Upper/lower bounds in calculations
3 exam-style questions. Answers and the mark for each step are on the last page.
- Question 1
A rectangle has length cm and width cm, each correct to 1 decimal place.
(a) Work out the upper bound for the area of the rectangle.
(b) Work out the lower bound for the perimeter of the rectangle.
- Question 2
(a) A sample has mass 35.6 g and volume 12.4 cm³, both rounded to the nearest 0.1 of their units. Density = mass volume. Calculate the lower bound for the density, giving your answer to 3 decimal places.
- Question 3
(a) A rectangle has perimeter 30 cm, rounded to the nearest centimetre, and width 6 cm, rounded to the nearest centimetre. Find the upper bound for its area. Show why using both limits is valid even though the length and width are linked by the perimeter.
Answers and marks
Question 1
(a)
- M1 Using both upper bounds, and .
- A1 The correct answer, .
(b) cm
- M1 Using both lower bounds in the perimeter.
- A1 The correct answer, cm.
Question 2
(a) g/cm³
- P1 Establishing or an equivalent valid method.
- P1 Establishing or an equivalent valid method.
- P1 Establishing or an equivalent valid method.
- A1 Correct answer: g/cm³
Question 3
(a) 56.875
- P1 Establishing or an equivalent valid method.
- P1 Establishing or an equivalent valid method.
- C1 Correct conclusion with the complete supporting argument: 56.875