Geometry and measures worksheet — GCSE Foundation

1.A cylindrical tin has a curved surface, a flat circular base and a flat circular lid. A label is stuck around the curved surface only. How many of the tin's faces are NOT covered by the label?

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

3.Three angles meet at a single point on one side of a straight line. Two of the angles are 48° and 65°. Work out the third angle.

4.A birthday cake is a cylinder of radius 10 cm and height 8 cm, with a thin ribbon fixed exactly once around the curved side, at half the height, and joined with no overlap. Work out the length of ribbon needed. Use π = 3.14.

5.A tile manufacturer cuts a hexagonal tile so that all six sides measure exactly 4 cm, but a check shows only two pairs of the six interior angles are equal to each other, not all six angles. The customer's order specifies regular hexagonal tiles. Based on the check, is this tile a regular hexagon?

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

7.A water tank is a cube with edges of length 2 m. Work out how many cubic centimetres the tank holds when it is full.

8.Quadrilateral WXYZ has WX parallel to ZY, and WZ = XY (the two non-parallel sides are equal in length). Give a reason why angle W = angle X.

9.A sector of a circle has radius 12 cm and angle 45°. Using π = 3.14, work out the area of the sector.

10.Two similar flags have widths in the ratio 2 : 5. The width of the smaller flag is 8 cm. Work out the width of the larger flag.

11.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.

12.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Work out angle F.

13.A tangent touches a circle with centre O at the point P. Q is a point on the tangent. Write down the circle fact that tells you the size of angle OPQ.

14.m is the column vector with top number 3 and bottom number −4. Which of these column vectors is a scalar multiple of m?

15.A construction for the perpendicular bisector of AB begins by opening a pair of compasses to more than half the length of AB, then drawing an arc centred at A. What is the next step?