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Solve a simple linear equation algebraically. The unknown appears on both sides of the equation.

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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.

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

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

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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.

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