Calculate the value of .
................................................
Calculate the area of the triangle.
.......................................... cm2
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Syllabus Edition
First teaching 2023
First exams 2025
Calculate the value of .
................................................
Calculate the area of the triangle.
.......................................... cm2
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Calculate the obtuse angle in this triangle.
= ...................................................
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Calculate SR.
SR = ............................................... cm
Calculate RQ.
RQ = ............................................... cm
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Work out the length of .
Give your answer correct to 3 significant figures.
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is a triangle.
Calculate the area of triangle .
Give your answer correct to significant figures.
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The diagram shows triangle .
Calculate the length of .
Give your answer correct to 3 significant figures.
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is a triangle.
is a point on .
Angle = 45°
Angle = 80°
= 7.4cm
= 5.8 cm
Work out the length of .
Give your answer correct to 3 significant figures.
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The diagram shows a field, ABCD, on horizontal ground.
BC = 192 m, CD = 287.9 m and BD = 168 m.
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AD = 10 cm, BC = 8 cm, BX = 5 cm, CX = 7 cm.
The diagonals of the cyclic quadrilateral ABCD intersect at X.
Calculate angle BXC.
Angle BXC = ................................................
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The diagram shows a trapezium .
is parallel to .
, , angle and angle .
Calculate .
........................................... 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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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.
.......................................... km
The bearing of Budapest from Hamburg is 133°.
Calculate the bearing of Budapest from Geneva.
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Calculate angle ACB.
Angle ACB = .................................................
Calculate angle ACD.
Angle ACD = ..................................................
Calculate the area of the quadrilateral ABCD.
........................................... 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.
Calculate the area of the pentagon.
......................................... cm2
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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 a quadrilateral, , formed from two triangles, and .
is a right-angled triangle.
Calculate angle .
Angle = ..............................................
Calculate .
= ......................................... cm
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The area of the triangle is 50cm2.
Calculate the value of .
= ..............................................
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Calculate the area of the triangle.
............................................. cm2
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Use the sine rule to find angle ABC.
Angle ABC = ..............................................
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Calculate the value of .
................................................
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Calculate angle LMN.
Angle LMN = ..............................................
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is a triangle.
Work out the area of triangle .
Give your answer as an exact value.
Work out the length of the side .
Give your answer as a simplified surd.
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Calculate the length of .
Give your answer correct to 3 significant figures.
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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.
QR = ............................................ m
Calculate RS.
RS = ............................................ m
Calculate the total area of the two triangles.
............................................ m2
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Use the cosine rule to find angle BAC.
Angle BAC = ...................................................
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The diagram shows triangle ABC.
BC = ............................................... m [4]
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.
........................................ 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.
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]
$ ................................................
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Find the area of a regular hexagon with side length 7.4 cm.
.......................................... cm2
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The diagram shows a cuboid.
AB = 8 cm, AD = 6 cm and DH = 6 cm.
Calculate angle HAF.
Angle HAF = .................................................
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The diagram shows an equilateral triangle ABC with sides of length 10 cm.
AMN is a sector of a circle, centre A.
M is the mid-point of AC.
Work out the area of the shaded region.
Give your answer in the form where and are integers.
......................................... cm2
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The area of triangle is m2.
Calculate the value of .
Give your answer correct to significant figures.
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and are triangles.
The area of triangle is 56 m2
Work out the length of
Give your answer correct to 1 decimal place.
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is a parallelogram.
= 9 cm
= 11 cm
Angle = 100°
Calculate the area of the parallelogram.
Give your answer correct to 3 significant figures.
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is an acute-angled triangle.
= 7cm
= 8cm
The area of triangle is 18 cm2.
Work out the size of angle .
Give your answer correct to 3 significant figures.
You must show all your working.
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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.
Angle CAB = 42° and angle ACG = 54°.
Calculate the value of .
................................................
Calculate AC.
AC = ........................................... cm
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The area of triangle DEF is 70 m2.
[4]
= .......................... or = .......................... [4]
DE = ............................................... m [1]
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The diagram shows a field ABCDE.
Calculate the perimeter of the field ABCDE.
................................................ m
Calculate angle ABD.
Angle ABD = ..........................................................
Calculate the area of the field ABCDE.
Give your answer in hectares.
[1 hectare = 10 000m2]
...................................... hectares
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Triangle has an area of 70 m2.
and angle =40°.
Calculate .
= .......................................... m
A different triangle also has an area of 70 m2.
and
Find angle .
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.
LM = ......................................... km
A ship sails directly from L to P.
Calculate the shortest distance from M to LP.
.......................................... km
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