Geometry and measures worksheet — GCSE Foundation

1.Which of these describes an obtuse angle?

2.A vertical flagpole casts a shadow 6 m long at the same time as a 1.2 m vertical post casts a shadow 1.8 m long. The flagpole and the post are both vertical, and the triangles formed by each object, its shadow, and the sun's ray are similar. Work out the height of the flagpole.

3.The diagram shows a solid made from two cuboids joined together. Which shape is the front elevation of this solid?

4.A bead starts at position (2, −1) on a grid, in centimetres. It is moved by the column vector u, with top number 3 and bottom number 5, and then moved by the column vector v, with top number −7 and bottom number 2. Work out the coordinates of the bead's final position.

5.Work out the exact value of sin 45° × cos 45°.

6.The point A(3, 2) is translated by the vector (−5, 4) to give point B. Work out the coordinates of B.

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

9.All four sides of a rhombus are the same length. One side of a rhombus is 7 cm long. Work out the perimeter of the rhombus.

10.Write down which quadrant contains the point (−3, 5) when plotted on a coordinate grid.

11.A tent's sloping side makes an angle of 45° with the ground. The sloping side is 3√2 m long. Using the exact value of sin 45°, work out the exact height of the tent.

12.Two points on a circle divide its circumference into two arcs of different lengths. Write down the name given to the shorter of the two arcs.

13.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.

14.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller angle.

15.Here are four trigonometric ratios of special angles. Write down the one that does not have a value.