Resultant force

Resultant vector

Resultant force

Resultant force

Solve two quadratic equations (with real coefficients) in the complex numbers. The solutions have non-zero imaginary part, fractions can appear (but the denominators are rather small).

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.

Problem with solving the simultaneous equations gven by the constraints - too unwieldy and not given enough marks for doing so. Best if the point of intersection is given graphically by putting the mouse over the intersection.

Student is shown a linear programming problem, with graphical solution. 

Asked to identify binding constraints, and decide if the optimal solution is changed by a named constraint either doubling or halving.

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.

Problem with solving the simultaneous equations gven by the constraints - too unwieldy and not given enough marks for doing so. Best if the point of intersection is given graphically by putting the mouse over the intersection.

Compute a table of values for a quadratic function. The student input is now disconnected from the graph so that they slide the points on the graph after they input the values and the answer fields are not updated. Now includes a graph in advice.

Drag points on a JSXgraph plot to sketch solution

Drag points on a JSXgraph plot to sketch solution

Asking users to input coefficients of a system of diff equations so that the phase space is a centre. All systems input by the user are graphed together with immediate feedback. Also included in the Steps are the graphs of the solutions for $x(t),\; y(t);\; x(0)=-5,\;y(0)=5.$

Nature of fixed points of a 2D dynamical system.

These examples are either centres or spirals.

Asking users to input coefficients of a system of diff equations so that the phase space is a centre. All systems input by the user are graphed together with immediate feedback. Also included in the Steps are the graphs of the solutions for $x(t),\; y(t);\; x(0)=-5,\;y(0)=5.$

Asking users to input coefficients of a system of diff equations so that the phase space is a stable spiral. All systems input by the user are graphed together with immediate feedback. Also included in the Steps are the graphs of the solutions for $x(t),\; y(t);\; x(0)=-5,\;y(0)=5.$

Asking users to input coefficients of a system of diff equations so that the phase space is a saddle. All systems input by the user are graphed together with immediate feedback. Also included in the Steps are the graphs of the solutions for $x(t),\; y(t);\; x(0)=-5,\;y(0)=5.$

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.

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.

Compute a table of values for a quadratic function. The student input is now disconnected from the graph so that they slide the points on the graph after they input the values and the answer fields are not updated. Now includes a graph in advice.

Doesn't work - used the old extension.

Mark a GeoGebra worksheet.

Needs a worked solution.

Given an ODE solution: $y=  b x^n + cx$

Use a condition: $y(1)=a$ to find the particular solution and hence the value of $y(d)$.

Hello! This test an extra opportunity to complete some practice questions on the material we have covered so far. Your results will NOT count towards your final grade, and there is no time limit to complete the test. You can check your answers as you go along, and even try new examples of the same type. Full solutions are also available for most questions. If there are any questions you don't understand, take a photo and we can discuss it in class or at a one-to-one appointment. 

Solve for $x$ each of the following equations: $n^{ax+b}=m^{cx}$ and $p^{rx^2}=q^{sx}$.

Solve for $x$: $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$. 

Make sure that your choice is a solution by substituting back into the equation.

Solve for $x$: $c(a^2)^x + d(a)^{x+1}=b$ (there is only one solution for this example).

Using the IF to find the General Solution.

Find the solution of $\displaystyle x\frac{dy}{dx}+ay=bx^n,\;\;y(1)=c$

Addition and Subtraction by hand questions, whole numbers and decimals. Fully worked solutions in feedback.

Subtraction questions, whole and decimal, to be carried out by hand. Full worked solutions given in feedback.

Addition calculations to be carried out by hand, full worked solutions in feedback.