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Given a generator matrix for a linear code, write a parity check matrix, compute the syndrome of a word, and decide if it's a codeword.

JSXGraph code based on original by Christian Lawson-Perfect

Regression and Correlation. Linear. line of best fit

rebel

rebelmaths

A quadratic is and a graph of it is given. A tangent is also sketched. The equation of the tangent line is asked for.

Linear program described in words. Student must write out constraints as equations in standard form, then identify the optimal solution in a finished simplex tableau.

A quadratic is and a graph of it is given. A tangent is also sketch. The equation of the tangent line is asked for.

Solve the equation  5x - 8 = 32

Assessment of application of different model selection approaches in multiple regression.

A quadratic is and a graph of it is given. A tangent is also sketch. The equation of the tangent line is asked for.

Given  $P(A)$, $P(A\cup B)$, $P(B^c)$ find $P(A \cap B)$, $P(A^c \cap B^c)$, $P(A^c \cup B^c)$ etc..

Linear combinations of $2 \times 2$ matrices. Three examples.

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

Multiple choice question. Given a randomised polynomial select the possible ways of writing the domain of the function.

Multiple choice question. Given a randomised polynomial select the possibe ways of writing the domain of the function.

Add, subtract, multiply and divide algebraic fractions.

Add, subtract, multiply and divide algebraic fractions.

No description given

Construct a line in a GeoGebra worksheet by writing its definition string by hand.

This isn't a very neat way of doing this. It's easier to define two points in GeoGebra, then make a line through those points. You can set the positions of the points from Numbas using vectors.

Construct a line through two points in a GeoGebra worksheet. Change the line by setting the positions of the two points when the worksheet is embedded into the question.

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

A plane goes through three given non-collinear points in 3-space. Find the Cartesian equation of the plane in the form $ax+by+cz=d$.

There is a problem in that this equation can be multiplied by a constant and be correct. Perhaps d can be given as this makes a,b and c unique and the method of the question will give the correct solution.

Find minimum distance between a point and a line in 3-space. The line goes through a given point in the direction of a given vector.

The correct solution is given, however the accuracy of 0.001  is not enough as in some cases answers near to the correct solution are also marked as correct.

Three 3 dim vectors, one with a parameter $\lambda$ in the third coordinate. Find value of $\lambda$ ensuring vectors coplanar. Scalar triple product.

(Green’s theorem). $\Gamma$ a rectangle, find: $\displaystyle \oint_{\Gamma} \left(ax^2-by \right)\;dx+\left(cy^2+px\right)\;dy$.

Given a pair of 3D position vectors, find the vector equation of the line through both.  Find two such lines and their point of intersection.

Given two 3 dim vectors, find vector equation of line through one vector in the direction of another. Find two such lines and their point of intersection.