Fairly simple questions using differentiation "power rule" and "sum or difference rules" to differentiate single term functions and polynomials.

Some co-efficients and indices can be negative and/or fractional.

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Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

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The student is presented with a scenario then asked to select a sample size to investigate and the number of bins for a histogram of the data. Theoretical distributions of normal, uniform and lognormal distributions can be overlayed on the histogram. Student is asked to identify the most likely distribution and the mean of this distribution (within a +/-10% margin of error).

Students are asked to move an x-axis slider representing standard deviation on a normal distribution to make the area between (mean - slider value) and (mean + slider value) equal to a certain percentage. The 3 possible percentages correspond to the mean plus or minus 1, 2 or 3 standard deviations.

Find the centroid of a shape made up of a rectangle and two triangles.

Friction

Students are asked to move an x-axis slider on a normal distribution to make the area to the left of the slider equal to a certain percentage. The 6 possible percentages correspond to the mean plus or minus 1, 2 or 3 standard deviations.

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Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

Find modulus and argument of two complex numbers. Then use De Moivre's Theorem to find positive powers of the complex numbers.

Find modulus and argument of the complex number $z_1$ and find the $n$th roots of $z_1$ where $n=5,\;6$ or $7$.

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).

This question assesses the learner's ability of calculating confidence intervals for numerical data and conducting a one-sample t-test.

Randomized input values: sample summary statistics and confidence level.

Adapted from question 7.12 in OpenIntro Statistics (4th ed).

Find the derivative of a function of the form $y=ax^b$ using a table of derivatives.

Factorise $\displaystyle{ax ^ 2 + bx + c}$ into linear factors. 

Given a generating matrix for a linear code, give a parity check matrix

Volume of a tetrahedron using integrals

Calculating the area enclosed between a linear function and a quadratic function by integration. The limits (points of intersection) are not given in the question and must be calculated.

Inputing Integrals tutorial

3 Repeated integrals of the form $\int_a^b\;\int_c^{f(x)}g(x,y)\;dy \;dx$ where $g(x,y)$ is a polynomial in $x,\;y$ and $f(x)$ is a degree 0, 1 or 2 polynomial in $x$.

Calculate a repeated integral of the form $\displaystyle I=\int_0^1\;\int_0^{x^{m-1}}mf(x^m+a)dy \;dx$

The $y$ integral is trivial, and the $x$ integral is of the form $g'(x)f'(g(x))$, so it straightforwardly integrates to $f(g(x))$.

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Rolling a pair of dice. Find probability that at least one die shows a given number.