Pythagoras' theorem

ABC is a right-angled triangle.

Calculate the value of x. Give your answer correct to 1 decimal place.

ABC is a right-angled triangle.

Calculate the value of x. Give your answer correct to 1 decimal place.

ABCDEFGH is a cuboid.

Angle GEF = 52° Angle BHG = 27° EF = 15 cm Work out the size of angle GEB. Give your answer to the nearest degree.

The diagram shows trapezium ABCD.

AB = 12 cm AD = 8 cm The trapezium has an area of 112 cm² Work out the perimeter of the trapezium. Give your answer correct to 3 significant figures.

The diagram shows trapezium ABCD.

AB = 12 cm AD = 8 cm The trapezium has an area of 112 cm² Work out the perimeter of the trapezium. Give your answer correct to 3 significant figures.

The diagram shows triangle ABC.

In the diagram, all measurements are in centimetres. AC = BC The perimeter of the triangle is 72 cm. Work out the area of the triangle.

The diagram shows triangle ABC.

In the diagram, all measurements are in centimetres. AC = BC The perimeter of the triangle is 72 cm. Work out the area of the triangle.

VABC is a solid pyramid. ABC is an equilateral triangle.

M is the midpoint of AB. F is the point on MC such that MF:FC = 1: 2 The vertex V is vertically above F. VA = VB = VC VF = 8 cm Angle VCM = 52° Work out the side length of the equilateral triangle ABC. Give your answer correct to 1 decimal place.

ABC is a right-angled triangle.

Calculate the length of AB. Give your answer correct to 1 decimal place.

ABC is a right-angled triangle.

Calculate the length of AB. Give your answer correct to 1 decimal place.

The diagram shows a cone.

The radius of the base of the cone is of the height of the cone. The total surface area of the cone is 54πcm² Work out the height of the cone.

ABC is a right-angled triangle.

Work out the length of CB. Give your answer correct to 3 significant figures.

ABC is a right-angled triangle.

Work out the length of CB. Give your answer correct to 3 significant figures.

The diagram shows two right-angled triangles.

All lengths are measured in centimetres. Given that sina = tanb work out the value of x.

The diagram shows a circle, radius r cm and two regular hexagons.

Each side of the larger hexagon ABCDEF is a tangent to the circle. Each side of the smaller hexagon PQRSTU is a chord of the circle. By considering perimeters, show that

ABC is a right-angled triangle.

Calculate the length of AB. Give your answer correct to 3 significant figures.

A is the point with coordinates (7, 13) B is the point with coordinates (−3, 21) C is the point with coordinates (15, 23) M is the midpoint of AB. N is the midpoint of BC. Work out the distance between M and N. Give your answer correct to 1 decimal place.

A, B, C and D are points on a circle such that ABCD is a square.

The square ABCD has sides of length 3.5 cm. Calculate the circumference of the circle. Give your answer correct to 1 decimal place. You must show all your working.

The diagram shows a triangular prism with a horizontal rectangular base ABCD.

M is the midpoint of AD. The vertex T of the prism is vertically above M. AB = 14.7 cm BC = 3.8 cm MT = 2.3 cm P is the point on AB such that AP: PB = 5: 2 Calculate the size of the angle between TP and the base ABCD of the prism. Give your answer correct to 1 decimal place.

ABCDEFGH is a cuboid.

AF = 6.8 cm FC = 13.6 cm Work out the size of the angle between FC and the plane ABCD.

The points A, B, C and D lie on a circle, centre O. ABCD is a rectangle.

AB = 8 cm BC = 10 cm Work out the circumference of the circle. Give your answer correct to 3 significant figures.

ABC is a right-angled triangle.

AB = 9.3 cm correct to the nearest mm. AC = 12.6 cm correct to the nearest mm. Calculate the lower bound for the size of the angle marked x. You must show all your working.

24The diagram shows 8 identical regular octagons joined to enclose a shaded shape.

Each octagon has sides of length a. Find, in terms of a, an expression for the area of the shaded shape.

ABD is a triangle. C is a point on BD.

Work out the length of DC. Give your answer correct to 1 decimal place.

Here is a solid sphere and a solid cone.

Volume of sphere = πr³ Volume of cone = πr²h All measurements are in cm. The volume of the sphere is equal to the volume of the cone.

Find r:h Give your answer in its simplest form.

Here is a different solid sphere and a different solid cone.

Surface area of sphere = 4πr² Curved area of cone = πrl All measurements are in cm. The surface area of the sphere is equal to the total surface area of the cone.

Find r:h

Work out the value of x. Give your answer correct to 3 significant figures.

Work out the value of x. Give your answer correct to 3 significant figures.

A and B are points on a centimetre grid. A is the point with coordinates (−7, 6) B is the point with coordinates (8, −5) Work out the length of AB. Give your answer correct to 1 decimal place.

ABCDEFGH is a cuboid.

AD = 9 cm FD = 13 cm Angle GHF = 49° Work out the size of angle FAH. Give your answer correct to the nearest degree.

A right-angled triangle is formed by the diameters of three semicircular regions, A, B and C as shown in the diagram.

Show that area of region A = area of region B + area of region C

Here is a right-angled triangle.

Work out the value of x.

Here is a right-angled triangle.

Work out the value of x.

ABC and ACD are right-angled triangles.

DC = 8 cm Angle ADC = 45° Angle ABC = 20° Work out the length of AB. Give your answer correct to 3 significant figures.

Here is a prism ABCDSPQR.

The base ABCD of the prism is a square of side 14 cm T is the point on BC such that BT: TC = 4: 3 The cross section of the prism is in the shape of a trapezium of area 147 cm² CR = 12 cm Find the size of the angle between the line ST and the base ABCD. Give your answer correct to 1 decimal place.

Here is a right-angled triangle.

The shaded shape below is made from two of these triangles.

Work out the perimeter of the shaded shape. Give your answer correct to 3 significant figures.

ABC is a right-angled triangle.

Work out the length of BC. Give your answer correct to 1 decimal place.

PQR is a right-angled triangle.

Work out the size of the angle marked x. Give your answer correct to 1 decimal place.

Here is a right‑angled triangle.

The shaded shape below is made from two of these triangles.

Work out the perimeter of the shaded shape. Give your answer correct to 3 significant figures.

ABC is a right‑angled triangle.

Work out the length of BC. Give your answer correct to 1 decimal place.

PQR is a right‑angled triangle.

Work out the size of the angle marked x. Give your answer correct to 1 decimal place.

The diagram shows two right-angled triangles ACB and DEB.

AD = 9 cm DE = 2 cm DB = 6 cm Calculate the length of CB. Give your answer correct to 2 decimal places.

Work out the value of x. Give your answer correct to 1 decimal place.

The diagram shows a right-angled triangle and a quarter circle.

The right-angled triangle ABC has angle ABC = 90 The quarter circle has centre C and radius CB. Work out the area of the quarter circle. Give your answer correct to 3 significant figures. You must show all your working.

Work out the value of x. Give your answer correct to 1 decimal place.

The diagram shows a right-angled triangle and a quarter circle.

The right-angled triangle ABC has angle ABC = 90 The quarter circle has centre C and radius CB. Work out the area of the quarter circle. Give your answer correct to 3 significant figures. You must show all your working.

The diagram shows a prism.

The cross section of the prism has exactly one line of symmetry. Work out the volume of the prism. Give your answer correct to 3 significant figures.

The diagram shows a cube.

AH = 11.3 cm correct to the nearest mm. Calculate the lower bound for the length of an edge of the cube. You must show all your working.

The diagram shows triangle AOB.

Angle AOB is not an obtuse angle.

Find the greatest value of x. You must show all your working.

The diagram shows triangle ABC.

ADC and DEB are straight lines.

AD = 4.4 cm BC = 8.6 cm E is the midpoint of DB.

Angle CDB = 90° Angle DCB = 40°

Work out the size of angle EAD. Give your answer correct to 1 decimal place. You must show all your working.

The cone has volume 56.8 cm³ and height 3.6 cm.

Calculate the size of angle AOB of sector OACB. Give your answer correct to 3 significant figures. You must show all your working.

ABC is a right-angled triangle.

ABC is a right-angled triangle.

The diagram shows a triangular prism.

Angle ABE and angle CBE are right angles. Angle EAB = 35° M is the point on DA such that DM: MA = 2: 3 Calculate the size of the angle between EM and the base of the prism. Give your answer correct to 1 decimal place.

ABC is a right-angled triangle.

Here is Sarah’s method to find the length of BC.

= 100 BC = 10

What mistake has Sarah made in her method?

He draws triangle XYZ.

Explain why Roy’s diagram is not correct.

The diagram shows a circle, centre O.

AB is the tangent to the circle at the point A. Angle OBA 30° Point B has coordinates (16, 0) Point P has coordinates (3 p, p) Find the value of p. Give your answer correct to 1 decimal place. You must show all your working.

Write down the exact value of tan 45°

Here is a right-angled triangle.

cos 60° = 0.5

Work out the value of x.

ABC is a right-angled triangle.

AC = 14 cm. Angle C = 90

size of angle B: size of angle A = 3: 2

Work out the length of AB. Give your answer correct to 3 significant figures.

ABC is a right-angled triangle.

AC = 14 cm. Angle C = 90

size of angle B: size of angle A = 3: 2

Work out the length of AB. Give your answer correct to 3 significant figures.

Here is a pyramid with a square base ABCD.

AB = 5 m

The vertex T is 12 m vertically above the midpoint of AC.

Calculate the size of angle TAC.

Here is a triangular prism.

Work out the volume of the prism. Give your answer correct to 3 significant figures.

ABCDEFGH is a cuboid.

AB = 7.3 cm CH = 8.1 cm Angle BCA = 48

Find the size of the angle between AH and the plane ABCD. Give your answer correct to 1 decimal place.

ABC is a right-angled triangle.

Work out the size of angle ABC. Give your answer correct to 1 decimal place.

The length of the side AB is reduced by 1 cm.

The length of the side BC is still 7 cm. Angle ACB is still 90

Will the value of cos ABC increase or decrease? You must give a reason for your answer.

ABC is a right-angled triangle.

Work out the size of angle ABC. Give your answer correct to 1 decimal place.

The length of the side AB is reduced by 1 cm.

The length of the side BC is still 7 cm. Angle ACB is still 90

Will the value of cos ABC increase or decrease? You must give a reason for your answer.

Here are two right-angled triangles.

Given that

tan e = tan f

find the value of x.

You must show all your working.

ABCD is a trapezium.

Work out the size of angle CDA. Give your answer correct to 1 decimal place.

ABCD is a trapezium.

Work out the size of angle CDA. Give your answer correct to 1 decimal place.

OAC is a sector of a circle, centre O, radius 10 m.

BA is the tangent to the circle at point A. BC is the tangent to the circle at point C.

Angle AOC

Calculate the area of the shaded region. Give your answer correct to 3 significant figures.

ABC and ADC are triangles.

The area of triangle ADC is 56 m²

Work out the length of AB. Give your answer correct to 1 decimal place.

This rectangular frame is made from 5 straight pieces of metal.

The weight of the metal is 1.5 kg per metre.

Work out the total weight of the metal in the frame.

The diagram shows 3 identical circles inside a rectangle. Each circle touches the other two circles and the sides of the rectangle, as shown in the diagram.

The radius of each circle is 24 mm.

Work out the area of the rectangle. Give your answer correct to 3 significant figures.

ABC is a right-angled triangle.

Calculate the length of AB. Give your answer correct to 3 significant figures.

A square, with sides of length x 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 x. Give your answer correct to 3 significant figures.

A, B and C are points on a circle of radius 5 cm, centre O. DA and DC are tangents to the circle. DO = 9 cm

Work out the length of arc ABC. Give your answer correct to 3 significant figures.