May TZ2 exams
Thursday 10 May 2018
I got my first look at the May 2018 TZ2 papers today and I thought I would write a quick reflection. Clealry it is important for us, as teachers, to have a good look through the papers so that we can prpeare ourselves for the G2 forms where we getr the chance to have our say and then so that we can think for ourselves about fine tuning we can do to prepare our suture stuents. It is a challenge for question writers to balance the need for an exam tha tests the syllabus and stays in the spiriti of the mathematical studies course, but also one that is not too predictable. I take my hat off to paper editors as it strikes my as a very difficult and probably thankless task! It is a really salient task to go through an exam ppaer like this and try to imagine how your students might have paporached the questions and relate it to the experiences they have had in the classroom. There is always room for a bit of reflection on how we might do this better. Anyway, here goes, here are my intial thoughts on this paper. (Note - obviously I can't publish the paper itself here is it is IB copyright - check with your exams officer to see a copy)
On the whole it seemed lile a fair paper. Perhaps there a more little twists than there are at other times which cvan be off putting......
Question 1 - Lines of best fit
A fairly gentle start and no complaints for me. that said I am a little disappointed that linear rgression did not appear anywhere else. I spend a lot of time helping students understand how to use their GDCs for 1 and 2 variable data and this question does just give them the answer. It also seems a bit odd to focus on lines of best fit by eye when students know how get their GDCs to find the accurate answers.
NOTE - Question emphaisises the importance of students knowing that a line of best fit must go through the mean point.
Question 2 - Truth tables
Another fairly gentle starter question. The catch is that, as the table is drawn the two columns being compared for implication are in the wrong order. I generally encourage my students to rewrite some columns so that the implication can be in the right order for easy analysis. perhaps the question could have helped there for question 2. i'll bet this caught a few out.
NOTE - Emphasis on managing implication where columns are in 'the wrong' order.
Question 3 - Standard form
I have seen esier standard form questions at the start of an exam. The context takes a bit of thinking about but is otherwise a fairly standard kind of question
NOTE - Are students exposed to enough variety of contexts for questions.
Question 4 - Number sets
No complaints and I like that the second part asks students to reflect on the nature of sets and subsets a bit more than these questions usually do. That said, I hoe that the markscheme alows for students to write the same number in each of the boxes for part A. I bet not many were brave enough.
NOTE - Show my IB1 students some different answers to this question.
Question 5 - Compound interest and currency exchange
Part a) was fairly standard and a bit of thinking required for part b). I find myself wondering how many students would have set this up as an equation. - and whether or not they needed to...
NOTE - to think about approaches I might expect students to take to this kind of question.
Question 6 - Linear functions
Good fair question - Once again, I wonder about the approaches my students might have taken to part b). I wonder how many of them used the simulatenous equetion solver, how many plotted the functions and found the intersection, how many did it by eye.
NOTE - Thinking about the merits of showing muliplte approaches to questions. How often do I let students show each other the multiple approaches they actually use?
Question 7 - Probability from the table
A good start with 3 marks fairly esily available. Part c) is a bit of 'without replacement'. I wonder how many students visualise a tree diagram here. For how many is there in instinct to think of combined events and multiplication. Sometimes I think the tables are easier, but for combined events I think the tree diagram leads students more successfully.
NOTE - To make more explicit links between different representations for probability.
Question 8 - Non right angmed trig
Not much to say about this one. Fairly straightforward. I would be curious to know how many candidates labelled the trinagle with As Bs and Cs. I think I have a helpful instinct to see D2 as an intersection and D3 as a union straught away. Increasingly find this is a helpful approach.
NOTE - Nothing coming to mind just yet for this one.......
Question 9 - Shading Venn Diagrams
Ooh, I think students may have struggled with Diagram 2 and 3. I dont object to the question though. I suspect that the subset structure in Diagram 2 is seen less often. Of course there will be more ways to say Diagram 3 - I am sure the markscheme allows for it!
NOTE - to think about activity that helps students decide if they are looking at an Intersection or a union.
Question 10 - Exponential models
Good question and I like part b) - I think we can expect to see more of this in the new applications and Interpretations course. For part c, I am guessing (hoping?) students multiplied their value of A by 40 and looked at the table function. Is that more instincitve than solving 2 to the t = 40? The later seems quicker....
NOTE - I want to think about asking more 'what does this represent?' type questions
Question 11 - Rational functio and asymptote
Hmmm - again, I hope that students who needed it plotted the function on their GDC. Its another case of looking at multiple methods though. STudents could look at the table for the gaps in the x and y column. I like them to think about what f(x) can never be. I wonder how many went from the condition that x cant be zero to the vertical asymptote..... Then i wonder how many used equation solver for part c.
NOTE - I am reflecting on the formal treatment of rational functions. Again, perhaps this will be more obvuious in the new course when students will be expected to reflect on the significance of the asymptotes.
Question 12 - Histograms and estimate of the mean.
Estimates of the mean are notorious stumbling blocks. Possibly even this question with a frequency missing might even encourgae some better thinking. Part a) does lead students a little in the right direction....
NOTE - ....
Question 13 - Quadratic models
This seems doable for a Q13. I think it can all be done on the GDC right?
NOTE - Alternative forms for quadratic models - how comfortable are students in dealing with these?
Question 14 - Calculus
It is nice that parts a and b are aproachable. Clearly at the business end, I can see that part c) will trip up a lot of students., although it is not really that hard once you have worked the question can be seen as finding the x value where the gradient is 8.
NOTE - Again - thinking about exposure to this kind of twist on the key ideas is difficult. I think this is where we as teachers need to try and make sure we are encouraging students to speculate with information. For example - ideally, a student would say something like 'So, if I know that the graident of the normal is this..... then what else can I find out?' and then the question could iopen up nicely. This is tough but important.
Question 15 - 3D Geometry
This is not too bad for a Q15. I think there is plenty of potential for students to get method marks for beginning to solve this by writing expressions for surface area. Sure, they will need to be fairly precise to solve the whole question, but I would hope that most students could get at least 2 or 3 marks on this question.
NOTE - I am reminded of what I often refer to as 'scrapping around for marks' and how pertinent that could be here. Also, I wonder how many of them didn't get to this question and have that chance. Exam technique!!!
Dangerous though it is to say so out loud, paper 2 did seem very approachable and did not contain many (if any) of the twists that we sometimes see...... but we will have to wait and see how students got on with it!
Question 1 - Sets and Probability
This looks like a nice question to start woth. There are plenty of approachable marks and probably the most challenging parts were not in a position where they could put you off or hinder progress on the rest of the question.
Question 2 - Cumulative Frequency
Again - this seems like an easy question without any twists or challenges really. I would hope students could cash in here. It does seem as hame though that there is a 15 mark paper 2 question on statistics that doesn't involve any interpretation at all. Clearly, those questions are harder to ask and assess (and maybe even harder to answer) but it is really the point of statistics. Thik there is room for more of this and I expect to see more of it in the new course.
Question 3 - Normal Distribution and Chi Squared test.
Another fairly straightforward question I think. perhaps in part b) students might be held up dealing with 1.5 standard deviations instead of a given maximum and minimum, but b)ii) asks them to sketch the curve which, in turn, invites them to work out the uppoer and lower limits. Here is another stats question without any significant interpretation though.
Question 4 - Sequences
The context can often make it a little harder to get in to, but I would expect students to spot this as a fairly standard sequences question - again without any real twists.
Question 5 - Trigonometry
Part a) really need students to have that 'speculative' approach I mentioned earlier. 'Given what I know - what else can I work out?'. otherwise, since it is a show that question, they could move on using 85° for the rest. There is a a bit of problem solving to do here, but nothing particularly tricky.
Question 6 - Calculus
And once more - compared to some optimisation questions that come up on paper 2, I think this is very approachable. I raised an eyebrow at the use of the term stationary points and certainly part f) will leave out a lot of people.