Geometry and measures worksheet — GCSE Higher

1.A ferris wheel's circular frame has centre O. A support strut runs from O to a point A on the rim, and a second strut runs from O to point B on the rim, with angle AOB = 76°. A cabin is mounted at point C on the major arc AB, and D is a separate point on the minor arc AB. Work out the difference between angle ACB and angle ADB.

2.A surveyor is marking out field ABCD for a new crop. The plan states that side AB is parallel to side DC, but AB and DC are not equal in length, and sides BC and AD are not parallel to each other. Which term correctly describes the shape of field ABCD?

3.A triangle has vertices X, Y and Z, with a right angle at Y. Side XY is twice as long as side YZ. Which of the following correctly describes this triangle?

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

5.Two sides of a triangle are 20 cm and 8 cm long. Write down which one of these lengths is possible for the third side.

6.A hexagon has interior angles of 130°, 142°, 125°, 150°, 135° and x°. Work out the value of x.

7.In triangle OAB, OA = a and OB = b. M is the midpoint of OA, and N is the midpoint of OB. Express the vector MN in terms of a and b.

8.Which of these statements about solving a triangle is correct?

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.The midpoint of the line segment AB is (3, 5). A is the point (1, 3). Work out the coordinates of B.

11.In parallelogram PQRS, angle P = 65°. Which reason correctly explains why angle R = 65°?

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

13.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.

14.A solid pyramid has a square base of side 6 cm. Its apex is directly above the centre of the base, at a vertical height of 8 cm. Work out the volume of the pyramid.

15.A trapezium-shaped allotment plot has two parallel sides that face each other, and two sloping sides that are equal in length (an isosceles trapezium). One of the angles next to the shorter parallel side is 118°. Work out the angle next to the other end of the same shorter parallel side.