Numeracy Intermediate June 2023 Unit 2 Q4
4.
(a)
Llandudno Pier is 700 m long.
What is the length of Llandudno Pier in feet?
You must use the following conversions. [3]
12 inches = 1 foot
1 inch ≈ 2·5 cm
(b)
Southend Pier is the longest pleasure pier in the world.
It is 1·34 miles long.
Gareth walks at a steady pace along Southend Pier.
He walks 84 metres every minute.
He starts walking along the length of the pier at 2 p.m.
At what time does Gareth reach the end of the pier?
Give your time correct to the nearest minute.
You must show all your working. [5]
Gareth reaches the end of the pier at ……………………, correct to the nearest minute.
| Scheme | Marks | Comments |
|---|---|---|
| (700 × 100 ÷ 2.5) ÷12 or 700 ÷ 0.3(0) or 70000 ÷ 30 or equivalent | M2 | Must be using given conversions May be seen in stages M1 for any one of the following:
|
| 2333(.3.... feet) or 2333(feet 4 inches) | A1 | CAO. Ignore if an incorrect unit is given |
| Scheme | Marks | Comments |
|---|---|---|
| 1.34 × 8 ÷ 5 or × 1.6 (to convert miles to km) | M1 | May be seen in any order Allow × 1.61 or × 1.609 Do not accept × 1.5 |
| × 1000 (to convert km to m) | M1 | (= 2144 m) Accept embedded ‘× 1000’, e.g. sight of 1340, (1.34 × 1200 =) 1608, (1.34 × 1500 =) 2010 (i.e. × 1500 is awarded M0 M1) |
| ÷ 84 (to find number of minutes) | M1 | (= 25.52…minutes) (Note: sight of ÷ 0.084 is equivalent to × 1000 (M1) and ÷ 84 (M1)) Ignore further incorrect stages of working, provided they do not involve multiplication or division by 1.6, 1000 or 84 |
| (Time correct to the nearest minute) 2(:) 26 p.m. or 14(:)26 | A2 | CAO. Answer space takes precedence A2 awarded only if there is no incorrect working Depends on M1 M1 M1 previously awarded, for rounding time to nearest minute and adding to 2 p.m. Allow 2.26 p.m. or 14.26(p.m.) Award A1 for any one of the following:
|
Alternative
4(b) Alternative method:
| Scheme | Marks | Comments |
|---|---|---|
| 84 ÷ 1.6 ÷ 1000 | M1 M1 | Initial 2 method marks may be in either order Or ÷ 1.61 or ÷ 1.609 ÷ 1500 is M0 M1 |
| 1.34 ÷ (84 ÷ 1.6 ÷ 1000) (time taken) | M1 | |
| (Time correct to the nearest minute) 2(:) 26 p.m. or 14(:)26 | A2 | CAO. Answer space takes precedence A2 awarded only if there is no incorrect working Depends on M1 M1 M1 previously awarded, for rounding time to nearest minute and adding to 2 p.m. Allow 2.26 p.m. or 14.26(p.m.) A1 as shown above FT from M0 M1 M1 and M2 as shown above |