Topics:
Algebra, Calculus, Trigonometeric Equations, Complex numbers & Partial Derivatives

Students must complete the exam within 120 mins (standard time).

Questions have variables to produce randomised questions.

Topics:
Algebra, Calculus, Trigonometeric Equations, Complex numbers & Partial Derivatives

Students must complete the exam within 120 mins (standard time).

Questions have variables to produce randomised questions.

Topics:
Algebra, Calculus, Trigonometeric Equations, Complex numbers & Partial Derivatives

Students must complete the exam within 120 mins (standard time).

Questions have variables to produce randomised questions.

Homework set.  Calculate Moment of Inertia for I beams, channels, angles, etc.

Find the number of people with heights greater then mean plus two times the standard deviation.

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Calculations involving Standard form.

Convert numbers between 0 and 1 intro standard form/scientific notation.

Convert numbers greater than 1 into standard form/scientific notation.

Given linear programming problems in standard form, write down the dual problem.

Public

Public

Most of the standard prefixes (not hecto, deca though), abbreviations, powers of 10, converting between prefixes for distance, capacity, mass.

A normal curve is shown, with the mean and +/- 1, 2 and 3 standard deviations marked. An area of the curve is shaded and students are asked to estimate the shaded area using the heuristic rule. There are 6 possible areas: (-infty, mu-2sd), (mu-2sd, mu-1sd), (mu-1sd,mu), (mu, mu+1sd), (mu+1sd, mu+2sd), (mu+2sd, infty). The mean and standard deviation are randomised.

Find and compare means and standard deviation using EXCEL (downloadable randomised dataset)

Convert numbers greater than 1 into standard form/scientific notation.

Find the number of people with heights greater then mean plus two times the standard deviation.

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.

The student must write code to compute the standard deviation of an unknown list of measurements.

The suggested answer uses numpy.std.

A measurement is performed multiple times for the same object, the student will

• calculate the mean result
• calculate the standard error on the mean 
• write the mean±error to the correct precision as defined by the error written to 1 significant figure 

Advice is provided including on performing the calculations in Python or spreedsheets together with further reading. 

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

Find the first 3 terms in the MacLaurin series for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

The student must write code to compute the standard deviation of an unknown list of measurements.

The suggested answer uses numpy.std.

Dane są średnia i odchylenie standardowe z próby. Należy przeprowadzić test istotności dla średniej i zweryfikować postawioną hipotezę.

This question is the one described in method 2 of the example "Apply a standard integral" in the Numbas documentation.

The student is shown a randomly chosen function to integrate. The function is one of $e^{kx}$, $x^k$, $\cos(kx)$, $\sin(kx)$, with $k$ a randomly chosen integer.

Just showing how to use the stdev function from the stats extension to calculate the standard deviation of a list of numbers.

Just showing how to use the stdev function from the stats extension to calculate the standard deviation of a list of numbers.