Calculate the Pearson correlation coefficient on paired data and comment on the significance.

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Scores  in 20 games and frequency given -- calculate mean.

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Statistics and probability. Questions asking student to calculate and interpret Pearson and Spearman correlation coefficients.

Questions on vector arithmetic and vector operations, including dot and cross product, as well as the vector equations of planes and lines.

5 questions on indefinite integration. Includes integration by parts and integration by substitution.

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

Applications of Derivatives 2

This is a formative assessment to see how well you have understood the content from the first 3 weeks of the course. It will not count towards your final mark. If you get less than 40%, then you should take immediate steps to improve your knowledge, such as attending Study Clinics.

Add, subtract, multiply and divide algebraic fractions.

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This questions is for thos epractising numerical reasoning tests. Here the focus is on manipulating the data using the 4 basic maths operations.

These questions focus on using the 4 basic maths operations to answer numerical reasoning tests.

This question focusses on being able to apply the 4 basic maths operations and also use the calculator effectively.

$2e^{x^3}+4e^x$

$2e^{x^3}+4e^x$

$2e^{x^3}+4e^x$

In this demo question, you can see either 2 or 3 gaps depending on the variable \(m\), and the marking algorithm doesn't penalise for the empty third gap in cases when it is not shown.

Reason to use it: for vectors or matrices containing only numbers, one can easily use matrix entry to account for a random size of an answer. But this does not work for mathematical expressions. There we have to give each entry of the vector as a separate gap, which then becomes a problem when the size varies. This solves that problem. For this reason I've included two parts: one very simple one that just shows the phenomenon of variable number of gaps, and one which is more like why I  needed it.

Note that to resolve the fact that when \(m=2\), the point for the third gap cannot be earned, I have made it so that the student only gets 0 or all points, when all shown gaps are correctly filled in.

Note the use of Ax[m-1] in the third gap "correct answer" of part b): if you use Ax[2], then it will throw an error when m=2, as then Ax won't have the correct size. So even though the marking algorithm will ignore it, the question would still not work.

Bonus demo if you look in the variables: A way to automatically generate the correct latex code for \(\var{latexAx}\), since it's a variable size. I would usually  need that in the "Advice", i.e. solutions, rather than the question text.

In this demo question, you can see either 2 or 3 gaps depending on the variable \(m\), and the marking algorithm doesn't penalise for the empty third gap in cases when it is not shown.

Reason to use it: for vectors or matrices containing only numbers, one can easily use matrix entry to account for a random size of an answer. But this does not work for mathematical expressions. There we have to give each entry of the vector as a separate gap, which then becomes a problem when the size varies. This solves that problem. For this reason I've included two parts: one very simple one that just shows the phenomenon of variable number of gaps, and one which is more like why I  needed it.

Note that to resolve the fact that when \(m=2\), the point for the third gap cannot be earned, I have made it so that the student only gets 0 or all points, when all shown gaps are correctly filled in.

Note the use of Ax[m-1] in the third gap "correct answer" of part b): if you use Ax[2], then it will throw an error when m=2, as then Ax won't have the correct size. So even though the marking algorithm will ignore it, the question would still not work.

Bonus demo if you look in the variables: A way to automatically generate the correct latex code for \(\var{latexAx}\), since it's a variable size. I would usually  need that in the "Advice", i.e. solutions, rather than the question text.

Simple vector addition and scalar multiplication in \(\mathbb{R}^2\).

Easy intro questions to be done when the students have seen the "vector space axioms" but not as axioms, just in the context of \(\mathbb{R}^n\).

Checking whether a given set is a plane or not. Depends on whether two vectors are parallel or not. Then checking whether the plane goes through the origin. This is not always obvious from the presentation.

Not randomised because it's the same as in our workbook.

Calculating with vectors in \(\mathbb{R}^4\), including resolving brackets. The fixed vector size is so that a test is fair to all students.

Checking whether a given set is a plane or not. Depends on whether two vectors are parallel or not. Then checking whether the plane goes through the origin. This is not always obvious from the presentation.

Not randomised because it's the same as in our workbook.

A demo of the mathematical expression part and its options.

Find the determinant of a $3 \times 3$ matrix.

Find a regression equation given 12 months data on temperature and sales of a drink. Includes an interactive diagram for experimenting with fitting a regression line.

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5 questions on  confidence intervals and hypothesis testing. Population variance given, z-test. Not given, t-test.

Numbas Worksheet

Graph Limits

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