Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Determine the single force which is equivalent to a force and a couple.

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.

Students are given an exponential equation and asked to evaluate it at two points.

The constants in the exponential are randomised.

An A-frame structure supporting a force and a moment. The feet are at the different vertical positions so the solution will require simultaneous equations, unless you rotate the coordinate system.

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Division (Rationalising) complex numbers in rectangular (Cartesian) Form.

Thanks are due to Christian for his Gap Fills in Fractions code and method

Implicit differentiation.

Given $x^2+y^2+dxy +ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Also find two points on the curve where $x=0$ and find the equation of the tangent at those points.

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This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

Students are given an exponential equation and asked to evaluate it at two points.

The constants in the exponential are randomised.

Exercises in solving simultaneous equations with 2 variables.

Questions asking for the factoring of simple case (a=1)

These first need to be changed to standard form.

Then use factors to solve.

Questions asking for the factoring of simple case (a=1)

These first need to be changed to standard form.

Cramers Rule applied to 3 simultaneous equations

Two ordered data sets, each with 10 numbers. Find the sample standard deviation for each and for their sum.

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant

Two questions on solving systems of simultaneous equations.

Solving pair of simultaneous (linear) equations

Just showing how to use the stdev function from the stats extension to calculate the standard deviation of a list of numbers.

rebelmaths

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant

Just showing how to use the stdev function from the stats extension to calculate the standard deviation of a list of numbers.

rebelmaths

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant

Calculate and work with measures of central tendency such as mean, median and mode, and measures of spread such as range and standard deviation.

Just showing how to use the stdev function from the stats extension to calculate the standard deviation of a list of numbers.

rebelmaths