Geometry and measures worksheet — GCSE Foundation

1.Write down the column vector that describes a translation of 4 units to the right and 4 units up.

2.A sprinkler waters a sector-shaped patch of a garden with radius 8 m and angle 90°. Work out the perimeter of the watered sector, to 1 decimal place. (Use π = 3.14.)

3.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.

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

5.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.

6.A triangular prism has a cross-section that is a triangle with a base of 3.5 cm and a perpendicular height of 4 cm. The prism is 10 cm long. Work out the volume of the prism.

7.Triangles PQS and RQS share the common side QS. PQ equals RQ, and PS equals RS. Which condition proves that triangle PQS is congruent to triangle RQS?

8.p is the column vector with top number 2 and bottom number 3. q is the column vector with top number −1 and bottom number 4. Work out 2p + q, giving your answer as a column vector in the form (top, bottom).

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

10.A solid is built from five centimetre cubes, standing side by side on a table in a single straight row. Looking down from directly above (the plan view), how many squares are visible?

11.A survey team measures the angle between two fences with a protractor and gets a reading of 254°. What type of angle is this?

12.A sector of a circle has angle 120° and an arc length of 31.4 cm. Using π = 3.14, work out the radius of the circle.

13.Two straight lines cross at a point. To find the points that are the same distance from both lines, which construction should be used?

14.Write down the term for the distance all the way around the edge of a circle.

15.A garden designer describes a flower bed as a shape with four straight sides: exactly one pair of sides is parallel, those two parallel sides are different lengths, and the other two sides are equal in length to each other but not parallel to each other. Which shape should the designer draw?