Match the question with the correct formula.

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Two column vectors are given, with one entry unknown. Given that the vectors are perpendicular, question is to determine the unknown entry.

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 $y_i-x_i,\;i=1,\dots 5$.

Slightly harder introductory exercises about the power set.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation

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

Finding the stationary points of a cubic with two turning points

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

Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

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A sample of what can be done with the differentiation extension, and the corresponding custom part type.

Kruskal-Wallis test with ties.

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

Percentage Error

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Multiplying and dividing decimals

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A random heating question, that randomly picks a material, and then heats it through either one or two phase changes, provides an example graph of the heating with scaled temperature ranges (though not with scaled latent and specific heats), and a table with the suitable constants.

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.

Provided with information on a sample with sample mean and known population variance, use the z test to either accept or reject a given null hypothesis.

Provided with information on a sample with sample mean and standard deviation, but no information on the population variance, use the t test to either accept or reject a given null hypothesis.

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

Work out the volume of a prism with a trapezium cross-section.

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

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.

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

A static block of given mass is sits on a flat plane with defined static and kinetic friction values. It is pushed with enough force to start it moving - calculate the speed of the block after a given distance.

Calculate the efficiency and heat from the hot reservoir in a Carnot Cycle (with carnot diagram)

Calculate the efficiency and heat from the hot reservoir in a Carnot Cycle (with carnot diagram)

A random heating question, that randomly picks a material, and then heats it through one phase change, provides an example graph of the heating with scaled temperature ranges (though not with scaled latent and specific heats), and a table with the suitable constants.