Numeracy Higher June 2022 Unit 1 Q1
1.
(a) People travel by bus or by train from Hiraddug Station.
On Tuesday, 420 people travelled by bus from the station.
The ratio of the number of people travelling by bus to the number of people travelling by train was 20 : 17.
On Tuesday, 420 people travelled by bus from the station.
The ratio of the number of people travelling by bus to the number of people travelling by train was 20 : 17.
Calculate the number of people who travelled by train from the station on Tuesday. [3]
(b) The price of a ticket to travel by bus to Glaswen Station has increased by 5% in each of the last 2 years.
Two years ago, the price of a ticket was £4.
Calculate the current price of a ticket. [3]
Two years ago, the price of a ticket was £4.
Calculate the current price of a ticket. [3]
| Scheme | Marks | Comments |
|---|---|---|
| 420 ÷ 20 × 17 | M2 | M1 for any of the following:
|
| 357 (people) | A1 | CAO. Allow embedded as 420 : 357 Award A0 for 357 : 420 |
Alternative method 1
| Scheme | Marks | Comments |
|---|---|---|
| (420 ÷ 20) × (20 + 17) – 420 (= 777 – 420) | M2 | M1 for any of the following:
|
| 357 (people) | A1 | CAO. Allow embedded as 420 : 357 Award A0 for 357 : 420 |
Alternative method 2
| Scheme | Marks | Comments |
|---|---|---|
| 420 – (20 – 17) × (420 ÷ 20) (=420 – 63) | M2 | M1 for any of the following:
|
| 357 (people) | A1 | CAO. Allow embedded as 420 : 357 Award A0 for 357 : 420 |
Alternative method 3
| Scheme | Marks | Comments |
|---|---|---|
| Full ratio method to find 357 people, e.g. (20 ×) \(\dfrac{420}{(20)}\) : 17 × \(\dfrac{420}{20}\) | M2 | Allow seen in stages, including written as an appropriate sum of equivalent ratios, e.g. attempting 17 + 340 (from 20 : 17 and 400 : 340) M1 for any of the following:
|
| 357 (people) | A1 | CAO. Allow embedded as 420 : 357 Award A0 for 357 : 420 |
| Scheme | Marks | Comments |
|---|---|---|
| (Price last year =) (£)4.2(0) | B1 | |
| (Price now =) 4.2(0) + 0.05 × 4.2(0) | M1 | FT ‘their 4.20’ |
| = (£)4.41 | A1 | A final answer of (£)4.4(0) (from 4 + 2 × 0.2) implies B1 M0 A0 If no marks awarded SC2 for sight of 4 × 1.1025 SC1 for sight of 4 × 1.052 |