Questions testing rather basic understanding of the index laws.

Questions testing rather basic understanding of the index laws.

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product rule. Find $g(x)$ such that $f^{\prime}(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$.

The student is asked to integrate a given function. The marking algorithm differentiates the student's answer, and checks that it is equivalent to the original function.

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This question shows how to use the programming extension's run_code function to run some Python code and use its result in the marking of a non-code part type.

Python is used to calculate the correct answer for a number entry part type. This could be done

In four parts, the student builds up the definition of a class representing a rectangle. First they write the constructor, then add methods to compute area and perimeter.

In the final part, they must use the methods to write a function which determines if a rectangle's area is larger than its perimeter.

In the first part, the student must write an R function to compute the first $n$ terms of the series $\frac{1}{k!}$.

In the second part, they must use that function to calculate an approximation to $e$ using a given number of terms of the series.

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.

Choose one from a list to identify the function shown in a graph. The function is a randomly selected sin, cos, or tan graph with random scale factor.

Simple application of "Power Rule" to differentiate single term functions.

All co-efficients and powers are integer (though some may be negative.

Finding composite functions of a quadratic function and a logarithmic function.

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.

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.

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

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.

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Calculating the integral of a function of the form $4ax(ax^2+b)^n$ using integration by substitution.

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Integrating a function of the form $\frac{a}{x}$ using a table of integrals / anti-derivatives.

Solve equation involving exponential function

Solve equation involving exponential function.

Solve equation involving exponential function.

Solve equation involving logarithmic function.

Solve equation involving logarithmic function.

This question asks the student to calculate three points of a given linear function then plot these points in a JSXGraph item and find the x and y intercepts of the line.

Set up and solve an equation = 1, to ensure a function is a CRV

A function $f(x) = cln(ax^2+bx) -x$ is sketched and tangent is also drawn. The equation of the tangent line is asked for and $x$-coordinate for horizontal tangent is asked for. Calculator.

Q1 is true/false question covering some core facts, notation and basic examples.  Q2 has two functions for which second derivative needs to be determined.