Geometry and measures worksheet — GCSE Foundation

1.A locus is described as the set of points exactly 4 cm from a fixed point O. What shape is this locus?

2.In triangle ABC the angle at A is 90° and BC = 10 cm. For the angle at B, sin B = 3/5. Work out the length of AC.

3.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?

4.Point A is at (2, 3). It is translated by the vector (4, −1) to give point A′. Work out the coordinates of A′.

5.A square tile has sides of length 4.5 cm. Work out the perimeter of the tile.

6.Point C is at (5, 2). It is reflected in the x-axis. Work out the coordinates of the image of point C.

7.Two sides of a triangle are 20 cm and 8 cm long. Write down which one of these lengths is possible for the third side.

8.A rectangular photograph has an area of 96 cm². One of its sides is 8 cm long. Work out the length of the other side.

9.A circle has centre O. Radii OA and OB are drawn, together with the arc AB, enclosing a sector. The straight chord AB is also drawn. Write down the name of the region enclosed between the chord AB and the arc AB.

10.A rectangular photograph is 12 cm long and 5 cm wide. Work out the perimeter of the photograph.

11.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.

12.Triangle ABC is extended so that side BC is extended beyond C to a point D, forming exterior angle ACD. Angle BAC = 48° and angle ABC = 67°. Which single angle fact gives angle ACD = 115° in one step, without first working out the interior angle at C?

13.A straight line crosses two parallel lines. An angle of 65° is formed at one crossing. At the other crossing, the angle that lies between the two parallel lines on the opposite side of the crossing line is also 65°. Write down the angle fact that explains why these two angles are equal.

14.How many vertices does a cylinder have?

15.A line segment joins two points on the circumference of a circle, without necessarily passing through the centre. Write down the general term for this line segment.