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Query: I've got data for the number of children absent from a certain class. The data is already in a table [supplied]. How do I find the mean of this data?
Response: Please click the graphic to view the data and the calculations to arrive at the mean.
Query: How do I estimate the height of this mast (see diagram)?
Response: The man's height has to be estimated first. Next, you calculate how many men of the same height (i.e. standing on each other's heads) it would take to reach the top of the mast.
Click on the graphic below to see how you would show this.
Query: What is the order of rotational symmetry of this shape?
Response: If you rotate the shape you can see that it will fit its own outline four times in each complete revolution.
Hence the order of rotational symmetry is 4.
Query: The sum of the first three terms of an AP is 15 and the sum of the first five terms is 40. Find the first term and the common difference.
Response: Always write down the first few terms of the series, so that you know what you're dealing with. Please view the graphic for the solution.
Query: John's pulse rate is taken every 6 hours over a three day period. The graph shows his pulse rate in beats per minute. [Please click on the graph to see it full size]
Find the difference between his lowest and highest pulse rate on the 3rd of May.
Response: From the graph the highest rate is 102 and the lowest is 97. Hence the difference is 102-97=5 beats per minute.
Query: I'm given that the cost of a taxi fare is made up of a fixed charge of $4.20 and 45 cents per mile travelled. How do I find the cost of a 30 mile journey?
Response: You'll need to work out 30 x 45 cents (use $0.45 in a calculator) and then add the $4.20 fixed charge to this.
The answer is $17.70.
Query: How do I find the shaded area, given that the circular shapes are quarters (i.e. quadrants) of circles whose radii of 12 cm. are equal to the side length of the square ABCD, with centres A and C.
Response: Please click on the graphic below to view the solution.
Query: Describe fully the transformation which takes shape A onto shape C. [Please click on the graphic to see the full size question].
Response: It can be seen that the shape A has been turned to arrive at position C, so a favoured method is to use tracing paper to investigate it further.
Proceed as follows: Trace the shape A and place it directly over A. Now put your pencil point on the point (0,0) and rotate the paper. Does the shape A cover position C? In this case it does, but in another question you would have to try other 'centres' with your pencil point, until one works.
You'll see that the transformation which maps A onto C is a clockwise rotation of 90o centered at the origin (0,0).
Query: How do I show that the point P(p2,1/p) lies on the curve y2x=1 for all non-zero values of p?
Response: Click on the graphic to view the solution.
Query: Cliff and Elvis support their local football team and decide to share the cost of a field season ticket for next season. The season ticket costs £240 and they split the cost in the ratio 3:2. Calculate how much Elvis pays?
Response: Elvis pays two-fifths of £240, i.e. £96.
