MT171 - FEEDBACK COMMENTS FOR QUESTION SHEET 1-18/19 Questions marked: Q1/Q2/Q3(b)/Q4(b) and (d)/Q5 Each question will be classified as 0-if it is mostly incorrect 1-if it is about half correct 2-if it is mostly correct. The maximum you can get is 10. For continuous assessment: if you didn't do enough work there will be a box encircling a zero at the top of the work you gave in. Otherwise your work will have gained a 'one' and nothing will appear written. Comment 1 (C1) Your presentation needs to be improved. Comment 2(C2) Your mathematical accuracy needs improvement. Comment 3(C3) Give a mathematical argument to justify your claim. Q1 (a) and (b) Comment 1.1 (C1.1) Use a ruler to draw axes and linear graphs. This is to be sketched by you on paper. Graphs have to be labelled and scales indicated on them. You miss marks for that in exams! Comment 1.2 (C1.2) Use your mathematical knowledge to draw the graphs and not tables of values! Justify each part of your sketch. For example in part (b) include: y = Vr is the parabola with the x-axis as axis, vertex the origin and passing through the point (1,1); y = 2 -x line having gradient -1 and passing through the point (1,1) whilst y = (2-x)2 is the parabola with vertex the point (2, 0), the line x = 2 as axis and passing through the point (3, 1). Q1 (c) Comment 1.3 (C1.3) -2 <<< 0, 0 <<< 2 and 2<x <3 Here you need to find the three different functional forms needed in the domain of the function: for which we have -2x-(2-) =- (x+2); - 2 << 0, 2x-(2-x)=3x-2; 0 << 2, y = 2x-(x-2)=x+2; 2 << 3. This should be calculated and then plotted .... do not use tables of values. 1
Q2 Comment 2.1 (C2.1) Well done but look up your definition of a circumference. The equation of the circumference in general is x2 + y2 = (radius)2 In here you have part of it so you need x2 + y2 =22 giving y =V 4- x2 in the interval p ? x ?2 . Q3 (b) Comment 3.1 (C3.1) You should deduce the functional forms for the extended domain !- 3? x ?3, by using the definition of even and odd functions (see solutions). Of course it is also possible to draw the graph and deduce from it the functional forms, which will give you the good answer if you are careful because the examples are simple. Comment 3.2 (C3.2) Use the definition of even function and odd function to guideline your search for the corresponding functional forms! Q4 (b) and (d) Comment 4.1 (C4.1) Plot the values only in the intervals you are asked to sketch the plot for. When a function is discontinuous, there shouldn't be any lines joining corresponding points (or at most use dotted lines). Comment 4.2 (C4.2) You should use the properties of a periodic function to evaluate the values