Calculating the derivative of a function of the form $e^{ax^2+bx+c}$ using the chain rule.

Calculating the derivative of a function of the form $\tan(a \ln(bx))$ using the chain rule.

Calculating the derivative of a function of the form $\cos(a \ln(bx))$ using the chain rule.

Calculating the derivative of a function of the form $\sin(a \ln(bx))$ using the chain rule.

Calculating the derivative of a function of the form $\tan(e^{ax}+bx^n)$ using the chain rule.

Calculating the derivative of a function of the form $\cos(e^{ax}+bx^n)$ using the chain rule.

Calculating the derivative of a function of the form $\sin(e^{ax}+bx^n)$ using the chain rule.

Calculating the derivative of a function of the form $\tan(ax^m+bx^n)$ using the chain rule.

Calculating the derivative of a function of the form $\cos(ax^m+bx^n)$ using the chain rule.

Calculating the derivative of a function of the form $k(ax^m+b)^n$ using the chain rule.

Calculating the derivative of a function of the form $k(ax+b)^n$ using the chain rule.

Calculating the derivative of a function of the form $(ax+b)^n$ using the chain rule.

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

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Two questions testing the application of the Sine Rule when given two angles and a side. In this question, the triangle is always acute.

A question testing the application of the Cosine Rule when given two sides and an angle. In this question, the triangle is always obtuse and both of the given side lengths are adjacent to the given angle (which is the obtuse angle).

Match the equivalence with the rule

Differentiate $f(x) = (a x + b)/ \sqrt{c x + d}$ and find $g(x)$ such that $ f^{\prime}(x) = g(x)/ (2(c x + d)^{3/2})$.

Two questions testing the application of the Cosine Rule when given two sides and an angle. In these questions, the triangle is always acute and both of the given side lengths are adjacent to the given angle.

Calculate the distance between two points along the surface of a sphere using the cosine rule of spherical trigonometry. Context is two places on the surface of the Earth, using latitude and longitude.

The question is randomised so that the numerical values for Latitude for A and B will be positive and different (10-25 and 40-70 degrees). As will the values for Longitude (5-25 and 50-75). The question statement specifies both points are North in latitude, but one East and one West longitude, This means that students need to deal with angles across the prime meridian, but not the equator.

Students first calculate the side of the spherical triangle in degrees, then in part b they convert the degrees to kilometers. Part a will be marked as correct if in the range true answer +-1degree, as long as the answer is given to 4 decimal places. This allows for students to make the mistake of rounding too much during the calculation steps.

Instructional "drill" exercise to emphasize the method.

Thanks to Christian for his method for use of gaps in fractions.

Instructional "drill" exercise to emphasize the method.

Thanks to Christian for his method for use of gaps in fractions.

Instructional "drill" exercise to emphasize the method.

Thanks to Christian for his method for use of gaps in fractions.

Instructional "drill" exercise to emphasize the method.

Thanks to Christian for his method for use of gaps in fractions.

Instructional "drill" exercise to emphasize the method.

Thanks to Christian for his method for use of gaps in fractions.

Instructional "drill" exercise to emphasize the method.

Thanks to Christian for his method for use of gaps in fractions.

Practice using the log rules to add and subtract logarithms

Cramers Rule applied to 3 simultaneous equations

Simple application of "Power Rule" to differentiate polynomials.

Some co-efficients and powers are non-integer and some may be negative.

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

Some co-efficients and powers are non-integer and some may be negative.