Geometry and measures worksheet — GCSE Foundation

1.Two straight lines AB and CD cross at point O. Angle AOC = 74°. Work out angle AOD.

2.A solid pyramid has a square base of side 6 cm. Its apex is directly above the centre of the base, at a vertical height of 8 cm. Work out the volume of the pyramid.

3.In a kite, one pair of opposite angles are equal in size. In kite WXYZ, angle X = 40° and angle Z = 100° are the two angles that are NOT equal to each other. The other two angles, W and Y, are equal to each other. Work out the size of angle W.

4.A sprinkler waters a sector-shaped patch of a garden with radius 8 m and angle 90°. Work out the perimeter of the watered sector, to 1 decimal place. (Use π = 3.14.)

5.At a point on a straight line, two angles are formed. One of them is 63°. Work out the size of the other angle.

6.A textbook contains the instruction 'Draw AB' and, on the next line, the statement 'AB = 5 cm'. Which statement about the notation AB is correct?

7.A tile is described as having two pairs of parallel sides, four equal sides, and diagonals that cross at right angles but are not equal in length. Give a reason why this tile cannot be a square.

8.Shape S is enlarged by a scale factor of 3, centre the origin. A vertex of S is at (2, 1). Work out the coordinates of the image of this vertex.

9.A circle has circumference 31.4 cm. Using π = 3.14, work out the radius of the circle.

10.A carpenter measures two triangular braces. Brace 1 has a 55° angle, a 65° angle, and, opposite the 55° angle, a side of 8 cm. Brace 2 has matching 55° and 65° angles and, opposite its 55° angle, a side of 8 cm. The carpenter says that because the equal 8 cm side is not between the two equal angles in either brace, he cannot be sure the two braces are the same size. Is the carpenter correct?

11.A ramp's sloped surface crosses two horizontal parallel rails. At the top rail, the angle between the ramp and the rail on the right of the ramp is (3x + 10)°. At the bottom rail, the angle between the ramp and the rail on the left of the ramp is (5x − 30)°. Work out the value of x.

12.A recipe uses 1.25 kg of flour. Work out how many grams of flour this is.

13.A solid is a single cube. Its plan view (from above), front elevation (from the front) and side elevation (from the side) are drawn separately. What shape is each of these three views?

14.A garden shed is shaped like a triangular prism: two identical vertical triangular end walls (the gable ends), joined by a sloping rectangular roof and a vertical rectangular back wall. Looking at the shed from directly above (the plan view), what shape is seen?

15.A right-angled triangle has angles of 90°, 40° and x°. Work out the value of x.