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This is a formative assessment and your score is not recorded. This tests assess integration by substitution. You should be able to use the appropriate substution and then use the integral table.

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

Two sample t-test to see if there is a difference between scores on questions between two groups when the questions are asked in a different order.

Write the expression $ax^2+bx+c$ in completed square form $a(x+p)^2+k$.

This question relies on using information in the pie chart to find a ratio.

These questions focus on finding a ratio (or fraction) from the information given.

This question focusses on calculating a percentage form a speific pie chart.

The derivative of $\displaystyle \frac{ax+b}{cx^2+d}$ is of the form $\displaystyle \frac{g(x)}{(cx^2+d)^2}$. Find $g(x)$.

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Demo of automatically generating latex strings to out put vectors/matrices of variable size and that are calculated by some formula.

Solving a system of three linear equations in 3 unknowns using Gaussian Elimination (or Gauss-Jordan algorithm) in 5 stages. Solutions are all integers. Introductory question where the numbers come out quite nice with not much dividing. Set-up is meant for formative assessment. Adapated from a question copied from Newcastle.

Solving a system of three linear equations in 3 unknowns using Gaussian Elimination (or Gauss-Jordan algorithm) in 5 stages. Solutions are all integers. Set up so that sometimes it has infinitely many solutions (one free variable), sometimes unique solution. Scaffolded so meant for formative. The variable d determines the cases (d=1: unique solution, d-0: infinitely many solutions). The other variables are set up so that no entries become zero for some randomisations but not others.

Simple questions to check comprehension of definition of Euclidean inner product and norm. Meant for formative use.

Finding a matrix from a formula for each entry, which involves the row and column numbers of that entry. Not randomized because it's the same as in our workbook. But the variables are made in a way that it should be easy to randomise the size of the matrix, and the to change the formula for the input in not too many places.

Finding a matrix from a formula for each entry, which involves the row and column numbers of that entry. Randomized size of the matrices and formula.

First compute matrix times vector for specific vectors. Then determine domain and codomain and general formula for the matrix transformation defined by the matrix.

First compute matrix times vector for specific vectors. Then determine domain and codomain and general formula for the matrix transformation defined by the matrix.

Randomising the number of rows in the matrix, m, makes the marking algorithm for part c) slightly complicated: it checks whether it should include the third gap or not depending on the variable m. For the correct distribution of marks, it is then necessary to do "you only get the marks if all gaps are correct". Otherwise the student would only get 2/3 marks when m=2, so the third gap doesn't appear.

Finding a matrix from a formula for each entry, which involves the row and column numbers of that entry. Randomized size of the matrices and formula.

First compute matrix times vector for specific vectors. Then determine domain and codomain and general formula for the matrix transformation defined by the matrix.

Randomising the number of rows in the matrix, m, makes the marking algorithm for part c) slightly complicated: it checks whether it should include the third gap or not depending on the variable m. For the correct distribution of marks, it is then necessary to do "you only get the marks if all gaps are correct". Otherwise the student would only get 2/3 marks when m=2, so the third gap doesn't appear.

This allows the student to input a linear system in augmented matrix form (max rows 5, but any number of variables). Then the student can decide to swap some rows, or multiply some rows, or add multiples of one row to other rows. The student only has to input what operation should be performed, and this is automatically applied to the system. This question has no marks and no feedback as it's just meant as a "calculator".

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

Zadanie pozwala ocenić umiejętność studenta w zakresie: formułowania hipotez, przeprowadzania testu istotności, wnioskowania statystycznego.

Zmienne losowe: dane surowe

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Give the student a larger area to write some free-form text, which isn't marked.

This question shows how to display a number like "1234" as "1,234", or "1 234", using the formatNumber function.

Use attributes of the form eval-<name> to dynamically set an attribute on an element based on question variables.