Question 1: Calculate the bearing from point A to point B, given the coordinates A(2, 3) and B(5, 7).

Answer: 045

Question 2: Construct a bearing of 135° from the north line and draw it starting at the origin on the grid.

Answer: Student draws accurate bearing line at 135° from north

Question 3: What is the error in measuring a bearing if the actual bearing is 060°, but a student records it as 065°?

Answer: 5°

Question 4: A ship is sailing on a bearing of 220°. If the ship changes course to a bearing of 200°, what is the angle of deviation?

Answer: 20

Question 1: A cyclist starts at point A and travels on a bearing of 030° for 10 km, then changes course to a bearing of 150° for another 8 km. Using a scale drawing, determine the straight-line distance from the starting point A to the final position B. Explain the steps and possible sources of error in measuring the bearings.

Answer: Student explanation includes steps to plot each segment and calculate the resultant distance; errors may include inaccurate plotting or misreading bearings.

Question 2: A pilot measures a bearing of 355° when flying towards a lighthouse. The true bearing is 355°, but due to a miscalculation, the compass was off by 3°. What is the actual bearing, and how might this affect navigation?

Answer: 358°; such errors can lead to missed targets or deviations from intended path.

Question 3: Explain why measuring bearings with a protractor in the field can lead to inaccuracies. Propose methods to improve measurement accuracy.

Answer: Student explains potential errors like parallax and misalignment; suggests using a compass with a proper bearing scale, or digital tools for improved accuracy.

Question 4: Given two bearings from different points, how can you verify if the measurements are consistent? Describe the process and calculations involved.

Answer: By calculating the relative positions and checking if the angles and distances satisfy the geometric constraints; involves using trigonometry or vector methods.

Question 1: A hiker measures a bearing of 045° from the base camp to the summit of a hill 5 km away. Later, the hiker finds the bearing from the summit back to the base camp to be 225°. Is this consistent? Explain your reasoning and identify any possible measurement errors.

Answer: Yes, the bearings are consistent as they are 180° apart; errors could involve misreading the compass or plotting inaccuracies.

Question 2: A rescue team is navigating towards a stranded vessel. They measure a bearing of 120° from their current position. If their GPS indicates they are 12 km from the vessel, how should they plot their course, and what common measurement mistakes should they avoid?

Answer: Plot a line at 120° from current position; avoid parallax errors when reading the compass and ensure correct scale usage.

Question 1: Construct a triangle on the grid with sides measuring 6 km, 8 km, and 10 km. Two of the sides are aligned with bearings of 045° and 135°. Identify the possible positions of the third vertex, considering measurement errors and misconceptions.

Answer: Student constructs the triangle and discusses the potential variations due to errors in measuring the bearings or lengths.

Question 2: A navigator records multiple bearings from different observation points to a landmark. The measurements are inconsistent. Describe how to identify and correct systematic measurement errors in bearing readings.

Answer: By comparing measurements, identifying patterns of deviation, and recalibrating instruments; considering environmental factors that can affect readings.

Question 1: Plot a line of bearing 270° starting from point C at (4,4). What are common pitfalls students face when plotting bearings, and how can they be avoided?

Answer: Pitfalls include misreading angles, incorrect scale, or parallax; avoid by double-checking measurements and using precise instruments.

Question 2: Calculate the bearing from point D(1, 2) to point E(7, 8). Show your working.

Answer: Student calculates the angle with respect to north, resulting in approximately 045°.

Question 3: Identify the common mistake made when students interpret bearings as angles from the east instead of north and explain how to correct it.

Answer: Misinterpretation leads to incorrect angles; correct by consistently defining bearings as measured clockwise from north.