Three Keywords : Exact Sketch and Plot
Exact Sketch and Plot are three words you may see in exam questions that have specific meanings.
This is the first of 2 or 3 posts I intend to make this week about words you may see in an exam question and the specific meanings of these words. I might run a quiz on these words in a few weeks time.
One of my students likes to reach for his calculator to given a numerical answer to questions – but this is what you should not do when a question asks for an exact answer.
In an exact answer questions, symbols like √2, e, and π are exact descriptions of values. 1.414, 2.718 and 3.142 are approximations.
A question that asks you to find an exact value, and you reach in your calculations π + e, then leave this as the answer. Do not write the answer as 5.860 (though that is correct to 3 s.f, its not exact)
If a questions ask for a sketch of the graph of a function, it is not asking you to find the values over a range, and plot each point. The idea behind a ‘Sketch’ question is to give a general idea of the shape of the graph. Certain points of interest of the graph are important in a sjetch
i) Points where the axes are crossed
ii) Turning points and points of inflection – where the gradient is 0
iii) Asymptotes – lines to which the curve is getting close to but not touching
iv) An idea of what the function does outside the range; Gets bigger/smaller, tends to 0, repeats (as in sine curve)
The diagram below shows a sketch of the graph of f(x) = 1/(1+x2)
In sketching this function, the important things to note are
i) Its always positive
ii) It will have a maximum when 1+x2 is minimum (when x=0). This will also be the pint the y axis is crossed
iii) To the left and right the line will get closer and closer to the x axis.
And here is my sketch of the function. I should mention here I find it much easier to sketch graphs with hand pencil and paper than I do with a mouse. This isn’t great but gives the idea
In an exam question on graphs, plot is asking for the opposite of sketch. This is where you are expected to work out values of the function, plot them on the graph and join up. Draw has a similar meaning.
In the next post I will give some of the words that signify a ‘proof’ type question, and what each one means