1MA0 Higher June 2017 Paper 2 Q11
*11 The diagram shows a plan of Brian’s lawn.
Diagram NOT accurately drawn
The edge of the lawn consists of two semicircles and two straight lines.
Each semicircle has centre \(O\).
The diameters of the semicircles are 9 m and 5 m.
Brian is going to put lawn edging around the edge of the lawn.
Lawn edging is sold in 2.4 metre rolls.
| Lawn edging |
|---|
| £3.99 per roll or 3 rolls for £10 |
Brian has £35
Has Brian got enough money to buy all the rolls of lawn edging he needs?
You must show all your working. (5)
| Answer | Mark | Notes |
|---|---|---|
| No (supported) | 5 | M1 for \(\pi \times 9 \div 2\) (=14.137…) or \(\pi \times 5 \div 2\) (=7.85…) or for \(\pi \times 9\) (=28.27…) or \(\pi \times 5\) (=15.7…) M1 for complete method to work out perimeter eg \(2 + 2 + (\pi \times 9 \div 2) + (\pi \times 5 \div 2)\) (= 25.99...) M1 (dep M1) for method to find number of rolls required for their perimeter, eg “their total perimeter” \(\div\) 2.4 eg \(25.99.. \div 2.4\) (=10.8), \(\text{``}47.97..\text{''} \div 2.4\) (=19.9) or \(\text{``}43.47..\text{''} \div 2.4\) (=18.3) M1 for method to work out cost eg \(3 \times 10 + 2 \times 3.99\) (= 37.98) or \(11 \times 3.99\) (=43.89), 20 \(\to\) 67.98, 19 \(\to\) 63.00 or for method to find how many rolls can be bought for £35 (= 10) C1 for a conclusion supported by fully correct answers eg 37.98 (for comparing with 35) e.g 10.8 and 10 OR M1 for \(\pi \times 9 \div 2\) (=14.137…) or \(\pi \times 5 \div 2\) (=7.85…) or for \(\pi \times 9\) (=28.27…) or \(\pi \times 5\) (=15.7…) M1 for complete method to work out perimeter eg \(2 + 2 + (\pi \times 9 \div 2) + (\pi \times 5 \div 2)\) (= 25.99...) M1 for a method to find how many rolls can be bought for £35 (=10) M1 for a method to work out the coverage of 10 rolls e.g. \(10 \times 2.4\) (=24) C1 for a conclusion supported by fully correct answers eg 25.9(...) and 24 |