Geometry and measures worksheet — GCSE Foundation

1.Work out the gradient of the line segment joining A(2, 3) and B(6, 11).

2.A polygon has 12 straight sides. What is the mathematical name for this polygon?

3.A radar station is at the origin of a grid, where each unit represents 1 km. A boat is detected at the point (7, 24). Work out the boat's distance from the station, then work out how many hours it will take the boat to reach the station travelling directly towards it at 5 km per hour.

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

5.A is the point (1, 3) and B is the point (7, 3). Work out the coordinates of the midpoint of AB.

6.A sign-maker is told a metal bracket outline must have two pairs of adjacent sides equal in length (not opposite pairs), exactly one pair of opposite angles equal, and exactly one line of symmetry. Which quadrilateral matches this description?

7.An isosceles trapezium has exactly one pair of parallel sides, and its two non-parallel sides are equal in length. How many lines of symmetry does it have?

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.Triangle ABC and triangle DEF both contain a right angle, at B and E respectively, and the hypotenuses AC and DF are equal in length. Which extra fact would prove the triangles are congruent by RHS?

10.Triangle PQR has angle P = 90°. The side PQ = 9 cm and the hypotenuse QR = 15 cm. Work out the length of PR.

11.To construct the perpendicular from a point P to a line l, where P is a point above l, an arc centred at P is drawn to cross l at two points, X and Y. What is the correct next step?

12.A solid has 4 triangular faces, 4 vertices and 6 edges. What is the name of this solid?

13.The bearing of a harbour B from a ferry's position A is 260°. What is the bearing of A from B?

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

15.A right-angled triangle has a hypotenuse of 8 cm, and one of its shorter sides is 4 cm. Work out the size of the angle between that 4 cm side and the hypotenuse.