Geometry and measures worksheet — GCSE Foundation

1.A roof truss is shaped like an isosceles triangle resting on a horizontal ceiling joist. The truss's sloping edges are equal in length, and the angle at its apex is 40°. The ceiling joist continues in a straight line beyond the foot of the truss. Work out the angle between the truss's sloping edge and the extended joist, on the outside of the truss.

2.Four angles meet at a point. Three of them measure 82°, 105° and 96°. Work out the size of the fourth angle.

3.A hiker walks on a bearing of 065°. She then turns clockwise through 90° and continues walking in a straight line. What bearing is she now walking on?

4.A triangle has vertices A(0, 0), B(10, 0) and C(5, 12). Work out the area of the triangle.

5.A bottle holds 2 litres of water. A glass holds 250 ml. Work out how many of these glasses can be filled from one full bottle.

6.The sum of the interior angles of a polygon is 1980°. Work out the number of sides of the polygon.

7.A line segment joins A(1, 1) and B(4, 7). Write down the sign of the gradient of this line.

8.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.

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

10.How many vertices does a cylinder have?

11.Which of the following is NOT one of the four basic conditions used to prove two triangles are congruent?

12.A circular clock face has a diameter of 18 cm. Work out the circumference of the clock face. Use π = 3.14.

13.A designer enlarges a drawing of a model car for a poster. She first enlarges the drawing by a scale factor of 1.5, and then enlarges that result by a further scale factor of 2. On the original drawing, the position of a wheel relative to the front bumper is given by the column vector with top number 4 and bottom number −3, in centimetres. What is the corresponding column vector on the poster, in centimetres?

14.Triangle T has a vertex at (8, 4). It is enlarged by a scale factor of 1/2, centre (2, 4). Work out the coordinates of the image of this vertex.

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