Find $\displaystyle \frac{d}{dx}\left(\frac{m\sin(ax)+n\cos(ax)}{b\sin(ax)+c\cos(ax)}\right)$. Three part question.

Given vectors  $\boldsymbol{v,\;w}$, find the angle between them.

Finding unknown sides/angles in right-angled triangles.

Version 1: b,c known

Version 2: a,x known

Version 3: a,y known

Version 4: b,x known

Version 5: b,a known

Version 6: c,a known

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

Missing: Application with bacteria, turning points, difficult chain rule

Manipulate surds and rationalise the denominator of a fraction when it is a surd.

Create a truth table for a logical expression of the form $(a \operatorname{op1} b) \operatorname{op2}(c \operatorname{op3} d)$ where $a, \;b,\;c,\;d$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and each of $\operatorname{op1},\;\operatorname{op2},\;\operatorname{op3}$ one of $\lor,\;\land,\;\to$.

For example: $(p \lor \neg q) \land(q \to \neg p)$.

Solve for $x$ and $y$:  \[ \begin{eqnarray} a_1x+b_1y&=&c_1\\   a_2x+b_2y&=&c_2 \end{eqnarray} \]

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.

Create a truth table for a logical expression of the form $a \operatorname{op} b$ where $a, \;b$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and $\operatorname{op}$ one of $\lor,\;\land,\;\to$.

For example $\neg q \to \neg p$.

Question on drug calculations

Question on drug calculations

Question on drug calculations

Question on drug calculations

Reduced or simplified form of a fraction by cancelling the greatest common divisor (gcd) of numerator and denominator (i.e dividing out by it)

The greatest common factor are designed to be one of the following 2,4,5,10,20,25,50,100,125,250

Conversions of units

Basic Percentages Question

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Basic Percentages Question

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Basic Percentages Question

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Simple exercises introducing the fundamental set operations, and NUMBAS syntax for sets.

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

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Convert from degrees to radians

Converting Binary to Decimal

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This question provides a list of data to the student. They are asked to find the mean, median, mode and range.

Identify when the student gives an expected incorrect answer, and give appropriate feedback as well as partial marks.

No description given

This uses an embedded Geogebra graph of a sine curve $y=a\sin (bx+c)+d$  with random coefficients set by NUMBAS.

Indefinite Integrals

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No description given

Load data on some items held in the Cooper Hewitt collection, and show a table of 5 randomly picked items.

Simple ratio question with custom marking and partial credit possible