# Past Paper Review

## Keeping an eye on the exams

This section is intended as place to keep records of the different exams that have been produced for the syllabus in which the first exams were taken in May 2014. Reviewing these exams is a really important part of being a Maths Studies teacher. This is particularly true at the beginning of a syllabus cycle when we are all anxious to see the style of questions that are going to go with the syllabus changes. Equally important is that teachers take the opportunity to fill out the 'G2' form giving the IB feedback on the exams. This can be found on the left hand menu of the online curriculum centre. I highly recommend that teachers take some time to go through the paper and fill in this form. From my experience, reading is often not enough. I find I actually need to do the questions to find out the fine details of the questions and try to have the experiences that students have. I am writing these notes here as I go through that process as well as some written solutions as a suggestion to students for how they might be expected to write answers. Eventually this page will be more like a directory as the number of exams produced increases. For the time being the reviews appear here.

*Note - the papers themselves are IB copyright and so I cant share them through this site. You should, however, have access to these through your IB coordinator.

## May 2014 - Timezone 2

### Paper 1 Overview

Question Number | Main Topic tested by the question |

1 | Standard index form/Scientific notation, circumference of a circle |

2 | Language of logic notation. Contrapositive, logical equivalence |

3 | Venn Diagram showing sets of numbers |

4 | Volume of spheres, units of volume |

5 | Box plots and 5 figure summaries |

6 | Generating and solving a quadratic equation in the context of area. |

7 | Gradients and straightline functions in the form ax + by + d = 0 |

8 | Chi Squared test using critical value |

9 | Exchange rates |

10 | Right angled trigonometry |

11 | Exponential functions |

12 | Linear regression |

13 | Calculus terminology, gradients and tangents |

14 | Normal Distribution |

15 | Calculus |

### Paper 1 Question Details

This section deals with the specific details of the question and the associated notes for teaching.

Question 1

- It is notable to see the geometric context used for the question. The formula for circumference of a circle is included in presumed knowledge section of the formula booklet.
- The front cover clearly states that answers should be given exactly or to 3 sf. I advise students to do both.
- Students should strictly use the unrounded answer to part b for the calculation in part c. The markscheme often allows for them not having done this.

I would have thought it better to ask for the answer to part c) to be given in standard form since this is a good example of its use and offers another opportunity to test the skill as opposed to simply asking students to multiply by 17. It is the first question though so offers a gentle introduction.

Solution

Question 2

- Students MUST remember the standard results for inverse, converse and contrapositive. This, from my experience, is rare because of how infrequently they are used.
- Part c) is a change for this new syllabus and has an implication for teaching examples of logical equivalence.

I think that it is a lot to ask for students to do the truth tables required to test logical equivalence of the statements. There is no structure given for the truth tables and the question is only worth 2 marks.

Solution

Question 3

- A straightforward question.
- Offering the example is a welcome addition
- Students must know the definitions of these sets.

Solution

Question 4

- Volume of a sphere is given in the formula booklet.
- Again, for part b) students should use the unrounded answer to part a)
- Students should take care to add the correct units to answers
- If students cant do part c) they should still attempt part d) with a guessed answer

Solution

Question 5

- Students should pay attention to units
- Students should take care to write the difference between the LQ and the UQ for the IQR rather than writing LQ - UQ

Part d) is a nice addition and demands that students understand what this diagram actually means. These is a nice point for teaching.

Solution

Question 6

- Students need to know which option they are going to use to solve a quadratic equation. Either Solver, finding roots/zeros or using the table function. It is preferable that students are aware of all of these methods.
- Students really should get method marks here for writing the quadratic equation.

Solution

Question 7

- It is worth noting that reading from scales is worth quite a few marks in maths studies.
- Students need to know how to work out the gradient when the equation of a line is given in the form ax + by + d = 0. They can either just know that the gradient is -a/b or be comfortable re-arranging the equation so that it is in the form y = mx + c
- Students often struggle to recognise that the intersections of y = ax +by + d = 0 are easily found by substituting y= 0 and x = 0

Solution

I like this question, but do find the context hopelessly unrealistic. It is fine to have questions involving abstract mathematics and equally fine to have genuine applications, but this semi reality in the middle is part of what can leave maths studies students cold.

Question 8

- Important to note, that the chi squared statistic will still be asked for in exams. The critical value is given. Questions can ask for the p-number as well. Both are possible.

Solution

Question 9

- Students must pay attention to the instruction at the top that all answers must be given to the nearest whole number

I like this question - it is a very real mathematical problem and part b) (ii) demands that students think about what they are doing.

Solution

Question 10

- Students MUST be using their calculators in 'Degrees' mode
- Again, attention should be paid to units

I was interested by the context. I did some quick research and found this diagram for Boeing planes. Of course the angle is not constant and all of the initial angles are 10 degrees or lower. I thought this could be a good context for an investigation. Watch this space!

Solution

Question 11

- Students should/could make use of the table function on their calculators for all three parts.
- To get an answer to part c) students would have to set the table to show 2 decimal places, thus 3 significant figures and choose the first value of t that gives a value of D less than .333
- Alternatively, students can use the solver function for part c)

Solution

Question 12

- This question simply demands fluent calculator skills.

Solution

Question 13

- Parts a, b and c involve conceptual understanding.
- For part e) students should know how to get their calculators to give them this equation. (A paper 2 question may involve more working out)

I find part d) of this question a little ambiguous. Given the lack of grid points, I am assuming they meant 'sketch'. To draw it would require knowing its equation first and then plotting it accurately which would be very difficult without the grid points/lines.

Solution

Question 14

- Parts a) and b) rely on understanding of the normal distribution and the standard results for 1,2 and 3 standard deviations from the mean.
- Parts c) and d) depend on calculator skills as well.
- As such, it is worth noting that we can expect questions that students are not expected to use their calculators for.

Given that the standard results (68%, 95% and 99%) are technically estimations and I would prefer that the question somehow makes it explicit that these estimations are expected for parts a) and b). It could be inferred by the fact that part c) says using your GDC. Are students further confused that part d) does not include that? I am happy with the other details of the question, but I do think this is a point to consider for future questions.

Solution

Question 15

- Students need to watch out for the negative index. I suggest rewriting f(x) using a negative index as opposed to a fraction.
- Calculator skills required for part b)

A surprisingly straight forward question 15. I hope students got to it!

Solution

### Paper 2 - Overview

Question Number | Topics covered |

1 | Probability, tree diagrams and conditional probability. |

2 | Non Right-angled Trigonometry, units and compound measures |

3 | Grouped data, estimating the mean and interpreting cumulative frequency diagrams |

4 | Arithmetic and Geometric sequences, compound interest |

5 | Modelling with Geometry, optimising with Calculus |

6 | Modelling with Quadratics, volume of prisms and percentage |

### Paper 2 - Question details and review

Question 1

- Students should understand complementary probabilities and how to calculate the probabilities for 2 combined events.
- Questions involve the 'and' and 'or' rules.
- For parts c) and d), students need to realise that a new set of 2 combined events are required that don't involve the 'ties'. Seems obvious, but this is quite a lateral shift for teachers to think about introducing.

A good question in terms of covering the topic. The following is not a complaint, but more of a question. The role of the 'semi-real' context is understood by Maths educators and it has a clear purpose. The context provides a model for application and actually makes the problem more approachable than it would be in the abstract. I wonder though, given the aims and objectives of this course, whether or not there should be an attempt at a more realistic context?

Solution

Question 2

- Students should practice laying out answers to these type of questions. It
*may*be advisable to draw repeated diagrams for the different parts of the questions. - Students should try to use the unrounded answers as much as possible. In either case, they should be clear about which answer they are using for subsequent parts.
- Students should be careful not to forget the role of units in this question.

Another good question.

Solution

Question 3

- Students should know how to use a second list as a frequency column and get the estimate from the calculator. this is only worth 2 marks.
- The first list should contain the mid-points of the interval.

Part e) (i) was not well worded. 'The time taken for 40 people to drink their coffee' We might ask which 40 people? This could have been written. I guess the intention was that it was the 40 people with he quickest drinking times.

There was a heavy emphasis on statistics in the first paper so I was surprised to see another stats question in this paper.

Solution

Question 4

- Students need to recognise the arithmetic and geometric sequences and model these options accordingly. It is possible to answer the questions without doing this, but it would take longer and there is more potential for error.
- Students should write out the formula they are going to use before substituting. this for the compound interest section as well.
- The table function can be used to solve part f) (set table step to 0.01 for an answer to 3sf). Alternatively they can use the solver function. They should write down the equation they are trying o solve in any case.

I just have a question about the degree of accuracy expected in part f). Obviously 3sf is the default, but this is rarely used in compound interest questions on this course.

Solution

Question 5

- Students need to recognise that not all the parts of the questions are dependent on each other. Eg part e) can be answered based on the equation given in part c)
- Parts g) and h) depend on part f) so even if students have not answered f) they should guess (from their graph for example) so that they have an answer to use for g) and h)
- Students must pay attention to the scales and instructions for drawing the function. This is worth 4 marks and students should be generating points from their calculators to plot the graph.
- Students can get the minimum value from their calculators as well.

I have a question mark about the domain of the function given. I am not sure why the value of w is limited to 20. I would have excluded that range from the 'show that' part of the question c) and included it as part of part d). Perhaps I am missing something simple.

Solution

Question 6

- Students need to know the properties of quadratic functions
- Fluent calculator use is very helpful here. Primarily, the graph function and calc/gsolve for finding values of y given x and x given y
- This question mostly requires care.

I have quite a few problems with the language/notation in this question...

- Part a) The question does not explicitly state that it goes through the origin. I know it seems obvious, but we teach our students not to assume.
- Part c) What do we mean by 'the edge' o the water tank?
- The second diagram appears before part d) implying that it is relevant when it is not.
- Part e) still has me confused. What do x and y represent? We assume we are still talking about the model offered at the begriming and not about any other part of the second diagram? I think this is not a good question.
- Part f) what is meant by 'the height of the water'? Is it the depth of the water or the height of the edge of the tank. As it happens this will not affect the outcome. I would suggest the should have said depth of water
- 6 Part g) ii) - Surely this should be Calculate the percentage of the tank that is filed with water.

Perhaps I am experiencing end of paper fatigue here but I thought this question has issues. It is not the most difficult though and I hope students have not left it to the end.

Solution