Geometry and measures worksheet — GCSE Foundation

1.Triangle XYZ has angle X = 90°. Angle Y = 34°. Work out angle Z.

2.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.

3.A sector of a circle has radius 5 cm and angle 72°. Work out the arc length of the sector, in terms of π.

4.A regular polygon has 5 lines of symmetry. What is the order of rotational symmetry of this polygon?

5.A square tile has sides of length 6 cm. Work out the area of the tile.

6.A tank holds 3.2 m³ of water. Work out this volume in litres.

7.A circle has centre O. Radii OA and OB are drawn, together with the arc AB, enclosing a sector. The straight chord AB is also drawn. Write down the name of the region enclosed between the chord AB and the arc AB.

8.Postcard P is similar to postcard Q. The 6 cm side of P corresponds to the 15 cm side of Q, and the 8 cm side of P corresponds to a matching side of Q. Work out the length of that matching side of Q.

9.A straight fence is 5 m long. Describe the shape of the region made up of every point on the ground within 2 m of any part of the fence.

10.What does the statement AB = CD mean, where A, B, C and D are all points?

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.Three of these are rational numbers and one is irrational. Write down the one that is irrational.

13.Point B is at (3, 5). It is reflected in the line y = 2. Work out the coordinates of the image of point B.

14.The point (2, 5) is translated 3 units right and 4 units down. Work out the coordinates of the image point.

15.A recipe uses 0.75 kg of sugar. Work out how many grams of sugar this is.