The diagram shows a circle, centre O.
AB is a chord of length 12 cm.
M is the mid-point of AB and OM = 4.5 cm.
Calculate the radius of the circle.
.......................................... cm
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Syllabus Edition
First teaching 2023
First exams 2025
The diagram shows a circle, centre O.
AB is a chord of length 12 cm.
M is the mid-point of AB and OM = 4.5 cm.
Calculate the radius of the circle.
.......................................... cm
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is an isosceles triangle.
Work out the area of the triangle.
Give your answer correct to 3 significant figures.
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Calculate the length of .
Give your answer correct to 3 significant figures.
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is a right-angled triangle.
Work out the size of angle .
Give your answer correct to 1 decimal place.
The length of the side is reduced by 1 cm.
The length of the side is still 7 cm.
Angle is still 90°
Will the value of cosincrease or decrease?
You must give a reason for your answer.
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A solid metal cone has radius 1.65 cm and slant height 4.70 cm.
Find the angle the slant height makes with the base of the cone.
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The diagram shows a trapezium .
is parallel to .
, , angle and angle .
Calculate the shortest distance from to .
............................................ m
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The straight line has equation .
Calculate the acute angle between and the -axis.
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In this question, all measurements are in metres.
The diagram shows a right-angled triangle.
Given that to 3 significant figures, calculate the smallest angle of the triangle.
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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 .
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The diagram shows a quadrilateral, , formed from two triangles, and .
is a right-angled triangle.
Calculate angle .
Angle = ..............................................
Calculate the shortest distance from to .
.......................................... cm
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The diagram shows a right-angled triangle.
............................................ cm
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The diagram shows a right-angled triangle.
Calculate the value of .
= ............................................
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Calculate the length of AC.
AC = ........................................ cm
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Calculate AC.
AC = .................................... m
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Here is a right-angled triangle.
Work out the length of .
Give your answer correct to 1 decimal place.
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is a right-angled triangle.
= 9.6 cm.
= 6.4 cm.
Calculate the size of the angle marked .
Give your answer correct to 1 decimal place.
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is a right-angled triangle.
= 17 cm
= 25 cm
Work out the size of angle .
Give your answer correct to 1 decimal place.
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is a right-angled triangle.
Calculate the length of .
Give your answer correct to 3 significant figures.
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is a right-angled triangle.
Work out the size of the angle marked .
Give your answer correct to 1 decimal place.
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ABDF is a parallelogram and BCDE is a straight line.
AF = 12cm, AB = 9 cm, angle CFD = 40° and angle FDE = 80°.
........................................... cm
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The diagram shows a prism with length 18 cm and volume 253.8 cm3.
The cross-section of the prism is a right-angled triangle with base 6 cm and height cm.
Calculate the value of .
= ...............................................
Calculate the total surface area of the prism.
........................................ cm2
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The diagram shows a circle, centre O.
The straight line ABC is a tangent to the circle at B.
OB = 8 cm, AB = 15 cm and BC = 22.4 cm.
AO crosses the circle at X and OC crosses the circle at Y.
Calculate angle XOY.
Angle XOY = .............................................
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In the diagram, AB and CD are parallel.
AD and BC intersect at right angles at the point X.
AB = 10 cm, CD = 5 cm, AX = 8 cm and BX = 6 cm.
Angle XAB = ..............................................
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Here is part of a field.
This part of the field is in the shape of a trapezium.
A farmer wants to put a fence all the way around the edge of this part of the field.
The farmer has 50m of fence.
Does he have enough fence?
You must show all your working.
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The diagram shows a rectangular framework.
The framework is made from 5 metal rods.
The metal rods have a weight of 0.9 kg per metre.
Work out the total weight of the framework.
Give your answer, in kg, correct to 3 significant figures.
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The diagram shows a rectangle and a diagonal of the rectangle.
Work out the length of the diagonal of the rectangle.
Give your answer correct to 1 decimal place.
.....................
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lies on a circle with diameter .
lies on and lies on such that is parallel to .
= 21 cm, = 18 cm and = 13.5 cm.
Work out the radius of the circle.
............................................ cm
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Point A has co-ordinates (1, 0) and point B has co-ordinates (2, 5).
Calculate the angle between the line AB and the -axis.
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A square, with sides of length cm, is inside a circle.
Each vertex of the square is on the circumference of the circle.
The area of the circle is 49 cm2.
Work out the value of .
Give your answer correct to 3 significant figures.
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Here is triangle
The point lies on .
Calculate the size of angle .
Give your answer correct to decimal place.
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The diagram shows the positions of three points , and in a field.
Calculate the shortest distance from point to .
............................................. m
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The diagram shows a field ABCD.
The bearing of B from A is 140°.
C is due east of B and D is due north of C.
AB = 400m, BC = 350m and CD = 450m.
Calculate the distance from D to A.
............................................. m
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The angle is correct to 3 significant figures.
D is the point on AC that is nearest to B.
Calculate the distance from D to A.
................................................ m
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The diagram shows a field ABCDE.
Calculate the perimeter of the field ABCDE.
................................................ m
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In the diagram, is a vertical wall standing on horizontal ground .
= 76.7 m.
is the point on where = 58 m.
The angle of elevation of from is 26°.
The angle of elevation of from is 72°.
Calculate .
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