No description given

No description given

No description given

No description given

No description given

Identifying y=mx+b given two points

Given one point and the gradient determine the equation of the line.

Given the graph of the line determine the equation of the line.

No description given

Identifying gradient and $y$-intercept from $y=mx+b$.

No description given

No description given

No description given

No description given

Given a 3 x 3 matrix, and two eigenvectors find their corresponding eigenvalues. Also fnd the characteristic polynomial and using this find the third eigenvalue and a normalised eigenvector $(x=1)$.

Example of an explore mode question. Student is given a 3x3 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 eigenvalue will be recognised by the marking algorithm, even multiples of the obvious one(s) (which can be read off from the reduced row echelon form)

Randomisation: Not randomised, just using particular matrices. I am still working on how to randomise this for 3x3; a randomised 2x2 version exists. I have several different versions for 3x3 (not all published yet), so I could make a random choice between these in a test.

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

Given $5$ vectors in $\mathbb{R^4}$ determine if a spanning set for $\mathbb{R^4}$ or not by looking for any simple dependencies between the vectors.

Real numbers $a,\;b,\;c$ and $d$ are such that $a+b+c+d=1$ and for the given vectors $\textbf{v}_1,\;\textbf{v}_2,\;\textbf{v}_3,\;\textbf{v}_4$ $a\textbf{v}_1+b\textbf{v}_2+c\textbf{v}_3+d\textbf{v}_4=\textbf{0}$. Find $a,\;b,\;c,\;d$.

A simultaneous equations question with integers only

Solve for $x$ and $y$:  \[ \begin{eqnarray} a_1x+b_1y&=&c_1\\   a_2x+b_2y&=&c_2 \end{eqnarray} \]

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.

Find $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d $.

A simultaneous equations question with integers only

Reduce a 5x6 matrix to row reduced form and using this find rank and nullity.

Factorise $\displaystyle{ax ^ 2 + bx + c}$ into linear factors. 

Find the equation of a line given a point and a parallel line.

No description given

Find the equation of a line given a point and a parallel or perpendicular line.

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

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

Calculate the length of a line segment given two points