IB MYP Mathematics: The twelve related concepts and their meanings (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 are aligned to the IB Mathematics guide for the Middle Years Programme (for use from September 2020/January 2021, first assessment 2022). They cover Table 2, the twelve related concepts, their glossary meanings and their branch links. They also apply the concepts in short problems. The guide has one list for the whole course, with no split between standard and extended mathematics. Mark values are for practice only. Read the study guide first if a concept is unfamiliar, and use the revision notes for a quick recap. The course hub is MYP Mathematics and the printable checklist tracks your topics.

Questions

1. (a) Explain what “equivalence” means in MYP mathematics. [1] (b) A student says (x + 1)² is equivalent to x² + 1. Justify whether this is true, using a value of x. [2]

2. Name the three related concepts that the guide lists for all four branches of the framework. [3]

3. (a) Estimate 7.9 × 31.2 by rounding the first number to the nearest whole number and the second to the nearest ten. [1] (b) The exact value is 246.48. Find the error in your estimate. [1] (c) State whether the estimate is too high or too low, and explain why in terms of the rounding. [2]

4. The area covered by lilies on a pond grows from 0.8 m² to 2.0 m² in 4 weeks. (a) Find the rate of change in m² per week. [2] (b) Find the percentage increase. [2]

5. Figures 1, 2 and 3 of a tile pattern use 7, 11 and 15 tiles. (a) Find a rule for the number of tiles in figure n. [2] (b) Find the number of tiles in figure 12. [1] (c) Which figure uses 87 tiles? [2]

6. A mobile plan costs C = 12 + 0.8g, where C is the monthly cost and g is the data used in GB. (a) Find the cost when 7.5 GB is used. [2] (b) Find the most data that can be used with a budget of 25. [2] (c) Describe one way the model may not match real use. [1]

7. A relationship is given by y = 5 − 2x. (a) Complete a table for x = 0, 1, 2 and 3. [2] (b) State the gradient and the y-intercept of the graph. [2] (c) Represent the same relationship in words. [1]

8. (a) Simplify (12a³b) / (8ab²). [3] (b) A round pond is modelled as a cylinder with radius 1.5 m and depth 0.8 m. Find its volume to 3 significant figures, and name the related concept shown by treating the pond as a cylinder. [2]

9. A model of a store room is built to scale 1:25. The model measures 12 cm by 8 cm by 6 cm. (a) Find the real dimensions in metres. [2] (b) Find the volume of the model in cm³ and of the real room in m³. [2] (c) Show that the volume of the real room is 25³ times the volume of the model. [2]

10. (a) Write 110101 (base 2) as a base 10 number. [2] (b) Write 29 as a base 2 number. [2]

11. A rectangular garden has length (x + 3) m and width x m, and its area is 40 m². (a) Show that x² + 3x − 40 = 0. [2] (b) Solve the equation. [2] (c) State which solution is valid, giving a reason, and write the dimensions of the garden. [2]

12. A school rain tank is monitored. Its volume V litres is recorded t hours after a leak starts.

t (hours)	0	2	4	6
V (litres)	1500	1380	1260	1140

(a) Find the rate of change of V. [2] (b) Write a model for V in terms of t. [2] (c) Use your model to find when the tank would be empty. [1] (d) Comment on the validity of using the model for t = 40. [2] (e) Name one related concept used in part (b) and one used in part (d). [1]

Answers

1. (a) Equivalence means two statements, quantities or expressions are identically equal, so one can replace the other [1]. (b) Try x = 1: (1 + 1)² = 4 [1] but 1² + 1 = 2, so they differ and the claim is false [1]. [3] Examiner insight: One value that breaks the claim is a full justification. A value that works, such as x = 0, would not show equivalence.

2. Equivalence [1], quantity [1] and systems [1]. [3] Examiner insight: Learn the branch table as a table, not a list. Naming a concept that appears in only some branches loses the mark.

3. (a) 7.9 ≈ 8 and 31.2 ≈ 30, so 8 × 30 = 240 [1]. (b) Error = 246.48 − 240 = 6.48 [1]. (c) Too low [1]. The 31.2 was rounded down by about 3.8%, which is more than the 1.3% by which 7.9 was rounded up, so the product falls short [1]. [4] Examiner insight: “Too low” with no reason earns little. Link the direction of the error to what you rounded up or down.

4. (a) Change = 2.0 − 0.8 = 1.2 m² [1]. Rate = 1.2 ÷ 4 = 0.3 m² per week [1]. (b) 1.2 ÷ 0.8 [1] × 100 = 150% [1]. [4] Examiner insight: Percentage change is measured against the starting value. Dividing by 2.0 gives 60%, which answers a different question.

5. (a) The terms rise by 4, so the rule has 4n [1]. At n = 1, 4n = 4, so add 3: 4n + 3 [1]. (b) 4 × 12 + 3 = 51 [1]. (c) 4n + 3 = 87 [1], so 4n = 84 and n = 21, so figure 21 [1]. [5] Examiner insight: Check the rule against all three given terms before using it. A rule that fits only the first term will fail part (b).

6. (a) C = 12 + 0.8 × 7.5 [1] = 18 [1]. (b) 12 + 0.8g ≤ 25 [1], so g ≤ 13 ÷ 0.8 = 16.25 GB [1]. (c) For example, the real plan may charge extra after a data limit, or round usage up to whole GB [1]. [5] Examiner insight: A limitation must be about the situation (price changes, rounding, a cap). Saying “the model is not accurate” is too vague.

7. (a) x = 0, 1, 2, 3 gives y = 5, 3, 1, −1 [2]. (b) Gradient −2 [1], y-intercept 5 [1]. (c) Start at 5 and subtract 2 for every increase of 1 in x [1]. [5] Examiner insight: Each representation should agree with the others. Check your gradient against the drop in your table.

8. (a) Divide by 4: (3a³b) / (2ab²) [1]. Cancel a: a³ ÷ a = a² [1]. Cancel b: b ÷ b² = 1/b, giving 3a² / (2b) [1]. (b) V = π × 1.5² × 0.8 = 5.65 m³ [1]. The related concept is simplification (or models) [1]. [5] Examiner insight: Show the factor you divide by. A test value, such as a = 2 and b = 1, is a quick way to check you have not changed the expression.

9. (a) 12 × 25 = 300 cm = 3 m; 8 × 25 = 200 cm = 2 m; 6 × 25 = 150 cm = 1.5 m [2]. (b) Model: 12 × 8 × 6 = 576 cm³ [1]. Real: 3 × 2 × 1.5 = 9 m³ [1]. (c) 25³ = 15 625 [1]. 576 × 15 625 = 9 000 000 cm³ = 9 m³, matching part (b) [1]. [6] Examiner insight: Keep units with each line. The conversion from cm³ to m³ divides by 1 000 000, which is not the same as 100.

10. (a) 32 + 16 + 0 + 4 + 0 + 1 [1] = 53 [1]. (b) 29 = 16 + 8 + 4 + 0 + 1 [1], so the digits are 11101 [1]. [4] Examiner insight: Write the place values above your digits (32, 16, 8, 4, 2, 1). It makes errors in position easy to spot.

11. (a) Area: x(x + 3) = 40 [1], so x² + 3x = 40 and x² + 3x − 40 = 0 [1]. (b) (x + 8)(x − 5) = 0 [1], so x = −8 or x = 5 [1]. (c) A width cannot be negative, so x = 5 is valid [1]. The garden is 5 m by 8 m (5 × 8 = 40) [1]. [6] Examiner insight: In a “show that” part, the final line must be the given equation. In part (c), the reason must refer to the context.

12. (a) Change = 1380 − 1500 = −120 in 2 hours [1], so the rate is −60 litres per hour [1]. (b) The starting value is 1500 [1], so V = 1500 − 60t [1]. (c) 1500 − 60t = 0 gives t = 25 hours [1]. (d) At t = 40 the model gives V = 1500 − 2400 = −900 [1]. A tank cannot hold a negative volume, so the model is not valid beyond t = 25 [1]. (e) Part (b): models, or patterns or representation. Part (d): validity [1]. [8] Examiner insight: A comment on validity needs a value or fact from the model and a statement about the situation. “It is wrong” alone is not enough.

Where marks are usually lost

• Describing a concept with its everyday meaning instead of the guide’s glossary sense.
• Listing concepts for a branch from memory, and including space outside spatial reasoning.
• Testing equivalence with a single value that happens to work.
• Not saying whether an estimate is too high or too low, or not giving a reason.
• Calculating a percentage change against the final value instead of the starting value.
• Fitting a rule to one term and not testing it on the others.
• Forgetting units, or converting cm³ to m³ by the wrong factor.
• Keeping a negative length because it solves the equation.
• Commenting on a model’s validity without a value, a fact or the context.

Next steps

• Recap with the revision notes.
• Re-read the study guide.
• Go to the MYP Mathematics hub and the printable checklist.
• Take one of the free 10-minute diagnostics.
• Book a free trial class.

Official syllabus

IB Mathematics guide, Middle Years Programme (for use from September 2020/January 2021; first assessment 2022), published by the International Baccalaureate Organization. Sections used: Table 2 (related concepts in mathematics), the branch descriptions with their links to MYP concepts, and the appendix glossary of related concepts.