4MA0 Higher June 2012 Paper 3 Q1
1
(a) The length of an Airbus A300 aeroplane is 54 m.
The ratio of the length of this aeroplane to its wingspan is 6 : 5
Work out the wingspan of the aeroplane. (2)
The ratio of the length of this aeroplane to its wingspan is 6 : 5
Work out the wingspan of the aeroplane. (2)
(b) A model is made of the Airbus A300 aeroplane.
The length of the model is 36 cm.
The length of the real aeroplane is 54 m.
Find the ratio of the length of the model to the length of the real aeroplane.
Give your ratio in the form 1 : \(n\) (3)
The length of the model is 36 cm.
The length of the real aeroplane is 54 m.
Find the ratio of the length of the model to the length of the real aeroplane.
Give your ratio in the form 1 : \(n\) (3)
| Scheme | Marks |
|---|---|
| \(54 \times \dfrac{5}{6}\) | M1 |
| 45 | A1 |
| (2) |
Notes
M1: for 54 × 5 or 270 or 54 ÷ 6 or 9
or \(\dfrac{5}{6}\) oe or \(\dfrac{6}{5}\) oe
A1: cao
Apart from Questions 9, 13, 18, 20 and 21 (where the mark scheme states otherwise) the correct answer, unless clearly obtained by an incorrect method, should be taken to imply a correct method.
| Scheme | Marks |
|---|---|
ratio 36 : 5400 oe inc 0.36 : 54, 36 cm : 5400 cm, 0.36 m : 54 m (condone omission of units from one side) or fraction \(\dfrac{5400}{36}\) oe inc \(\dfrac{54\text{ m}}{0.36\text{ m}}\) (condone omission of units from either numerator or denominator) | M2 |
| 150 | A1 |
| (3) | |
| (Total 5 marks) |
Notes
M2: M1 for ratio or fraction with no units
0.36 or 3.6 or 36 or 360 or 3600... : 0.54 or 5.4 or 54 or 540 or 5400 ... oe
\(\dfrac{0.54 \text{ or } 5.4 \text{ or } 54 \text{ or } 540 \text{ or } 5400...}{0.36 \text{ or } 3.6 \text{ or } 36 \text{ or } 360 \text{ or } 3600...}\) oe
eg 36 : 54, \(\dfrac{54}{36}\), 36 : 540, \(\dfrac{540}{36}\), 360 : 54, \(\dfrac{54}{360}\), 1 : 1.5, 54 ÷ 36, 1 : 0.15
A1: cao Do not award A1 for 150 cm, 150\(n\) etc