Geometry and measures worksheet — GCSE Foundation

1.The angle between north and a cycle path is 40°, but it is measured anticlockwise from north. What is the three-figure bearing of the cycle path?

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

3.A carpenter measures two triangular braces. Brace 1 has a 55° angle, a 65° angle, and, opposite the 55° angle, a side of 8 cm. Brace 2 has matching 55° and 65° angles and, opposite its 55° angle, a side of 8 cm. The carpenter says that because the equal 8 cm side is not between the two equal angles in either brace, he cannot be sure the two braces are the same size. Is the carpenter correct?

4.The cross-section of a tent is an isosceles triangle. The angle at the top, between the two equal sloping sides, is 62°. The other two angles are equal to each other. Work out the size of each of those two angles.

5.Which of the following is the correct definition of a regular polygon?

6.A triangle has a base of 8 cm and a perpendicular height of 5 cm. Work out its area.

7.A rectangular name card has a perimeter of 30 cm. The card is 9 cm long. Work out the width of the card.

8.The perimeter of a square is 20 cm. Work out the area of the square.

9.A cylinder has a radius of 5 cm. Its volume is 471 cm³. Using π = 3.14, work out the height of the cylinder.

10.Point D is at (3, 4). It is rotated 90° clockwise about the origin (0, 0). Work out the coordinates of the image of point D.

11.A solid has 5 faces, 9 edges and 6 vertices. Two of its faces are triangles and the other three are rectangles. Which solid is it?

12.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.

13.A trapezium-shaped garden bed has parallel sides of 2.5 m and 4.5 m, and a perpendicular width of 3 m. A gardener wants to know the area of the bed before ordering topsoil. Work out the area of the garden bed.

14.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).

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