Content created by Newcastle University

Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean and standard deviation of a sample. The population variance is not given and so the t test has to be used. Various scenarios are included.

Finding the confidence interval at either 90%, 95% or 99% for the mean given the mean of a sample. The population variance is given and so the z values are used. Various scenarios are included.

English sentences which are propositions are given and the appropriate logical expression chosen for the negation of the sentence.

Three parts, where the student has to collect together polynomials in $\mathbb{Z}_3$, $\mathbb{Z}_5$ and $\mathbb{Z}_7$, respectively.

The answer to part a has no $X$ term, because they cancel out.

Choose which of 5 matrices are in a) row echelon form but not reduced b) reduced row echelon form c) neither.

Nature of fixed points of a 2D dynamical system.

Student is shown a linear programming problem, with graphical solution. 

Asked to identify binding constraints, and decide if the optimal solution is changed by a named constraint either doubling or halving.

Questions used in a university course titled "Group theory".

The questions deal with permutations written in cycle or two-line notation.

Linear program described in words. Student must write out constraints as equations in standard form, then identify the optimal solution in a finished simplex tableau.

Express $\displaystyle a \pm  \frac{c}{x + d}$ as an algebraic single fraction.

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

Calculation of the length and alternative form of the parameteric representation of a curve.

Practice bank of multivariable calculus questions

Calculation of the length and alternative form of the parameteric representation of a curve, involving trigonometric functions.

Statistics and probability. Two questions: using LSD and Tukey yardsticks.

Outward normals to the surfaces enclosing a region; volume of that enclosed region.

Multiple response question (4 correct out of 8) covering properties of convergent and divergent series and including questions on power series. Selection of questions from a pool.

Divergence of vector fields.

Cartesian form of the parametric representation of a surface, normal vector, and magnitude.

No description given

Unit normal vector to a surface, given in Cartesian form.

Statistics and probability. A question on two factor ANOVA.

Statistics and probability. 2 questions, 1 on two sample t-test and 1 on paired t-test.

Statistics and probability. Two way-anova question.

Outward normals to the surfaces enclosing a region; volume of that enclosed region.

Interpreting the minitab output from a logistic regression model of salary against obesity as measured by BMI.

Find a regression equation given 12 months data on temperature and sales of a drink. 

A multiple linear regression model of the form:

\[Y=\beta_0+\beta_1X_1+ \beta_2X_2+\beta_3X_3+\beta_4X_4+\epsilon \]

is fitted to some data in Minitab which generates a table showing estimates of the parameters with associated $p$-values. Determine which variable to exclude first.

Asking users to interpret a minitab output to give the coefficients of a multiple regression together with a prediction based on the subsequent equation.