Geometry and measures worksheet — GCSE Foundation

1.Put sin 30°, tan 30° and cos 30° in order of size, starting with the smallest.

2.A cake recipe takes 135 minutes from start to finish. Write this time as hours and minutes.

3.A roof truss has two horizontal parallel rafters, one above the other. A straight strut crosses both rafters. Where the strut crosses the lower rafter, the angle above the rafter and to the left of the strut is 65°. Work out the size of the angle above the upper rafter and to the right of the strut, where the strut crosses it.

4.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.

5.A rectangular tile measures 4.5 cm by 6 cm. Work out the area of the tile.

6.Write down which one of these statements about quadrilaterals is true.

7.A rectangle has vertices A(1, 1), B(4, 1), C(4, 5) and D(1, 5). Work out the perimeter of the rectangle.

8.A cylinder has a radius of 5 cm. Its volume is 471 cm³. Using π = 3.14, work out the height of the cylinder.

9.Write down the exact value of tan 0°.

10.Two similar shapes have lengths in the ratio 1 : 3. A side of the smaller shape is 4 cm long. Work out the length of the corresponding side of the larger shape.

11.A hiker starts by walking on a bearing of 245°. She turns clockwise through 50°, then turns clockwise through a further 15°, and continues walking in a straight line. What bearing is she now walking on?

12.Write down the name given to a quadrilateral that has exactly one pair of parallel sides.

14.Two angles lie on a straight line. One angle is 37°. Work out the size of the other angle.

15.A ship's radar can detect other ships up to 20 km away, over a sector-shaped area with angle 90°. A monitoring company charges £0.50 per square kilometre covered by one radar sweep. Using π = 3.14, work out the total charge for one sweep.