Numeracy Foundation November 2019 Unit 1 Q6
6. Every year, Aber Young Farmers club organises a sponsored walk.
(a) This year, the length of the walk is 20 miles.
Calculate the length of the walk in km. [2]
Calculate the length of the walk in km. [2]
(b) Last year, the walk raised a total of £3600.
It cost £180 to organise the walk last year.
Give the cost of organising the walk as a percentage of the total raised. [2]
It cost £180 to organise the walk last year.
Give the cost of organising the walk as a percentage of the total raised. [2]
(c)
This year, walkers will be charged to take part.
Aber Young Farmers decided that:
charge in pence = 3 × height of the walker in cm
What is the height of the shortest walker who will need to pay a charge of more than £5?
Give your answer correct to the nearest cm.
You must show all your working. [3]
| Scheme | Marks | Comments |
|---|---|---|
| 8 × 20 ÷ 5 or 1.6 × 20 or equivalent 32 (km) | M1 A1 | Allow calculation 1.5 × 20 or 1.61 × 20 Allow FT answer (1.5 × 20 =) 30 (km) or (1.61 × 20 =) 32.2 (km) If no workings shown accept an answer of 32 (km) and allow an answer of 30 (km) or 32.2 (km) |
| Scheme | Marks | Comments |
|---|---|---|
| (100 ×) 180 ÷ 3600 or \(\dfrac{180}{3600}\) or 1/20 or equivalent | M1 | M0 for 3600 ÷ 180 unless sight of 1/20 or equivalent Allow M1 for sight of 180 ÷ 3600 (= 20 or 30 or ....) Accept ‘10% = 360, 5% = 180’ for M1 A1 |
| 5 (%) | A1 | Allow M1 A1 form sight of 3600/180 = 5(%) If no marks, award SC1 for an answer of 95% |
| Scheme | Marks | Comments |
|---|---|---|
| 5 ÷ 3 or 500 ÷ 3 1.6(66...) or 166(.66...) | M1 A1 | Accept 501 ÷ 3 Ignore further incorrect digits beyond either 1.6 or 166 Accept 1.67 or 167. Allow 160,170 or 1.7 |
| 167 (cm) or 1.67 (m) | A1 | CAO Do not accept 1.67 cm or 167 m (units incorrect) |
6(c) Alternative method using trials
| Scheme | Marks | Comments |
|---|---|---|
| Charge for 1(.)66 is (£)4(.)98(p) or 1(.)67 is (£)5(.)01 | M2 | M1 for correctly evaluated charge for at least 2 heights, provided trial is 184 ≥ h ≥ 150 |
| 167 (cm) or 1.67 (m) | A1 | CAO Do not accept 1.67 cm or 167 m (units incorrect) Note: 166 × 3 = 498, 167 × 3 = 501 |