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Simlify (expand) logarithmic expressions 

Expand $\ln(\dfrac{a^{x}}{b^{y}})$ into $x\ln(a)-y\ln(b)$, x and y randomised.

Expand $\ln(a^{x}b^{y})$ into $x\ln(a)+y\ln(b)$, x and y randomised.

In the first part, the student is asked to enter dimensions of a box in a spreadsheet.

The values are extracted as a list of numbers by changing the interpreted_answer note in the first part's marking algorithm, and the calculated volume is used as the answer to the second part, through adaptive marking.

Using basic derivatives to calculate the gradient function of a hill $y=-e^x+b\ln\left(x\right)+c$, and then substituting values to find the gradient at specific distance from the sea. 

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Given price, marginal cost and fixed cost, find the quantity that maximises profits.

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This question assesses learners' ability to conduct a two sample t-test. 

This question assesses the learner's ability to compute a confidence interval for a difference of two means, given two samples.

Randomized variables: sample raw data and confidence level. 

Adapted from section 7.3.1 in OpenIntro Statistics (4th ed).

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

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

rebelmaths

This question plots a general amplitude modulated carrier signal defined by $v_s(t) = (V_{DC} + V_m \cos(2\pi f_m t))\cos(2\pi f_c t)$, where $V_{DC}$ is a DC offset, $V_m$ is the message amplitude, $f_m$ is the message frequency and $f_c$ is the carrier frequency ($f_c = 20f_m$ in this question). The student must identify the values of $V_{DC}$ and $V_m$ and enter these values into the appropriate gaps in the equation of the AM signal.

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3230 Radiation and Matter Core Exercises, Unit One

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Given a graph of the form either a.cos(bx) or a.sin(bx), identify the amplitude and period.

Drag a point into the specified quadrant. Uses jsxgraph

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Choosing whether given random variables are qualitative or quantitative.

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.

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Question Covering SSD & frequency response