Numeracy Higher November 2022 Unit 1 Q2
2. Whales are sometimes spotted in the Irish Sea, off the west coast of Wales.
A minke whale was spotted on a bearing of:
- 010° from Aberporth
- 280° from Aberystwyth.
On screen this diagram may not be shown at actual size. To measure it, use the question paper (PDF) printed at 100%.
(a) Scientists decide to search for other whales in the Irish Sea.
The search area is the region within 20 km of the position where the minke whale was spotted.
The search area is the region within 20 km of the position where the minke whale was spotted.
Using the scale given, show this search area on the map above. [4]
(b) This minke whale has a length of 20 feet.
Remember: 1 inch ≈ 2·5 cm, 1 foot = 12 inches
Use these facts to complete the following statement. [3]
The minke whale has a length of …………… metres.
(c) The brain of a minke whale has 12·8 billion neocortical neurons.
A female human brain has 19 billion neocortical neurons.
A female human brain has 19 billion neocortical neurons.
Remember: 1 billion = 1000 million
(i) Calculate an estimate for the number of neurons in a minke whale brain expressed as a percentage of the number of neurons in a female human brain.
You must show all your working. [2]
You must show all your working. [2]
Approximately …………… %
(ii) 10% of all neocortical neurons are lost over a human lifespan.
Calculate the number of neocortical neurons in a female human brain at the end of a lifespan.
Give your answer in standard form. [4]
Calculate the number of neocortical neurons in a female human brain at the end of a lifespan.
Give your answer in standard form. [4]
| Scheme | Marks | Comments |
|---|---|---|
| Whale indicated or implied on bearing 010° from Aberporth and 280° from Aberystwyth. | B2 | Accept indication from one bearing line drawn with the second bearing shown on this line, including one line terminating at the correct intersection point B1 for either of the bearings correctly shown or unambiguously indicated, e.g. by an unambiguous mark on the correct bearing |
| Region in the sea inside a circle, centred at the whale, of correct (4cm) radius ± 2mm | B2 | FT ‘their position of the whale’ For B2 the region must be entirely within the sea or on FT indicated as a region within the sea Allow intention of circle provided it lies completely within the tolerance given by the overlay B1 for (intention of a) circle, radius out of tolerance but within ± 4 mm, centred at the whale including any region on the land |
| Scheme | Marks | Comments |
|---|---|---|
| 20 × 12 × 2.5 ÷ 100 | M2 | M1 for any 3 of these 4 terms correct in a calculation which may be shown in stages |
| 6 (m) | A1 | CAO Answer given within the statement takes precedence Sight of 600 is awarded M1 and also SC1 provided not from incorrect working |
| Scheme | Marks | Comments |
|---|---|---|
| (i) \(\dfrac{13}{20}\) (× 100) or \(\dfrac{12.5}{20}\) (× 100) or \(\dfrac{12.8}{19}\) (× 100) or \(\dfrac{12}{20}\) (× 100) or \(\dfrac{12}{19}\) (× 100) or \(\dfrac{12.8}{20}\) (× 100) or \(\dfrac{13}{19}\) (× 100) or equivalent OR A trial and improvement method, considering percentages or decimals of 19 or 20 with a correct calculation shown between (60% of 19) 0.6 × 19 (= 11.4) and (70% of 20) 0.7 × 20 (= 14) inclusive | B1 | Allow:
|
| An answer in the inclusive range 60(%) to 70(%) | B1 | Only award if B1 previously awarded, however allow B2 for an unsupported answer in this range. If no marks, award SC1 for any of the following answers:
|
| (ii) (19 – 0.1 × 19) × 1000 000 000 or (19 – 0.1 × 19) × (1) × 109 or 0.9 × 19 × 1000 000 000 or 1.9 × 1010 × 9 × 10-1 or equivalent | M2 | Must have engaged with at least one stage of interpretation of the size of ‘billion’ in figures M1 for any one of the following:
|
| 1.71 × 1010 | A2 | A1 for any of the following:
Treat use of an estimate of 19 as a MR-1 from an accuracy mark, e.g. use of 20 gives an answer of 1.8 × 1010, award (M2 A2 MR-1) 3 marks |