Numeracy Foundation November 2021 Unit 2 Q7
7. Ms Ritter is buying a new dining table.
She has seen a table with a circular top and another with a rectangular top.
The circular top has a diameter of 1·5 m.
The rectangular top measures 2 m by 0·8 m.
(a) Which of the table tops has the greater perimeter?
You must show all your working. [3]
You must show all your working. [3]
(b) Does the table top with the greater perimeter also have the greater area?
You must show all your working. [3]
You must show all your working. [3]
| Scheme | Marks | Comments |
|---|---|---|
| Perimeter (circumference of the circular table) π × 1.5 or 2 × π × 0.75 | M1 | |
| 4.7(...m) | A1 | |
| Rectangular table perimeter 5.6 (m) AND the conclusion that rectangular perimeter is greater | E1 | 5.6 (m) must be seen or implied by the difference between 5.6 (m) and ‘their circumference’ FT depends on M1 previously awarded |
Corrected by Westie's Workshop
- The board's mark scheme printed “AND the usion that rectangular perimeter is greater”. Changed to “AND the conclusion that rectangular perimeter is greater” because the start of the word is cut off in the printed scheme and it can only be “conclusion”.
Original: see the board's mark scheme PDF (link above).
| Scheme | Marks | Comments | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Circular table area π × (1.5 ÷ 2)2 | M1 | ||||||||||||||||
| 1.76(... m2) or 1.77 (m2) or 1.8 (m2) | A1 | Allow an answer truncated to 1.7(m2) | |||||||||||||||
| Rectangular table area 1.6 (m2) AND the conclusion ‘no’ (the circular table area is greater) | E1 | 1.6 (m2) must be seen or implied by the difference between 1.6 (m2) and ‘their area of circle’ STRICT FT from ‘their conclusion in (a)’ for the conclusion in (b), provided M1 previously awarded in (b)
‘Their conclusion’ from (a) may be inferred If ‘yes’ or ‘no’ is not stated then it must be unambiguously implied If no marks, award SC1 for meeting all three of the following requirements: 1. π × 1.52 = 7(.0...m2) or 7.1(m2) OR ½ × π × 1.52 = 3.5(...m2) 2. Rectangular area 1.6 (m2) OR implied by the difference between 1.6 (m2) and ‘their area of circle’ 3. Appropriate conclusion of ‘yes’ or ‘no’ |