Geometry and measures worksheet — GCSE Higher

1.The bearing of a campsite B from a walker's position A is 070°. What is the bearing of A from B?

2.A right-angled triangle has a hypotenuse of 29 cm and one shorter side of 20 cm. Work out the length of the other shorter side.

3.A trundle wheel has a diameter of 0.5 m. It is rolled along the ground and makes 20 complete turns. Using π = 3.14, work out the total distance rolled, in metres.

4.A ship's radar shows a lighthouse at the point (12, −4) on a grid measured in nautical miles. The ship is at (2, 5). The ship sails along the vector that takes it directly to the lighthouse, then sails along that same vector again. Work out the ship's final position.

5.Triangle PQR and triangle XYZ have angle P = angle X, angle Q = angle Y and angle R = angle Z, with no side lengths given for either triangle. Which of the following correctly describes the relationship between the two triangles?

6.An isosceles triangle ABC has AB equal to AC. AM is a line from vertex A, perpendicular to BC, meeting BC at point M. Which condition proves that triangle ABM is congruent to triangle ACM?

7.Two straight paths cross at a junction in a park. One of the angles between them, measured with a protractor, is 76°. What is the size of the angle immediately next to it on a straight line?

8.Work out the distance between the point (0, 0) and the point (5, 12).

9.P is the point (3, 4) and Q is the point (6, 0). Work out the distance of each point from the origin, and write down which point is closer to the origin.

10.Two similar triangular flower beds have lengths in the ratio 3 : 7. The area of the smaller bed is 45 m². Work out the area of the larger bed.

11.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.

12.A regular polygon has an interior angle of 156°. Work out the number of sides of the polygon.

13.Postcard P is similar to postcard Q. The 6 cm side of P corresponds to the 15 cm side of Q, and the 8 cm side of P corresponds to a matching side of Q. Work out the length of that matching side of Q.

14.A hiker walks on a bearing of 065°. She then turns clockwise through 90° and continues walking in a straight line. What bearing is she now walking on?

15.A hexagonal prism has 8 faces and 12 vertices. Using F + V − E = 2, work out how many edges it has.