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.

Find roots and the area under a parabola

Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 

Finding the stationary points of a rational function with specific features.

Step by step solving for integration by substitution

Integration by susbtitution, no hint given

Rate of change problem involving velocity & acceleration

Simple Indefinite Integrals

Find the common ratio of a given geometric sequence, write down the formula for the nth term and use it to calculate a given term in the sequence.

Simple counting exercise, with combinations

Simple counting exercise, with combinations

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

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

Simple ratio question with custom marking and partial credit possible

A block of given mass is sliding down the plane with a given acceration. Find the normal reaction force, the parallel force and the missing value of a and mu.

Express various integers and rationals mod $\mathbb{Z}_3, \;\mathbb{Z}_5,\;\mathbb{Z}_7,\;\mathbb{Z}_{11}$

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

Questions about percentage and ratio, applied to finance.

Based on section 3.2 of the Maths-Aid workbook on numerical reasoning.

Questions about percentage and ratio, applied to finance.

Based on section 3.2 of the Maths-Aid workbook on numerical reasoning.

The student must perform an indefinite integration, and include a constant of integration.

A custom marking algorithm identifies the name of the student's constant of integration, and replaces it with 'c' before comparing with the expected answer.

If the student enters something like '2c' instead of 'c', it'll be marked wrong, which is an error in the marking.

Straightforward question: student must find the general solution to a second order constant coefficient ODE. Uses custom marking algorithm to check that both roots appear and that the solution is in the correct form (e.g. two arbitrary constants are present). Arbitrary constants can be any non space-separated string of characters. The algorithm also allows for the use of $e^x$ rather than $\exp(x)$.

Unit tests are also included, to check whether the algorithm accurately marks when the solution is correct; when it's correct but deviates from the 'answer'; when one or more roots is incorrect; or when the roots are correct but constants of integration have been forgotten.

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

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

No description given

Identifying some of the basic properties (intercepts, asymptotes, quadrants) of a rational function (quadratic over linear)

Evaluate $\int_1^{\,m}(ax ^ 2 + b x + c)^2\;dx$, $\int_0^{p}\frac{1}{x+d}\;dx,\;\int_0^\pi x \sin(qx) \;dx$, $\int_0^{r}x ^ {2}e^{t x}\;dx$

Rationalise the denominator with increasingly difficult examples involving compound denominators. 

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