ABC. XYZ. Start with the base AB = 6.5 cm. Then open the pair of compasses to 5 cm and draw an arc, centre A.

Transcription

1 onstructing triangles Questions are targeted at the grades indicated 1 Here is a sketch of triangle. Start with the base = 6.5 cm. Then open the pair of compasses to 5 cm and draw an arc, centre. 5 cm 6.5 cm 7 cm onstruct an accurate drawing of triangle. 2 Here is a sketch of triangle XYZ. Z 4 cm 5 cm Y 3 cm X onstruct an accurate drawing of triangle XYZ. 313

2 onstructing triangles 3 Here is a sketch of the triangle QR. R 8 cm 5cm 5cm Q onstruct an accurate drawing of the triangle QR. 4 onstruct an equilateral triangle with sides of length 4.5 cm. Hint It is a good idea to draw a sketch first. 313

3 onstructing triangles 5 onstruct the triangle with sides = 4.5 cm, = 5.5 cm and = 5.5 cm. 6 onstruct the triangle QR with sides Q = 4.8 cm, QR = 5.8 cm and R = 6.8 cm. 313

4 onstructing triangles 7 onstruct triangle XYZ with sides XY = 4.0 cm, YZ = 5.8 cm and ZX = 7.1 cm. 8 Here is a sketch of the quadrilateral EF. F 3.2 cm E 4 cm 5.5 cm 4.5 cm 6.4 cm Make an accurate drawing of quadrilateral EF. 313

5 erpendicular lines 1 onstruct the perpendicular bisector of each of the lines. Questions are targeted at the grades indicated raw arcs above and below the line to be bisected. 2 onstruct the perpendicular bisector of each of the lines XY. X Y Y X X Y 315

6 erpendicular lines 3 onstruct the perpendicular from the point on the line in each of the following cases. Remember to start by drawing arcs, centre, which cut on either side of. 4 onstruct the perpendicular from the point to the line in each of the following cases. Remember to draw arcs, centre, to cut. 315

7 erpendicular lines 5 onstruct the perpendicular from to the side QR of the triangle QR in each case. Q R Q R 315

8 onstructing and bisecting angles Questions are targeted at the grades indicated 1 In each case, construct the bisector of the angle. Remember to start by drawing arcs centre to cut and. 317

9 Loci 1 raw the locus of all points that are equidistant from X and Y. Questions are targeted at the grades indicated Think what property the perpendicular bisector of XY has. X Y 2 raw the locus of all points that are equidistant from and. 3 raw the locus of all points that are 1.5 cm from the point. Hint Think about the shape this will produce. 4 raw the locus of all points that are 3 cm from the line segment. Remember to think carefully about what happens at the ends, and 319

10 Loci 5 raw the locus of all points that are equidistant from the lines Q and R. R Q 319

11 Regions Questions are targeted at the grades indicated 1 Shade the region of points that are less than 2.5 cm from the point. 2 Shade the region of points less than 1.8 cm from the line segment. Think carefully about what to do about the points and. 3 Shade the region of points closer to than. 4 Shade the region of points closer to the line than to the line. 321

12 Regions 5 Show, by shading, the region of points more than 1.6 cm from the point Q. Q 321

13 earings Questions are targeted at the grades indicated 1 Measure and write down the bearing of from. a b c d e N N N N N N N Use the protractor to draw diagrams of the following bearings. a The bearing from to is 075. b The bearing of to is 210. c The bearing from E to F is

14 earings 3 The bearing of x from y is 067. Work out the bearing of y from x The bearing of Heathrow airport from a plane is 237. Work out the bearing of the plane from Heathrow airport The bearing of a lighthouse from ship is 307. The ship is 5 km from the lighthouse. The bearing of a second ship from ship is 270. Ships and are 4 km apart. a raw a scale diagram showing the positions of the two ships. Hint Use a scale of 1 cm = 1 km b How far away from the lighthouse is ship?... 6 boat leaves a port on a bearing of 069. Work out the bearing the boat needs to use to return to port

15 Scale drawings and maps Questions are targeted at the grades indicated 1 The Eiffel tower is 324 m high. model has a scale of 1 : 400. alculate its height map has a scale of 1 : Karen measured the following distances on the map. What are the distances in the real world, in km? Newton to rotchley 12 cm Real world distance = cm = cm = 6 km a Snedbury to Fley 9 cm b St John s hurch to Kipley ross 2.5 cm c raybridge to Gleet 29 cm d ridge to Weir 17 mm 3 central London map has a scale of 1 : Find the distance on the map, in cm, for each real distance given below. Work to the nearest mm. Trafalgar Square to Tottenham ourt Road 1.5 km 1.5 km = m = cm Map distance = cm = 13.0 cm (to nearest mm) a iccadilly ircus to arliament Square 1.9 km... b Marble rch to Hyde ark orner 2.07 km

16 Scale drawings and maps c ritish Library to Oxford ircus 1.84 km... d ovent Garden to Leicester Square 520 m... 4 The body of a hinook helicopter is 52.1 m long. scale model is 20.8 cm long. a Find the ratio of the scale model in the form 1 : n b The rotor blade length is 30.2 m. Find the width of the model, to the nearest mm. 5 This earson logo was enlarged so that its length was 1.7 m. a Find the scale of the enlargement in the form 1 : n b Find the height of the enlargement, to the nearest cm. 325

17 Scale drawings and maps 6 This map of the Isle of Wight has a scale of 1 : owes Northwood Freshwater Newport Ryde Seaview embridge Sandown Shanklin Ventnor i Measure the distance between the two towns, in cm, to 1 decimal place. ii alculate the real distance between the towns, in km. a owes to Ryde i... ii... b Ryde to Sandown i... ii... c Sandown to Shanklin i... ii... d Newport to Freshwater i... ii... e Freshwater to Ventnor i... ii... f Ventnor to owes i... ii... g embridge to Freshwater i... ii... h Sandown to Ventnor i... ii... 7 This is a plan of an art gallery. East wall a The East wall has a real length of 12 m. Find the scale of the map in the form i 1 cm represents n m... ii 1 : n

18 Scale drawings and maps b raw an accurate scale drawing on centimetre squared paper. 325