Geometry and measures worksheet — GCSE Foundation

1.A solid cylinder is lying on its curved side on a table, with its circular ends facing left and right. What shape is its plan view, looking down from above?

2.A church tower is due east of a village. What is the three-figure bearing of the church tower from the village?

3.A map has a scale of 1 : 20 000. The distance between two villages is 3.4 km in real life. How long is this distance on the map, in centimetres?

4.Which of the following is NOT one of the four basic conditions used to prove two triangles are congruent?

5.A circle has a radius of 1 cm. Work out the circumference of the circle. Give your answer in terms of π.

6.A roof has two triangular sections, P and Q. Section P has a sloping edge of 3.6 m and a base edge of 2.4 m, with an angle of 70° between them. Section Q has a sloping edge of 3.6 m and a base edge of 2.4 m, with an angle of 70° between them, arranged the same way round. A roofer wants to cut identical triangular felt panels for both sections without measuring Section Q separately. Which condition confirms that the two sections are congruent?

7.A sector of a circle has radius 9 cm and angle 120°. Using π = 3.14, work out the arc length of the sector, to 1 decimal place.

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

9.The point (4, −3) is reflected in the y-axis. Work out the coordinates of the image point.

10.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.

11.A ramp is built from two straight metal supports that rest on the flat ground and meet each other at the top, forming a triangle with the ground. One support meets the ground at 34°. The angle between the two supports where they meet is 71°. Work out the angle between the second support and the ground.

12.A solid ball has a radius of 7 cm. Work out the surface area of the ball. Use π = 3.14.

13.A sailmaker cuts two triangular sail panels from a pattern. Panel X has a 10 m side, with angles of 50° and 75° at its two ends. Panel Y also has a 10 m side, with angles of 50° and 75° at its two ends, in the same arrangement. The sailmaker wants to check the panels will match exactly, without cutting a third measurement. Which condition proves the two panels are congruent?

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.Write down the column vector that describes a translation of 5 units to the left and 3 units down.