Student is given a set of constraints for a linear program. Asked to enter the constraints as inequalities, and then to identify the optimal solution.

Given a linear programming problem in standard form, write down the dual problem.

Given a linear programming problem in standard form, write down the dual problem.

Student is given a set of constraints for a linear program. Asked to enter the constraints as inequalities, and then to identify the optimal solution.

Find a regression equation given 12 months data on temperature and sales of a drink. Includes an interactive diagram for experimenting with fitting a regression line.

rebelmaths

Some simple questions around injectivity, surjectivity, bijectivity (and the inverse function) of linear functions $\mathbb R\to \mathbb R$ (i.e., $x\mapsto mx+b$ for some real numbers $m$, $b$).

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

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

Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.

This is a set of questions for students to practice identifying parabolas, hyperbolas and exponentials.

There are also a few questions asking students to draw graphs, and to evaluate the curves at specific points.

10 questions are selected from a larger pool. 

In the first question students are asked to identify the type of a graph.

In the second question students are asked to identify the type of an equation.

Then next 6 questions are basic questions about evaluating points on a curve or matching curves and equations.

The last 2 questions are applications - e.g. compound interest, displayed as an equation, a table or a graph.

Practise solving simultaneous linear equations graphically and algebraically.

Customised for the Numbas demo exam

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

A graph is drawn. A student is to identify the derivative of this graph from four other graphs.

A graph is drawn. A student is to identify the derivative of this graph from four other graphs. There are four version of this question: I: cubic, II: linear, III: quadratic, IV: sinusoisal.

Students are given a word problem with the distance travelled and the time taken by a cyclist. They need to choose the correct form for the linear equation, compute the gradient, and plot the line.

The distance travelled and time taken are randomised.

Speed, distance and time are all integer values.

Describe a given linear transformation as a vector in Cartesian coordinates.

Studnents are asked to write down equations for cost and income for a business.

They are then asked to graph the two lines.

This demonstrates how to construct a JSXGraph diagram in JME code.

The construction shows a triangle and its orthocentre, circumcentre and centroid. They are always collinear. You can move the vertices of the triangle.

Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.

Express a sum of linear terms in $x$ and $y$ as a single linear term in $x$ and $y$.

Expand $ax(cx+d)$ and expand $(rx+s)(px)$

Expand $(ax+b)(cx+d)$.

Expand $(pw+q)(aw^2+bw+c)$.

Expand $(az^2+bz+c)(pz+q)$.

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

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