Geometry and Measures

On the grid, draw a shape congruent to triangle A.

This shape is made from a semicircle and a square. The side of the square is 6 cm. Work out the total area of the shape. Give your answer in terms of π.

J (0, 12) and K (5, 10) are points on the straight line JKLM. JK = KL = LM Work out the coordinates of M.

Here is a solid prism. How many faces does the prism have?

The prism has volume = 3500 cm³ and length = 20 cm Work out the area of the cross-section of the prism.

Write down the value of sin 90°

A large circle and a small circle are shown. The radius of the large circle is 12 cm. radius of large circle : radius of small circle = 4 : 1 Work out the shaded area. Give your answer in terms of π.

Measure the shortest distance from point P to the line. Give your answer in millimetres.

The vector (^-3₇) translates A to B. Write down the vector that translates B to A.

Here is a cone. Curved surface area of a cone = πrl, where r is the radius and l is the slant height. Beth tries to work out the curved surface area in terms of π. Her working is: Curved surface area of the cone = π × 5 × 12 = 60π cm² What mistake has she made?

Adam uses π = 3 to estimate the area of the base of the cone. Work out his estimate.

Beth uses π = 3.14 to estimate the area of the base of the cone. Is Beth's estimate more than or less than Adam's estimate? Give a reason for your answer.

Describe fully the single transformation that maps shape A to shape B.

A sector has radius 12 cm and angle 60°. Work out the length of the arc. Give your answer in terms of π.

Show that the value of 6 sin 30° + 2 cos 30° × 4 tan 30° is an integer.

Points A, B and C are plotted on a grid. Write down the coordinates of C.

Write down the coordinates of the midpoint of AC.

AB is a straight line. Work out the size of angle x.

Work out the size of angle y.

Three straight lines intersect as shown. What type of triangle is made? You must show your working.

The time Shaz takes to run a race is 1 minute 28 seconds less than 2 hours. Work out her time in hours, minutes and seconds.

In the grid below, shade one quarter of the squares so that the grid has exactly two lines of symmetry. Shade complete squares only. Which of the following is the correct shading?

Here is a right-angled triangle. Use Pythagoras' theorem to show that x = 0.8

Use trigonometry to work out the value of x.

Here are three solids. How many faces does the cube have?

How many edges does the square-based pyramid have?

How many vertices does the cone have?

The diagram shows a triangle ABC on a coordinate grid. Work out the coordinates of B.

Point C (4, -1) is reflected in the line x = 6 to point D. Work out the coordinates of D.

Choose a word from the list below to complete the sentence. <br> <br> arc, centre, circumference, diameter, radius, sector, segment, tangent <br> <br> The length of the __________ is double the length of the radius.

Choose a word from the list below to complete the sentence. <br> <br> arc, centre, circumference, diameter, radius, sector, segment, tangent <br> <br> A __________ is a region created by drawing a chord through a circle.

Choose a word from the list below to complete the sentence. <br> <br> arc, centre, circumference, diameter, radius, sector, segment, tangent <br> <br> A radius meets a __________ at a right angle.

In the grid below, shade one quarter of the squares so that the grid has exactly two lines of symmetry. Shade complete squares only.

Here is a right-angled triangle. <br> <br> Use Pythagoras' theorem to show that x = 0.8

A phone screen is similar to a tablet screen. <br> The area of the tablet screen is 420 cm². <br> A screen costs £7000 per square metre. <br> Work out the cost of a screen for the phone.

Work out an estimate for the total distance covered by the ball.

Is your estimate from the previous question an overestimate or an underestimate? <br> Give a reason for your answer.

Here is a cyclic quadrilateral. <br> f : g = 2 : 3 <br> Work out f : h <br> Give your answer in its simplest form.

A building in the shape of a cylinder has diameter 40 m and height 55 m. On the centimetre grid, draw a plan of the building. Use a scale of 1 cm to 10 m.

On this centimetre grid, draw the front elevation of the building. Use a scale of 1 cm to 10 m.

Use the sine rule to work out length x. You must show your working.

The metal used to make a sphere costs £4320. The metal costs £3.60 per gram. Each cubic centimetre of metal has a mass of 17.3 grams. Work out the radius, r, of the sphere. The volume of a sphere is given by V = (4/3)πr³.