IB MYP Mathematics: Criteria C and D by year: communicating and applying mathematics (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 Criterion C (Communicating) and Criterion D (Applying mathematics in real-life contexts) from the IB MYP Mathematics guide (for use from September 2020 and January 2021, first assessment 2022), using the Year 1, Year 3 and Year 5 criteria. The marks shown are Marlbridge practice tariffs only. The explanations are in the study guide and the revision notes. The course hub is MYP Mathematics and the printable list is the MYP Mathematics checklist.

Questions

1. A learner writes: “Area = 6 x 4 = 24 + 5 = 29 cm2. The mass is 4.5E3 g.” Identify and correct four errors of mathematical language or notation. [4]

2. A taxi charges £3.20 plus £1.80 for each kilometre travelled.

(a) Make a table of the cost C for journeys of 1, 2, 3 and 4 km. [1] (b) Write a rule for C in terms of the distance k km. [1] (c) Describe the graph of C against k, naming two features and what each means. [1] (d) Use the rule to find the distance for a fare of £30.20. [2]

3. For each task choose the most suitable form of representation (table, graph, equation or diagram) and give a reason. [3]

(i) Showing a shop’s sales for each month of the year so that a rise or fall is easy to see. (ii) Giving a rule so that any term of a number pattern can be found. (iii) Giving a customer the exact price for each of five sizes of a product.

4. A learner tests 3 + 5 = 8, 7 + 9 = 16 and 11 + 13 = 24 and writes: “The sum of two consecutive odd numbers is always a multiple of 4.”

(a) Explain why this does not show the statement is always true. [1] (b) Write a complete, coherent and concise argument that it is always true. [3]

5. A wall is 5.4 m wide and 2.5 m high. It is to be painted with two coats. One litre of paint covers 9 m². Paint is sold in 2.5 litre cans. The wall colour is grey.

(a) Identify one fact that is not relevant to the calculation. [1] (b) Calculate the volume of paint needed. [2] (c) Find the number of cans to buy and explain why you round the way you do. [2]

6. In question 5 the width and height are measured to the nearest 0.1 m.

(a) Find the smallest and largest volume of paint the measurements allow, to 3 significant figures. [2] (b) Justify that buying two cans is enough. [2]

7. Water leaks from a bucket. A model for the volume V litres after t minutes is V = 30 − 0.8t. Measurements: at 5, 15 and 30 minutes the volumes are 26.1, 18.3 and 7.1 litres.

(a) State the values of t for which the model is valid, with a reason. [2] (b) Compare the model with the three measurements. [2] (c) Justify whether the model is reliable for predicting the volume at 40 minutes. [2]

8. Use the Year 1, Year 3 and Year 5 criteria.

(a) Which strand of Criterion C is not demonstrated in Year 1? [1] (b) What extra quality does Year 5 ask for in lines of reasoning, compared with Year 3? [1] (c) What change in Criterion D strand iv separates Year 3 from Year 5? [1]

9. Two companies hire bikes. Company X charges £5 plus £3 for each hour. Company Y charges £11 plus £1.50 for each hour. Both charge for every hour started.

(a) Write an equation for the cost of each company for h hours. [2] (b) Find the number of hours for which the costs are equal, and the cost. [2] (c) Complete a table for h = 2, 3, 4, 5 and 6 for both companies. [2] (d) A customer rides for 3.5 hours. Explain which company to choose and why the charging rule matters. [2]

10. A savings account holds £800 and pays 4% interest, added once a year. A model for the balance after n years is B = 800 × 1.04ⁿ.

(a) Find the balance after 6 years to the nearest penny. [2] (b) Find the first whole year in which the balance exceeds £1000. [2] (c) Justify whether the model gives a reliable balance after 18 years. [3]

11. A learner solves 5(x − 2) = 3x + 8 and writes: “5x − 10 = 3x + 8 = 2x = 18 = 9”. Rewrite the solution as a complete, well-organised piece of reasoning. [5]

Answers

1. The multiplication sign x should be × [1]. The chain of equals signs joins unequal values, so write 6 × 4 = 24 and then 24 + 5 = 29 as separate lines [1]. cm2 should be cm² [1]. 4.5E3 is calculator notation and should be 4.5 × 10³ g [1]. [4] Examiner insight: Name the exact symbol and its correction, rather than writing “bad notation”, because a reader cannot credit a vague comment.

2. (a) The costs are £5.00, £6.80, £8.60 and £10.40 for 1, 2, 3 and 4 km [1]. [1] (b) C = 3.2 + 1.8k [1]. [1] (c) The graph is a straight line with vertical intercept 3.2, the fixed charge, and gradient 1.8, the cost per kilometre [1]. [1] (d) 3.2 + 1.8k = 30.2 [1] gives 1.8k = 27, so k = 15 km [1]. [2] Examiner insight: A graph feature is more convincing when you say what it means in context, so write “3.2 is the fixed charge” and not just “the intercept is 3.2”.

3. (i) A graph, because a line shows the trend across the months [1]. (ii) An equation, because it gives any term by substitution [1]. (iii) A table, because it lists the exact value for each size [1]. [3] Examiner insight: Tie each form to the job it does, since a choice with no reason shows less communication.

4. (a) Three cases do not cover every pair of consecutive odd numbers, so they cannot show the result is always true [1]. [1] (b) Let the odd numbers be 2n − 1 and 2n + 1, where n is an integer [1]. Their sum is (2n − 1) + (2n + 1) = 4n [1]. Since 4n is 4 times an integer, the sum is a multiple of 4 [1]. [3] Examiner insight: Define the variable and finish by linking the result back to the claim.

5. (a) The colour of the paint (grey) is not needed for the calculation [1]. [1] (b) Area = 5.4 × 2.5 = 13.5 m², and two coats give 27 m² [1]. Paint = 27 ÷ 9 = 3 litres [1]. [2] (c) 3 ÷ 2.5 = 1.2, so round up to 2 cans [1], because one can (2.5 litres) is too little and cans are sold whole [1]. [2] Examiner insight: In real-life problems the rounding direction should come from the situation, and you should say so.

6. (a) Smallest wall: 5.35 × 2.45 = 13.1075 m², so two coats cover 26.215 m² and the paint is 26.215 ÷ 9 = 2.91 litres [1]. Largest wall: 5.45 × 2.55 = 13.8975 m², so 27.795 m² and 27.795 ÷ 9 = 3.09 litres [1]. [2] (b) Two cans give 5 litres [1]. The largest amount the measurements allow is 3.09 litres, which is less than 5, so two cans are enough [1]. [2] Examiner insight: “Justify” calls for evidence, so a range of values from the measurement limits is stronger than the statement “it is about right”.

7. (a) V cannot be negative, so 30 − 0.8t ≥ 0 gives t ≤ 37.5 [1]. The model is valid for 0 ≤ t ≤ 37.5, since time cannot be negative [1]. [2] (b) The model gives 26, 18 and 6 litres [1]. The measurements are higher by 0.1, 0.3 and 1.1 litres, so the gap grows with time [1]. [2] (c) At t = 40 the model gives −2 litres, which is impossible, and 40 is outside the valid domain [1]. The growing gap also suggests the real leak slows down, so the model is not reliable for large t and the real volume need not match the line [1]. [2] Examiner insight: Cite specific numbers from the data rather than a general remark that models can be wrong.

8. (a) Strand iii, moving between forms of representation [1]. [1] (b) Year 5 reasoning should also be concise, in addition to being complete and coherent [1]. [1] (c) In Year 3 you explain the degree of accuracy, and in Year 5 you justify it [1]. [1] Examiner insight: Quote the verbs the criteria use, because the difference between years is in the verbs.

9. (a) C_X = 5 + 3h [1] and C_Y = 11 + 1.5h [1]. [2] (b) 5 + 3h = 11 + 1.5h gives 1.5h = 6, so h = 4 hours [1]. Cost = 5 + 12 = £17 for both [1]. [2] (c) For 2, 3, 4, 5 and 6 hours, X costs £11, £14, £17, £20 and £23 [1], and Y costs £14, £15.50, £17, £18.50 and £20 [1]. [2] (d) 3.5 hours is charged as 4 started hours, so both companies cost £17 [1]. If hours were charged exactly, X would cost £15.50 and Y £16.25, so the charging rule changes the advice and the customer should choose on other grounds [1]. [2] Examiner insight: State the context rule you used (charged per started hour) so a reader can see why your numbers differ from a pro rata calculation.

10. (a) 800 × 1.04⁶ [1] = £1012.26 [1]. [2] (b) After 5 years: 800 × 1.04⁵ = 973.32, below £1000 [1]. After 6 years: £1012.26, above £1000, so the first year is year 6 [1]. [2] (c) The model gives 800 × 1.04¹⁸ = £1620.65 [1]. The model assumes the rate stays at 4% and no money is added or taken out for 18 years [1]. Rates often change over long periods, so the figure is only an estimate [1]. [3] Examiner insight: Name the assumption that could fail and say what it does to the answer, not only that the answer is uncertain.

11. Solve 5(x − 2) = 3x + 8 [1]. Expand: 5x − 10 = 3x + 8 [1]. Subtract 3x and add 10: 2x = 18, so x = 9 [1]. Check: left side 5(9 − 2) = 35, right side 3(9) + 8 = 35 [1]. Conclusion: x = 9 [1]. [5] Examiner insight: One equation per line, with each line following from the one before, shows structure better than a long chain of equals signs.

Where marks are usually lost

• Using the equals sign to join steps that are not equal.
• Leaving out units, or writing calculator notation such as E3.
• Describing a graph feature without saying what it means in context.
• Treating a few examples as a proof.
• Writing “it is approximate” with no cause or size of error.
• Rounding material amounts without checking the context.
• Not stating the domain of a model.
• Not defining the variable before using it.

Next steps

• Read the revision notes for the one-page version.
• Revisit the study guide for the worked examples.
• Use the MYP Mathematics hub and checklist.
• Take the free 10-minute diagnostics.
• Book a free trial class.

Official syllabus

IB Middle Years Programme Mathematics guide (for use from September 2020/January 2021), first assessment 2022, published by the International Baccalaureate Organization. These questions are original and are based on the Criterion C and D objectives and the Year 1, Year 3 and Year 5 criteria.