Upper and lower boundsIB MYP Maths Extended: Subtopic test

1. 1
   A rectangular plot has length $48$ m and width $35$ m, each measured correct to the nearest metre.

   (a)

   Write down the lower bound of the length of the plot.

   [1 mark]

   • A$47$ m
   • B$47.9$ m
   • C$48.5$ m
   • D$47.5$ m

   (b)

   Find the upper bound of the perimeter of the plot.

   [1 mark]

   • A$166$ m
   • B$168$ m
   • C$170$ m
   • D$164$ m

   (c)

   Find the lower bound of the area of the plot.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A runner covers a distance of $100$ m, measured to the nearest metre, in a time of $12.4$ seconds, measured to the nearest $0.1$ second.

   (a)

   Write down the lower bound of the time.

   [1 mark]

   • A$12.35$ s
   • B$12.3$ s
   • C$12.45$ s
   • D$12.0$ s

   (b)

   Which calculation gives the upper bound of the runner's average speed?

   [1 mark]

   • A$\frac{99.5}{12.45}$
   • B$\frac{100.5}{12.45}$
   • C$\frac{100.5}{12.35}$
   • D$\frac{99.5}{12.35}$

   (c)

   Calculate the lower bound of the runner's average speed, correct to 3 significant figures.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A parcel contains $6$ identical books and an empty box. Each book has mass $450$ g, correct to the nearest $10$ g. The box has mass $1.2$ kg, correct to the nearest $0.1$ kg.

   (a)

   Find the upper bound of the total mass of the parcel, in kilograms.

   [3 marks]

   (b)

   Find the lower bound of the total mass. Hence state the total mass to a suitable degree of accuracy and justify your answer.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A metal block is a cuboid measuring $6.0$ cm by $5.0$ cm by $4.0$ cm, each correct to the nearest $0.1$ cm. Its mass is $540$ g, correct to the nearest $10$ g. A calculator may be used.

   (a)

   (i) Find the upper bound of the mass and the lower bound of the volume of the block.
   (ii) Hence find the upper and lower bounds of the density of the block, in g/cm$^3$, correct to 3 significant figures.

   [6 marks]

   (b)

   The density of the block is between $4.32$ and $4.68$ g/cm$^3$. (i) A seller says the block is titanium, with density $4.51$ g/cm$^3$. Explain whether the measurements support this. (ii) A second seller says it is steel, with density $7.8$ g/cm$^3$. Explain whether this is possible. (iii) Explain why the density cannot be given correct to 2 significant figures.

   [6 marks]

   Total for question 4: 12 marks

End of questions