The diagram shows the positions of three points , and in a field.
Show that is 118.1 m, correct to 1 decimal place.
Calculate angle .
Angle ................................................
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Syllabus Edition
First teaching 2021
Last exams 2024
The diagram shows the positions of three points , and in a field.
Show that is 118.1 m, correct to 1 decimal place.
Calculate angle .
Angle ................................................
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The diagram shows two triangles.
Calculate QR.
Â
QR = ............................................ m
Calculate RS.
Â
RS = ............................................ m
Calculate the total area of the two triangles.
Â
 ............................................ m2
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Use the cosine rule to find angle BAC.
Angle BAC = ...................................................
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The diagram shows triangle ABC.
Â
BC = ............................................... m [4]
Â
Angle ACB = ................................................... [3]
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The diagram shows a field, ABCD, on horizontal ground.
Use the cosine rule to find angle BAC.
Angle BAC = ...................................................
Use the sine rule to find angle CAD.
Angle CAD = ...................................................
Calculate the area of the field.
............................................... m2
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 Calculate the area of triangle PQR.
Â
........................................ cm2
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The diagram shows a field, ABCD, on horizontal ground.
BC = 192 m, CD = 287.9 m and BD = 168 m.Â
Angle CBD rounds to 106.0°, correct to 1 decimal place.
Calculate the area of triangle BCD.
 ............................................ m2
Tomas buys the triangular part of the field, BCD.
The cost is $35 750 per hectare.
Calculate the amount he pays.
Give your answer correct to the nearest $100.
[1 hectare = 10000m2]
 Â
$ ................................................
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The diagram shows a field, ABCD, on horizontal ground.
BC = 192 m, CD = 287.9 m and BD = 168 m.
 Â
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 AD = 10 cm, BC = 8 cm, BX = 5 cm, CX = 7 cm. Â
The diagonals of the cyclic quadrilateral ABCD intersect at X. Â
Calculate angle BXC.
Â
 Angle BXC = ................................................
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The diagram shows a trapezium .
is parallel to .
, , angle and angle .
Calculate .
Â
........................................... m
Calculate .
........................................... m
Calculate the area of .
 .......................................... m2
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The diagram shows two triangles and .
and .
Angle , angle and angle .
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In the diagram, is a vertical wall standing on horizontal ground .
is the point on where = 58 m.
The angle of elevation of from is 26°.
The angle of elevation of from is 72°.
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Â
In the diagram, AB = 18 cm, BC = 21.3 cm and BD = 11.6 cm.
Angle BDC = 123.5° and angle ABC is a right angle.
Angle BCD = ............................................... [3]
AD = ......................................... cm [5]
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The diagram shows the positions of three cities, Geneva (G), Budapest (B) and Hamburg (H).
Use the cosine rule to calculate the distance from Geneva to Budapest.
Â
.......................................... km
The bearing of Budapest from Hamburg is 133°.
Calculate the bearing of Budapest from Geneva.
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Â
Calculate angle ACB.
Â
Angle ACB = .................................................
Calculate angle ACD.
Â
Angle ACD = ..................................................
Calculate the area of the quadrilateral ABCD.
Â
........................................... cm2
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In the pentagon , angle = angle = 90°.
Triangle is equilateral with side length 12 cm.
= = 6 cm.
Calculate angle .
Angle = .............................................
Calculate the area of the pentagon.
......................................... cm2
Calculate.
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The diagram shows a quadrilateral formed from two triangles, and .
Calculate
 ............................................ cm [3]
 ............................................ cm [3]
........................................... cm2 [4]
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The diagram shows triangle ABC with point G inside.
CB = 11 cm, CG = 5.3 cm and BG = 6.9 cm.Â
Angle CAB = 42° and angle ACG = 54°.
Calculate the value of .
Â
................................................Â
Calculate AC.
Â
AC = ........................................... cm
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The area of triangle DEF is 70 m2.
Â
[4]
Â
= .......................... or = .......................... [4]
Â
DE = ............................................... m [1]
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The diagram shows a field ABCDE.
Calculate the perimeter of the field ABCDE.
Â
................................................ m
Calculate angle ABD.
Â
Angle ABD = Â ..........................................................
Calculate the area of the field ABCDE.
Give your answer in hectares.
[1 hectare = 10 000m2]
Â
...................................... hectares
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Triangle has an area of 70 m2.
and angle =40°.
Calculate .
Â
= .......................................... m
A different triangle also has an area of 70 m2.
andÂ
Â
Find angle .
Â
Angle = ..............................................
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The diagram shows a design made from a triangle AOC joined to a sector OCB.
AC = 8cm, OB = OC = 7 cm and angle ACO = 78°.
Use the cosine rule to show that OA = 9.47 cm, correct to 2 decimal places.
Calculate angle OAC.
Angle OAC = ................................................
The perimeter of the design is 29.5 cm.
Show that angle COB = 41.2°, correct to 1 decimal place.
Calculate the total area of the design.
......................................... cm2
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The diagram shows two ports, L and P, and a buoy, M.
The bearing of L from P is 201° and LP = 248 km.
The bearing of M from P is 127°.
Angle PML = 42°.
Use the sine rule to calculate LM.
Â
LM = ......................................... km
A ship sails directly from L to P.
Calculate the shortest distance from M to LP.
Â
 .......................................... km
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