648 results authored by Christian Lawson-Perfect - search across all users.
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This question shows how to make the correct answer to a "choose one from a list" part depend on randomised question variables, in a couple of ways. The first part uses JME expressions to define the marks available for each choice. The second part uses the "custom marking matrix" option.
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A randomised line in a GeoGebra worksheet - construct the definition of the line manually Should not be used
Construct a line in a GeoGebra worksheet by writing its definition string by hand.
This isn't a very neat way of doing this. It's easier to define two points in GeoGebra, then make a line through those points. You can set the positions of the points from Numbas using vectors.
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Construct a line through two points in a GeoGebra worksheet. Change the line by setting the positions of the two points when the worksheet is embedded into the question.
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Practice bank of multivariable calculus questions
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Gradient of f(x,y,z).
Should include a warning to insert * between multiplied terms
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Find the coordinates of the stationary point for f:D→R: f(x,y)=a+be−(x−c)2−(y−d)2, D is a disk centre (c,d).
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Find the stationary points of the function: f(x,y)=ax3+bx2y+cy2x+dy by choosing from a list of points.
Inputting the values given into the partial derivatives to see if 0 is obtained is tedious! Could ask for the factorisation of equation 1 as the solution uses this. However there is a problem in asking for the input of the stationary points - order of input and also giving that there is two stationary points.
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Two double integrals with numerical limits
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Calculate a repeated integral of the form I=∫10dx∫xm−10mf(xm+a)dy
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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3 Repeated integrals of the form ∫badx∫f(x)cg(x,y)dy where g(x,y) is a polynomial in x,y and f(x) is a degree 0, 1 or 2 polynomial in x.
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Questions on adding, subtracting, multiplying and dividing numbers in standard form.
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Given the first few terms of an arithmetic sequence, write down its formula, then find a couple of particular terms.
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Work with measurements of weight, mass and density.
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Questions involving the calculation of the volumes of shapes.
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Questions on manipulating logarithms.
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Calculate a speed in m/s given distance and time taken, then convert that to km/hour
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A collection of questions on working with units of measurement, mainly in the SI/metric system.
Several 'real-world' examples.
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The gambler's fallacy - probability of getting heads again after repeatedly getting heads Ready to use
Previous throws don't affect the probability distribution of subsequent throws. Believing otherwise is the gambler's fallacy.
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Some questions on working with surds.
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Calculations and graphs involving measurements of speed.
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Solve a simple linear equation algebraically. The unknown appears on both sides of the equation.
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Given five fractions, identify the one which is not equivalent to the others by reducing to lowest terms.
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Given five fractions, identify the odd fraction out. The denominators are mainly two or three digits long.
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Estimate whether you can afford an extra item in a shop by rounding prices to the nearest 10p.
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Estimate the number of buckets of paint to buy, by rounding measurements of a room up to the nearest metre and estimating the total area.
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Questions involving various techniques for rearranging and solving quadratic expressions and equations
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Choose the probability of getting a tails, from four options.
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A bag contains balls of three different colours. You're told how many there are of each, and asked the probability of picking a ball of a particular colour.
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Given the probability that a basketball shot misses the hoop, find the probability that it's on target - use the law of total probability.
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Calculations involving elementary probability, and several questions designed to draw out misconceptions to do with probability.
