Geometry and measures worksheet — GCSE Foundation

1.A straight line passes through points A, B and C, with B between A and C. A fourth point D is not on the line. Angle ABD = 132°. Work out the size of angle DBC.

2.Every point on a circle is exactly the same distance from one particular point. Write down the name of that point.

3.A sector of a circle has radius 15 cm and angle 216°. Using π = 3.14, work out the arc length of the sector.

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

5.A translation moves the point (1, 1) to the point (9, 4). Write down the column vector of this translation.

6.Two angles lie on a straight line. One angle is 37°. Work out the size of the other angle.

7.A circle has diameter 10 cm. Using π = 3.14, work out the circumference of the circle.

8.A triangular sail for a small boat has a base of 2.4 m and a height of 1.75 m. Sailcloth costs £12.50 per m². Work out the total cost of the sailcloth needed for the sail.

9.A garden shed is shaped like a triangular prism: two identical vertical triangular end walls (the gable ends), joined by a sloping rectangular roof and a vertical rectangular back wall. Looking at the shed from directly above (the plan view), what shape is seen?

10.A right-angled triangle has its two shorter sides equal to 8 cm and 15 cm. Work out the value of cos θ, where θ is the angle opposite the 8 cm side. Give your answer as a fraction.

11.A designer creates a repeating tile pattern. Each tile is translated from the one before it by the column vector with top number 4.5 and bottom number −2.5 (in centimetres). The first tile has its bottom-left corner at (1.5, 3). Work out the coordinates of the bottom-left corner of the third tile.

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

13.A scale drawing of a rectangular lawn uses a scale of 1 : 125. On the drawing, the lawn measures 4 cm by 2.4 cm. Work out the perimeter of the real lawn, in metres.

14.A scale drawing of a park uses a scale of 1 : 2000. A path is drawn 8.5 cm long on the drawing. A cyclist rides the length of the path and then rides straight back again along the same path. How far does the cyclist travel in total, in metres?

15.To construct a perpendicular to a line at a given point P on the line, compasses are first opened to draw two arcs crossing the line, one on each side of P. What is the correct next step?