Basic solving of linear equations

Solving linear equations

Straightforward solving linear equations question

This question allows you to practice identifying the coordinates of points on graphs.

This question allows you to practice identifying the coordinates of points on graphs.

Straightforward solving linear equations question.

Adapted from 'Simultaneous equations by substitution 2 with parts' by Joshua Boddy.

GIve a random linear program and ask the students to convert it to canonical form.

A portfolio of NUMBAS questions created for first year Natural Sciences students. The questions cover the topics: 

• Linear functions
• Quadratic functions
• Differentiation
• Integration
• Explonatial and logarithms 
• Further differentiation
• Further Integration
• Trigonometric Functions

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.

In this question the students have to solve a linear recurrence of order 2. The sequence is asked in recurrence form and the goal is to find its closed form.

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

Describe the effect of changing the value of a constant term in a linear function. Part of HELM Book 2.5.1.

Compute the inverse of a linear or hyperbolic function. Part of HELM book 2.3.

Find the inverse of a linear function. Part of HELM book 2.3.

Graph a linear or quadratic function and state its domain and range. Part of HELM Book 2.2.1.

Given 2 randomised functions f(x) (linear) and g(x) (quadratic), find one of f(f), f(g), g(f) or g(g) at a randomised integer x-value

Given 2 randomised functions f (linear) and g (quadratic), find one of f(f), f(g), g(f) or g(g)

Reading gradient and intercept from y=mx+c.

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.

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

In the first part, the student must write any linear equation in three unknowns. Each distinct variable can occur more than once, and on either side of the equals sign. It doesn't check that the equation has a unique solution.

In the second part, they must write three equations in two unknowns. It doesn't check that they're independent or that the system has a solution. The marking algorithm on each of the gaps just checks that they're valid linear equations, and the marking algorithm for the whole gap-fill checks the number of unknowns.

This question shows how to generate a random set of $(x,y)$ samples, where $y = mx + c + \mathrm{noise}$.

The JSXGraph extension is used to show a scatter plot of the data. This isn't necessary if you just want to generate the data.

Evaluate a linear function at 3 numerical inputs.

Evaluate a given, randomised, linear function at a given, randomised, value.

Rearrange a linear formula au + bv + cw = d to make one of u,v,w the subject.

Rearrange a linear function in x and y to make y the subject. Line variables are randomised.

evaluate the function y=ax+b for given values of a,b and x, each of which may be positive or negative.

Drag points on an axis to plot a linear graph (integer gradient and intercept only)

Practice question solving linear homogeneous second order differentials using the auxiliary equation method.

No description given