coefficient of 1.

Calculating two unknown coefficients of a cubic expression when given two of the expression's linear factors.