This question tests the student's ability to solve Integer Programming problems applying Population-based Metaheuristics.

Use a calculator to compute (base)^index. Part of HELM Book 1.2

Asks students to compute (base)^index without a calculator for two simple questions. Part of HELM Book 1.2

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

DIAGNOSYS is a knowledge-based test of mathematics background knowledge for first-year university students, created by John Appleby at Newcastle University.

The questions have been translated directly into Numbas, with as few changes as possible.

Bulk Deformation Question Based on Materials Lab Session

Stress & Strain Question based on Tensile testing of materials lab session

Find modulus and argument of the complex number $z_1$ and find the $n$th roots of $z_1$ where $n=5,\;6$ or $7$.

Calculating a salesperson's income based on years of service and commission from sales

Given the stakes of three people in a lottery syndicate, and the amount the syndicate won, work out each person's share of the winnings.

Based on question 4 from section 3.2 of the Maths-Aid workbook on numerical reasoning.

Draws a triangle based on 3 side lengths.  Randomises asking angle or side.

Draws a triangle based on 3 side lengths.  Randomises asking angle or side.

Draws a triangle based on 3 side lengths.  Randomises asking angle or side.

Example of an explore mode question. Student is given a 2x2 matrix and is asked to find the characteristic polynomial and eigenvalues, and then eigenvectors for each eigenvalue. The part asking for eigenvectors can be repeated as often as the student wants, to be used for different eigenvalues.

Assessed: calculating characteristic polynomial and eigenvectors.

Feature: any correct eigenvector is recognised by the marking algorithm, also multiples of the "obvious" one(s) (given the reduced row echelon form that we use to calculate them).

Randomisation: a random true/false for invertibility is created, and the eigenvalues a and b are randomised (condition: two different evalues, and a=0 iff invertibility is false), and a random invertible 2x2 matrix with determinant 1 or -1 is created (via random elementary row operations) to change base from diag(a,b) to the matrix for the question. Determinant 1 or -1 ensures that we keep integer entries.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".

Draws a triangle based on 3 side lengths.
NOT ACCESSIBLE

This question tests the ability to read and interpret numerical data summarised in a table and make predictions based on algebraic skills.

Example of an explore mode question. Student is given a 2x2 matrix with eigenvalues and eigenvectors, and is asked to decide if the matrix is invertible. If yes, second and third parts are offered where the student should give the eigenvalues and eigenvectors of the inverse matrix.

Assessed: remembering link between 0 eigenvalue and invertibility. Remembering link between eigenvalues and eigenvectors of matrix and its inverse.

Randomisation: a random true/false for invertibility is created, and the eigenvalues a and b are randomised (condition: two different evalues, and a=0 iff invertibility is false), and a random invertible 2x2 matrix with determinant 1 or -1 is created (via random elementary row operations) to change base from diag(a,b) to the matrix for the question. Determinant 1 or -1 ensures that we keep integer entries.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".

The student is given a number in base 10 and asked to write it in a given base, between 2 and 16. The number has at most 3 digits in the other base.

Until it's possible to derive the expected answer for a part in the marking algorithm (see the issue tracker), this question has "show expected answer" turned off, because it just shows the base 10 number.

Based on Chapter 8, quite loosley.Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Draws a triangle based on 2 angles and a side length.

Converting integers from one base to another. Includes binary to decimal.

Draws a right angled triangle based on a length and an angle.

Draws a right angled triangle based on a length and an angle.

Draws a triangle based on 3 side lengths.

Draws a triangle based on 2 angles and a side length.

Draws a triangle based on 2 angles and a side length.

The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

Given two distributions, calculate the measures of average and spread and make some decisions based on the results.

5 questions on indefinite integration. Includes integration by parts and integration by substitution.