Geometry and measures worksheet — GCSE Foundation

1.The diagram shows the plan, front elevation and side elevation of a solid. Which solid could this be?

2.Triangle JKL has a right angle at K, hypotenuse JL = 13 cm, and side JK = 5 cm. Triangle MNO has a right angle at N, hypotenuse MO = 13 cm, and side MN = 5 cm. Using only the facts given, and without working out any further lengths, write down the congruence condition that proves triangle JKL is congruent to triangle MNO.

3.Point A and point B are 5 cm apart. How many points are exactly 4 cm from A and exactly 3 cm from B?

4.A pop-up canopy has two sloping supports that meet at the top. Each support makes an angle of 30° with the ground and is 6 m long. Using the exact value of cos 30°, work out the total width of the canopy's base.

5.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.

6.Point D is at (3, 7). It is reflected in the line y = x. Work out the coordinates of the image of point D.

7.The point (2, 5) is translated 3 units right and 4 units down. Work out the coordinates of the image point.

8.A goat is tied by a rope 7 m long to a post at a corner of a rectangular field, where two fences meet at a right angle. The goat can reach anywhere inside the field that the rope allows. Using π = 3.14, work out the area the goat can graze, to the nearest square metre.

9.Every diameter of a circle is an example of a more general type of straight line joining two points on the circle. Which term names that more general type of line?

10.Work out the exact value of sin 30° + cos 60°.

11.The point (4, −3) is reflected in the y-axis. Work out the coordinates of the image point.

12.Write down the column vector that describes a translation of 4 units to the right and 4 units up.

13.Which pair of points lies on a horizontal line when the points are plotted on a coordinate grid?

14.Angle ABC is 130°. The line BF divides angle ABC into two equal parts. Work out the size of angle FBC.

15.A scale model of a bridge is built so that 2 cm on the model represents 5 m of the real bridge. The real bridge is 45 m long. Work out the length of the model bridge, in centimetres.