Find a regression equation.

Given two propositions in mathematics using quantifiers, choose the corresponding negation of the proposition. For example, the negation of: $\displaystyle \exists a \in \mathbb{R^+},\;\exists b \in \mathbb{N},\;\exists c \in \mathbb{N}\;\left[(c \lt b+1) \land \left(\frac{1}{2^n} \geq 3a\right)\right]$

Given a 3 x 3 matrix, and two eigenvectors find their corresponding eigenvalues. Also fnd the characteristic polynomial and using this find the third eigenvalue and a normalised eigenvector $(x=1)$.

A question testing the application of the Cosine Rule when given three side lengths. In this question, the triangle is always acute. A secondary application is finding the area of a triangle.

Two questions testing the application of the Sine Rule when given two sides and an angle. In this question, the triangle is always acute and one of the given side lengths is opposite the given angle.

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

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

Spearman rank correlation calculated. 10 paired observations.

Spearman rank correlation calculated. 8 paired observations.

Match up equations with the corresponding lines on a graph.

Some conceptual questions about parallel lines - fill in the gaps in some statements.

Identify the lines corresponding to given equations, and the lines parallel to lines with given equations.

Choose from one of several pre-defined scenarios, and set variables to the corresponding values, defined in lists.

This question has three variables: city, population, and percent_like_chocolate. These differ for each city. We've defined a list for each variable, with the corresponding values. A variable called scenario picks a random position in the list, so the value of city, for example, is cities[scenario].

This question concerns the evaluation of the eigenvalues and corresponding eigenvectors of a 2x2 matrix.

For a sample of size n from a normal distribution, given mean of the sample mean and the standard deviation , find the t-statistic corresponding to a null hypothesis $\mu=m$ and a given confidence level. Check if the result is significant at this level.

Find a regression equation.

Given three vectors with integer components, find the corresponding magnitude and direction.

Given three vectors with integer components, find the corresponding magnitude and direction.

Given three vectors with integer components, find the corresponding magnitude and direction.

This question concerns the evaluation of the eigenvalues and corresponding eigenvectors of a 2x2 matrix.

This question concerns the evaluation of the eigenvalues and corresponding eigenvectors of a 2x2 matrix.

Given three vectors with integer components, find the corresponding magnitude and direction.

Given a 3 x 3 matrix, and two eigenvectors find their corresponding eigenvalues. Also fnd the characteristic polynomial and using this find the third eigenvalue and a normalised eigenvector $(x=1)$.

Differentiation question with customised feedback to catch some common errors and corresponding partial marks.

malrules

Find a regression equation.

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

Given a 3 x 3 matrix, and two eigenvectors find their corresponding eigenvalues. Also fnd the characteristic polynomial and using this find the third eigenvalue and a normalised eigenvector $(x=1)$.

Given a statement in words of a relationship between two variables, write down a corresponding formula. It's marked correct if values satisfying the relationship satisfy the formula, and values not satisfying the relationship don't.

Then, given a value for one of the variables, work out the value of the other one. They're substituted into the formula given in the first part and marked correct if it's satisfied.

Both parts use custom marking algorithms.

Given two propositions in mathematics using quantifiers, choose the corresponding negation of the proposition. For example, the negation of: $\displaystyle \exists a \in \mathbb{R^+},\;\exists b \in \mathbb{N},\;\exists c \in \mathbb{N}\;\left[(c \lt b+1) \land \left(\frac{1}{2^n} \geq 3a\right)\right]$

For a sample of size n from a normal distribution, given mean of the sample mean and the standard deviation , find the t-statistic corresponding to a null hypothesis $\mu=m$ and a given confidence level. Check if the result is significant at this level.

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Students are given six graphs, corresponding to curves $\gamma(t)$. They must match each with its signed curvature function, $\kappa(t)$.

The graphs are generated by calculating $\theta(t)=\int \kappa(t) \mathrm{d}t$ (by hand: these are given to the question as functions of a variable '#', in string form), and solving $x^{\prime}=\cos(\theta(t)-\theta(0))$ and $y^{\prime}(t)=\sin(\theta(t)-\theta(0))$ numerically (using the RKF method) with a JavaScript extension.