Determining the range of a function of the form $f = m|x| + a$.

Rewrite the expression $\frac{mx^2+nx+k}{(x+a)(x^2+bx+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{Bx+C}{x^2+bx+c}$.

Rearrange a specific formula. No randomisation.

Rewriting fractions of the form $\frac{\sqrt[m]{x^n}}{\sqrt[p]{x^q}}$ to $x^{\frac{n}{m}-\frac{q}{p}}$.

Factorising a quadratic expression of the form $ax^2+bx+c$ by completing the square.

Factorising a quadratic expression of the form $x^2+bx+c$ by completing the square.

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

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

In this question the students have to solve a linear recurrence of order 1. The sequence is asked in recurrence form and the goal is to find its closed form.

In this question the students have to solve a linear recurrence of order 2. The sequence is asked in recurrence form and the goal is to find its closed form.

The student is asked to find the square root of an integer of the form $\pm n^2$. If the root is not real, they should enter "nan".

A custom marking algorithm extends the built-in one to deal with "nan".

There's some custom javascript to set the expected answer correctly. In the future this will be possible in the marking algorithm - see https://github.com/numbas/Numbas/issues/856

Multlipying and subtracting mixed numbers. It is expected that a calculator is used to perform this question.

Public

Public

Public

Public

Substitute values into formulae for the area or volume of various geometric objects.

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

A quick knowledge and understanding check of:

1) Work done concept.

2) Work done formulae: W = Fx and W = Fxcos(y).

3) Equivalent units of work.

Graphing $y=ab^{\pm x+d}+c$

Graphing $y=ab^x+c$

Graphing exponentials with a base between 0 and 1 and no transformations take place.

The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

Here you need to choose which formula you would use to find the red dashed value from the solid green values.  The view is three-dimensional and you can rotate it to get a better view.

Variable defintions in the formulas:
$\theta$ is an angle
Adj. is the length of the side adjacent to the known angle
Opp. is the length of the side opposite the known angle
Hyp. is the length of the hypotenuse


Your goal is to get twenty correct answers quickly. Incorrect answers show a highlight of the correct answer to select to continue.  The timer starts as soon as you choose your first answer and continues until you get 20 correct.  Select save answer after your results show in the applet.

The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

Graphing $y=a\log_{b}(x)+c$