Scale Drawings
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Either paper 4 marks
A plan of a field is drawn to a scale of 1 cm to 25 m.
(a)On the plan, the track is \(7\) cm long.
Find the real length of the track.
(b)The real fence is \(50\) m long.
Calculate how long the fence should be on the plan.
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Either paper 4 marks
The diagram is a scale drawing of a rectangular field. The scale is 1 cm to 10 m.
On the drawing the field is \(9\) cm long and \(7\) cm wide.
(a)Find the real length of the field.
(b)A barn in the field is \(30\) m across.
Work out how wide the barn should be drawn on the scale drawing.
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Either paper 4 marksPart of a plan of a school is shown in the table. The scale of the plan is 1 cm to 3 m.
Room Length on the plan Real length Corridor 6 cm 18 m Classroom 2 cm Hall 21 m (a)Calculate the real length of the classroom.
(b)Calculate the length of the hall on the plan.
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Either paper 3 marks
Here is a plan of a flat with three rectangular rooms.
The plan is not drawn to scale.
Make an accurate scale drawing of the plan on the centimetre grid below, by plotting every corner of every room.
Use a scale of 1 cm represents 3 feet.
The bottom left corner of the Bedroom is at the point \(P\).
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Either paper 3 marks
A plan of a flat is drawn with the scale 1 cm represents 0.3 m.
On the plan, an alcove is \(6.7\) cm wide and \(3\) cm deep.
Noah wants to put a sofa in the alcove. The sofa is \(170\) cm wide and \(85\) cm deep.
Will the sofa fit in the alcove? You must show your working.
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Either paper 5 marks
Here is a map of a town.
Each square of the grid is 1 cm by 1 cm.
Scale: 1 cm represents 136 m
North is at the top of the map.
(a)Which place is exactly south west of the station?
Circle your answer.
library, monument, museum, school, town hall
(b)Circle the three-figure bearing of the town hall from the station.
000° 090° 180° 270°
(c)What is the distance, in metres, from the station to the town hall?
(d)Why might the shortest walking distance from the station to the town hall be greater than your answer to part (c)?
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Either paper 2 marks
Here is a sketch of a shape made from a square and a semicircle. The diameter of the semicircle is one side of the square.
The sketch is not drawn to scale.
The point \(A\) is marked on the centimetre grid.
On the grid, make an accurate drawing of the shape.
Draw it with corner \(A\) at the marked point and facing the same way as the sketch.
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Calculator 6 marks
Here is a map showing points \(P\) and \(Q\).
(a)Kemal wants to measure the bearing of \(P\) from \(Q\).
Kemal draws the line \(QP\) and a north line at \(P\), then measures the angle clockwise from the north line to the line \(QP\). The angle is \(121^\circ\).
Kemal says that the bearing of \(P\) from \(Q\) is \(121^\circ\).
Is Kemal's method correct? Give a reason for your answer.
(b)On a different map, the bearing of \(D\) from \(C\) is \(225^\circ\).
Nina says, "\(D\) is south west of \(C\)."
Is Nina correct? Give a reason for your answer.
(c)A map of an island is drawn on a grid of squares of side \(1.5\) cm. An airport, \(E\), is marked on the map.
Scale: \(1\) cm represents \(42\) km.
A plane flies due south from the airport. On the map the coast is \(4\) squares due south of \(E\).
How far does the plane fly until it reaches the sea?
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Either paper 3 marks
A map has a scale of \(1 : 8000\).
On the map, the distance from the school to the library is \(6\) cm.
Is the actual distance from the school to the library less than \(500\) m?
Tick a box. Yes / No
Show working to support your answer.
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Either paper 3 marks
A map is drawn to a scale of \(1 : 20000\).
On the map, the distance from Garsdale to Hollowbrook is \(8\) cm.
Calculate the real distance from Garsdale to Hollowbrook, in kilometres.
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(a) \(175\ \text{m}\)
(b) \(2\ \text{cm}\) -
(a) \(90\ \text{m}\)
(b) \(3\ \text{cm}\) -
(a) \(6\ \text{m}\)
(b) \(7\ \text{cm}\) - Bedroom: 3 cm wide and 4 cm high, from (2, 2) to (5, 6). Kitchen: 4 cm wide and 5 cm high, from (5, 2) to (9, 7). Lounge: 4 cm wide and 6 cm high, from (9, 2) to (13, 8).
- Yes. The alcove is \(201\) cm by \(90\) cm and the sofa is \(170\) cm by \(85\) cm.
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(a) Library
(b) 090°
(c) \(544\ \text{m}\)
(d) The answer to part (c) is the straight-line distance, but a walk has to follow roads and paths, which cannot go in a straight line between the two places, so the route is longer. - Square with corners \((11, 7)\), \((11, 11)\), \((7, 11)\) and \((7, 7)\), and a semicircle outside it on the side from \((7, 11)\) to \((7, 7)\), centre \((7, 9)\), radius \(2\) cm
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(a) No: the angle was measured at P, but a bearing of P from Q is measured at Q
(b) Yes: a bearing of 225° points south west
(c) \(252\ \text{km}\) - Yes: the actual distance is \(480\) m, which is less than \(500\) m
- \(1.6\ \text{km}\)
Takes a couple of seconds the first time a sheet is made.