IB MYP Mathematics: Global contexts: the six contexts and statements of inquiry (MYP Mathematics) – Practice Questions

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs – the IB holds copyright in its own papers. Use these alongside the official past papers available through your school or the IB store.

These questions practise the global contexts and statements of inquiry material in the IB MYP Mathematics guide (for use from September 2020/January 2021, first assessment 2022). MYP mathematics has no SL or HL. The marks shown are Marlbridge’s own, for self-checking: the guide assesses against criteria with achievement levels, so they are not an official tariff. Questions that use framework content say whether it is MYP 1-3 or MYP 4-5.

Read the study guide and revision notes first. See also the MYP mathematics hub and the printable checklist.

Questions

1. Name the global context that best fits each unit description: (i) designing a floor from repeating tiles; (ii) comparing the daily water allowance per person in two villages; (iii) planning a journey across time zones. [3]

2. State two things the guide says about how teachers use global contexts. [2]

3. Name the three key concepts that mathematics contributes to the MYP. [3]

4. A unit has the statement of inquiry “Choosing a suitable model helps a community plan its use of limited resources.” Identify a key concept, two related concepts and the global context it most suggests. [4]

5. Three drafts are offered for a unit on proportion. Draft A: “Proportion”. Draft B: “Why does proportion matter?”. Draft C: “Comparing quantities on a fair basis shapes the decisions a community makes.” Choose the best statement of inquiry and give two reasons. [3]

6. (MYP 1-3 and MYP 4-5) A map has scale 1 : 20 000. A path runs 9 cm east and then 12 cm north on the map. A walker moves at 4.5 km/h.

(a) Find the length of the path in kilometres. [2] (b) Find the length of the straight line between the start and the end, in kilometres. [2] (c) Find how many minutes the walker saves by taking the straight line. [2]

7. (Fairness and development) A fund of 12 000 dollars is to be shared between town P (2 500 people) and town Q (3 500 people).

(a) The fund is split equally. Find the amount per person in each town, to the nearest cent. [3] (b) The fund is instead shared in proportion to population. Find each town’s share. [2]

8. (MYP 4-5, personal and cultural expression) A craftsperson plans tiling patterns with regular polygons.

(a) Find the interior angle of a regular hexagon. [1] (b) Show that regular pentagons alone cannot tile a flat surface without gaps by finding the gap left by three pentagons at a point. [3] (c) Show that two regular hexagons and two equilateral triangles can fit round a point. [2]

9. (MYP 4-5, scientific and technical innovation) A solar panel keeps 99% of its output each year, so after n years the output is 100 × 0.99ⁿ percent of the original.

(a) Find the output after 10 years, to 3 significant figures. [2] (b) Find the output after 25 years, to 3 significant figures. [2] (c) Give one reason why the model may not match a real panel. [2]

10. (MYP 4-5 standard, globalization and sustainability) Data supplied: sea freight produces 0.011 kg of carbon dioxide per tonne-kilometre and air freight 0.6 kg per tonne-kilometre. A shop moves 5 tonnes of goods. Sea freight covers 12 000 km. Air freight covers 8 000 km.

(a) Find the emissions for the sea route. [2] (b) Find the emissions for the air route, in standard form. [2] (c) Find how many times greater the air emissions are, to 3 significant figures. [2] (d) State one limitation of comparing the two routes in this way. [2]

11. (MYP 4-5 standard, linear functions) A bike-share scheme charges a start fee of 1.50 dollars plus 0.40 dollars for each minute, so the cost in dollars is C = 1.50 + 0.40t for a ride of t minutes. A class is planning a unit on this model.

(a) Find the cost of a 25 minute ride. [2] (b) A rider pays 8.30 dollars. Find the length of the ride. [2] (c) Write a statement of inquiry for the unit. Name your key concept, two related concepts and the global context. [4] (d) Write one factual question and one conceptual question that follow from your statement. [2]

12. (Fairness and development) A school’s planning rule, given here as data, says a ramp may rise no more than 1 m for every 12 m of horizontal distance. A doorway step is 0.45 m high. The space available along the ground is 5.0 m.

(a) Find the least horizontal distance a single straight ramp needs. [2] (b) Find the length of the sloping surface of that ramp, to 3 significant figures. [3] (c) Explain what your results mean for the school’s plan. [3]

Answers

1. (i) Personal and cultural expression [1]. (ii) Fairness and development [1]. (iii) Orientation in space and time [1]. [3] Examiner insight: Some units can sit in more than one context. When that happens, name the one that best explains why the inquiry matters, and give a short reason.

2. Teachers have to pick a global context for their teaching, and may create extra contexts that show why an inquiry matters [1]. Many mathematics inquiries fit scientific and technical innovation, but teachers are encouraged to offer the other contexts too [1]. [2] Examiner insight: For a two-part “state” question, give two separate points. A single long sentence that blends them is harder to credit.

3. Form [1], logic [1], relationships [1]. [3] Examiner insight: Do not mix these up with the related concepts. Words such as models, patterns or systems are related concepts, not key concepts.

4. Key concept: relationships [1]. Related concepts, any two sensible ones such as models [1] and quantity or systems [1]. Context: globalization and sustainability [1]. [4] Examiner insight: Several answers can be sensible. Pick concepts that match the words in the statement, and be ready to say which words point to each.

5. Draft C is best [1]. It is a full sentence stating a general idea, not a topic name or a question [1]. It places the mathematics in a context (decisions a community makes) and names a concept (fair comparison, relationships) [1]. [3] Examiner insight: A reason such as “it is longer” earns little. Say what makes a statement of inquiry different from a topic or a question.

6. (a) Path on the map = 9 + 12 = 21 cm [1]. 21 × 20 000 = 420 000 cm = 4.2 km [1]. [2] (b) Straight line = the square root of 9² + 12² = 15 cm [1]. 15 × 20 000 = 300 000 cm = 3.0 km [1]. [2] (c) Times: 4.2 ÷ 4.5 × 60 = 56 minutes and 3.0 ÷ 4.5 × 60 = 40 minutes [1]. Saving = 16 minutes [1]. [2] Examiner insight: Show the unit conversion from centimetres to kilometres. A common slip is dividing by 1 000 rather than 100 000.

7. (a) Equal split: 6 000 dollars each [1]. P: 6000 ÷ 2500 = 2.40 dollars per person [1]. Q: 6000 ÷ 3500 = 1.71 dollars per person [1]. [3] (b) P: 12 000 × 2500 ÷ 6000 = 5 000 dollars [1]. Q: 12 000 × 3500 ÷ 6000 = 7 000 dollars [1]. [2] Examiner insight: Round money to the nearest cent only at the end. Give a one-line comment that equal totals are not equal per person.

8. (a) (6 - 2) × 180 ÷ 6 = 120° [1]. [1] (b) Interior angle of a regular pentagon = 3 × 180 ÷ 5 = 108° [1]. Three pentagons give 3 × 108 = 324° [1]. Gap = 360 - 324 = 36°, so they do not fill the point [1]. [3] (c) The triangle’s angle is 60° [1]. 2 × 120 + 2 × 60 = 360°, so they fit with no gap [1]. [2] Examiner insight: On a “show that” question, state the target value and finish with a clear statement that it has been reached.

9. (a) 100 × 0.99¹⁰ [1] = 90.4% [1]. [2] (b) 100 × 0.99²⁵ [1] = 77.8% [1]. [2] (c) The model assumes the same percentage loss every year [1]. Real output also varies with weather, dirt or temperature, so the model is a simplification [1]. [2] Examiner insight: A model comment is stronger when it names a specific assumption and says how reality could differ from it.

10. (a) 5 × 12 000 × 0.011 [1] = 660 kg [1]. [2] (b) 5 × 8 000 × 0.6 = 24 000 [1] = 2.4 × 10⁴ kg [1]. [2] (c) 24 000 ÷ 660 [1] = 36.4 times greater [1]. [2] (d) Any one, such as: only transport is counted, so production and storage are ignored [1]. The comparison therefore only shows part of the environmental picture [1]. [2] Examiner insight: Keep the units in each line of working. Say what the limitation does to the conclusion, not only what is missing.

11. (a) C = 1.50 + 0.40 × 25 [1] = 11.50 dollars [1]. [2] (b) 8.30 = 1.50 + 0.40t, so 0.40t = 6.80 [1]. t = 17 minutes [1]. [2] (c) Key concept: relationships [1]. Related concepts: models and representation [1]. Context: for example identities and relationships, or scientific and technical innovation [1]. Statement, for example “Modelling a rate and a fixed charge lets people predict and compare the costs of everyday choices” [1]. [4] (d) Factual, for example “What does the 0.40 represent in the formula?” [1]. Conceptual, for example “Why can a linear model be useful even when it is only approximate?” [1]. [2] Examiner insight: Make sure the statement, concepts and context agree with each other. A statement mentioning prediction should not name unrelated concepts.

12. (a) 0.45 × 12 [1] = 5.4 m [1]. [2] (b) Length = the square root of 5.4² + 0.45² [1] = the square root of 29.3625 [1] = 5.42 m [1]. [3] (c) The space is 5.0 m, which is less than 5.4 m, so one straight ramp does not meet the rule [1]. The school would need a different design, such as a longer or turning ramp with a landing [1]. This links the mathematics to fairness, because the rule exists so that all pupils can use the entrance [1]. [3] Examiner insight: The final part rewards a sentence in context. Say whether the solution makes sense for the real situation, not only what the numbers are.

Where marks are usually lost

• Naming a topic instead of a general idea as a statement of inquiry.
• Confusing key concepts with related concepts.
• Giving a context with no explanation of why it suits the mathematics.
• Forgetting to convert map centimetres to kilometres.
• Comparing totals when a rate per person is needed.
• Rounding too early, then giving an answer that is slightly out.
• Leaving out the final comment on whether the answer makes sense.
• Presenting a model as an exact description of the real world.

Next steps

• Re-read the revision notes and the study guide.
• Go to the MYP mathematics hub and tick off topics on the printable checklist.
• Take any of the free 10-minute diagnostics to find weak spots.
• Practise criterion D with criteria in practice.
• Book a free trial class.

Official syllabus

IB Mathematics guide (MYP), for use from September 2020/January 2021, first assessment 2022, published by the International Baccalaureate Organization.