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

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

Applied questions that could be done with modulo arithmetic.

Applied questions that could be done with modulo arithmetic.

Compute the experimental probability of a particular score on a die given a sample of throws, and compare it with the theoretical probability.

The last part asks what you expect to happen to the experimental probability as the sample size increases.

Given the common difference and first term of an arithmetic sequence, work out the index of the nth term of the sequence.

Framed as a word problem with ticket numbers in an ice cream shop.

Given the first and last terms of a finite arithmetic sequence, calculate the number of elements and then the sum of the sequence.

Each part is broken into steps, with the formula given.

Given sequences with missing terms, find the common difference between terms.

Given arithmetic sequences with some terms missing, fill in the missing terms.

This question tests the student's ability to find remainders using the remainder theorem. 

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

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

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

Graphing $y=ab^x+c$

Graphing $y=ab^x+c$

Students seem to struggle with Sigma notation, this is about the easiest question possible for sigma notation.

Students seem to struggle with Sigma notation, this is about the easiest question possible for sigma notation.

Students seem to struggle with Sigma notation, this is about the easiest question possible for sigma notation.

Students seem to struggle with Sigma notation, this is a simple question to ensure they understand the index can change without affecting the sum.

Recognising that $(x-a)^2+(y-b)^2=r^2$ is a circle of radius $r$ with centre $(a,b)$ 

A cubic with a maximum and minimum point is given. Question is to determine coordinates of the minimum and maximum point. Non-calculator. Advice is given.

An example of using the GeoGebra extension to ask the student to create a geometric construction, with marking and steps.

Three graphs are given with areas underneath them shaded. The student is asked to calculate their areas, using integration.  Q1 has a polynomial. Q2 has exponentials and fractional functions. Q3 requires solving a trig equation and integration by parts.

Three graphs are given with areas underneath them shaded. Student is asked to determine the minimum and maximum $x$-values of the regions. This will involve solving a linear equation and two trigonmetric equations.

Graphs are given and students are required to match them with their equation.

Just showing how to use the stdev function from the stats extension to calculate the standard deviation of a list of numbers.

rebelmaths

Evaluate $\int_0^{\,m}e^{ax}\;dx$, $\int_0^{p}\frac{1}{bx+d}\;dx,\;\int_0^{\pi/2} \sin(qx) \;dx$. 

No solutions given in Advice to parts a and c.

Tolerance of 0.001 in answers to parts a and b. Perhaps should indicate to the student that a tolerance is set. The feedback on submitting an incorrect answer within the tolerance says that the answer is correct - perhaps there should be a different feedback in this case if possible for all such questions with tolerances.

Dealing with functions in Numbas.

Uses JSXGraph to generate a plot for a cubic, with given critical points, along with three other incorrect graphs with modified properties. JSXGraph code is commented.

An experiment is performed twice, each with $5$ outcomes

$x_i,\;y_i,\;i=1,\dots 5$ . Find mean and s.d. of their differences $y_i-x_i,\;i=1,\dots 5$.