Solving an inequality of the form ax+b < c where a is negative.

Recovering original function given some information such as derivative and value at some point.

This question uses a Geogebra applet to solve a linear program with two variables using the graphical method. It contains three steps:

1. Construct the feasible area (polygon) by adding the constraints one by one. The students can see what happens when the constraints are added.
2. Add the objective function, and the level set of the objective value is shown, as well as its (normalised) gradient.
3. Compute the optimal solution by moving the level set of the objective around.

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

Factorise an expression of the form $ax^n+bx^m$.

Factorise an expression of the form $ax+bxy$ for variables $x$ and $y$.

Factorise an expression of the form $ax+bx^2$.

Simplifying single term expressions involving indices.

Simplifying single term expressions involving more than one letter.

simplifying pL1^a/n+kL2^bL1^c/m

Adding two algebraic fractions with the same variable in the numberators.

Given the following three vectors $\textbf{v}_1,\;\textbf{v}_2,\;\textbf{v}_3$ Find out whether they are a linearly independent set are not. Also if linearly dependent find the relationship $\textbf{v}_{r}=p\textbf{v}_{s}+q\textbf{v}_{t}$ for suitable $r,\;s,\;t$ and integers $p,\;q$.

Using indices rules to write expressions as negative powers.

Topics:
Algebra, Calculus, Trigonometeric Equations, Complex numbers & Partial Derivatives

Students must complete the exam within 120 mins (standard time).

Questions have variables to produce randomised questions.

Topics:
Algebra, Calculus, Trigonometeric Equations, Complex numbers & Partial Derivatives

Students must complete the exam within 120 mins (standard time).

Questions have variables to produce randomised questions.

Topics:
Algebra, Calculus, Trigonometeric Equations, Complex numbers & Partial Derivatives

Students must complete the exam within 2hrs 30mins (extra time (1)).

Questions have variables to produce randomised questions.

Topics:
Algebra, Calculus, Trigonometeric Equations, Complex numbers & Partial Derivatives

Students must complete the exam within 120 mins (standard time).

Questions have variables to produce randomised questions.

This exercise will help you rearrange a linear equation to find the value of a given variable

When saving the data necessary to resume an attempt, Numbas only saves the values of variables which use the random number generator.

If you naively generate a large random sample in one variable, it'll be marked as a source of randomness so Numbas will save every value in the sample. Loading this value when you resume the attempt can be very slow.

Instead, you can generate a seed value in one variable and then use it with the seedrandom function in the variable that stores your random list. Only the value of the seed needs to be saved.

Question requires students to interchange units of Hz with MHz, GHz, THz. Question is not very efficient at present- frequencies spanning many orders of magnitude are generated by variables in a clumsy way. Could be improved by having frequency generated by a 10^((random(1000..4000)/1000) variable instead, for example. 

Used for LANTITE preparation (Australia). MG = Measurement & Geometry strand. Student must calculate distance swum in km given number of laps of 50m pool, days of week and weeks in term. These variables are randomly selected.

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students calculate the cost of the halogen globes given electricity cost, number of globes, number of years, replacement cost and lifespan of globes. Some of these variables are randomly selected. There are more than 10 different versions of this question.

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Shows two different ways

Shows how to mark a boolean expression, by checking all possible values of the free variables. There's an information step containing a reminder of the syntax for boolean operations.

Simplify (qx+a)/(rx+b) +/- (sx+c)/(tx+d)

x is a randomised variable. a,b,c,d,q,r,s,t are randomised integers. a,b,c,d run from -5 to 5, including 0. q,r,s,t run from -3 to 3, and can be 0 if the constant term is nonzero, but are mostly 1.

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You can enter an equation in 2 or more variables and rearrange it in the following steps. Numbas checks that the lines of working are all equivalent to the original equation. 

Uses the $\chi^2$ test to see if there is any significant difference in preferences.