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G10 Mathematics 2025-01

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While out swimming one day you spot a coin at the bottom of the pool. The pool is ten metres deep, and the angle between the top of the water and the coin is . How far away is the coin from you along the bottom of the pool?

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Determine the midpoint of line  with points  and .

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The figure below shows quadrilateral with and .

Match the steps and reasons below to prove that is a parallelogram.

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From a boat at sea (), the angle of elevation of the top of a lighthouse , on a cliff  is 27°. The lighthouse is 10m high and the cliff top is 75m above sea level. How far is the boat from the base of the cliff to the nearest metre? (  answer  without units. )

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A ship's navigator observes a lighthouse on a cliff. According to the navigational charts the top of the lighthouse is 35 metres above sea level. She measures the angle of elevation of the top of the lighthouse to be .

Ships have been advised to stay at least 4 km away from the shore. Is the ship safe?

True it is safe.

False it is not safe

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You are standing on top of a building, looking at a park in the distance. The angle of depression is 53°. If the building you are standing on is 100 m tall, how far away is the park? Ignore your own height

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The escalator at the mall slopes at an angle of 30° and is 20 m long.

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Through what height would a person be lifted by travelling on the escalator? (Round your answer to two decimal places, without units. Use "," and NOT "." as a decimal point)

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  below is a kite.

Image of a kite ABCD with two bisecting lines BD and AC intersecting at point E. CD = BD and AB = DA

Which of the following statements is definitely true about the diagonals of ?

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Study the quadrilateral with opposite angles  and angles  carefully. 

Match the steps and reasons below to prove that   is a parallelogram.

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and  are points in the Cartesian plane.  is the mid-point of Find the values of and 

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