Form 1 MathematicsA boat at point x is 200 m to the south of point Y. The boat sails X to another point Z. Point Z is 200m on a bearing of 310^{0} from X, Y and Z are on the same horizontal plane. (a) Calculate the bearing and the distance of Z from Y ( 3 marks) (b) W is the point on the path of the boat nearest to Y. Calculate the distance WY ( 2 marks) (c) A vertical tower stands at point Y. The angle of point X from the top of the tower is 6^{0} calculate the angle of elevation of the top of the tower from W (3 marks) Form 1 Mathematics
(a) Using a ruler and a pair of compasses only, construct a quadrilateral PQRS in which PQ = 5 cm, PS = 3 cm, QR = 4 cm, PQR = 135° and SPQ is a right angle.
(b) The quadrilateral PQRS represents a plot of land drawn to a scale of l:4000. Determine the actual length of RS in metres. Form 2 MathematicsA boat which travels at 5 km/h in still water is set to cross a river which flows from the north at 6km/h. The boat is set on a course of x^{0} with the north. (a) Given that cos x^{0} = ^{3}/_{5} , calculate (i) The resultant speed of the boat ( 2 marks) (ii) The angle which the track makes with the north ( 2 marks) (b) If the boat is to sail on a bearing of 135^{0}, calculate the bearing of possible course on which it can be set ( 4 marks) Form 1 MathematicsFor electricity posts, A,B,C, and D stand on a level ground such that B is 21 m on a bearing of 060^{0} from A, C, is 15 m to the south of B and D is 12 m on a bearing of 140^{0} from A.
Answer
Form 1 MathematicsForm 1 MathematicsForm 1 Mathematics
The figure below represents a piece of land in the shape of a quadrilateral in which AB =240M, BC = 70m CD = 200m ˂BCD = 150^{0} ˂ABC = 90^{0}
Calculate
(a) The size of ˂BAC correct to 2decimal places (b) The length AD correct to one decimal place (c) The area of the piece of land, in hectares, correct to 2 decimal places Form 2 MathematicsThree points O, A and B are on the same horizontal ground. Point A is 80 metres to the north of O. Point B is located 70 metres on a bearing of 060^{0} from A. A vertical mast stands at point B. The angle of elevation of the top of the mast from o is 20^{0}. Calculate: a) The distance of B from O. (2mks) b) The height of the mast in metres (2mks) Form 1 Mathematics
Four points B,C,Q and D lie on the same plane. Point B is 42km due South – West of point Q. Point C is 50km on a bearing of S 60^{0} E from Q.
Point D is equidistant B, Q and C.
Form 1 MathematicsForm 2 Mathematics
In the diagram below PA represents an electricity post of height 9.6 m. BB and RC represents two storey buildings of heights 15.4 m and 33.4 m respectively.
The angle of depression of A from B is 5.5^{0} While the angle of elevation of C from B is 30.5^{0} and BC = 35m.
(a) Calculate, to the nearest metre, the distance AB
(b) By scale drawing find, (i) The distance AC in metres (ii) Angle BCA and hence determine the angle of depression of A from C Form 1 Mathematics
The figure below is drawn to scale. It represents a field in the shape of an equilateral triangle of side 80m
The owner wants to plant some flowers in the field. The flowers must be at most, 60m from A and nearer to B than to C. If no flower is to be more than 40m from BC, show by shading, the exact region where the flowers may be planted
Form 1 MathematicsA helicopter is stationed at an airport H on a bearing 060^{o} and 800km from another airport P.A third airport is J is on bearing of 140^{0} and 1,200km from H. Determine:
Form 1 MathematicsA rally car traveled from point R to point S. S is 128 km on a bearing 060^{0} from R. The car then set off S at 9.30 am towards T at an average of 150 km/h. It was expected at T at 11.30 am. After traveling for I hour and 20 minutes it broke down at point P. The bearing of T and P from S is 300^{0}.
Calculate the:
Form 1 Mathematics  Topical Questions and AnswersShopping centers X, Y and Z are such that Y is 12 km south of X and Z is 15 km from X.Z is on a bearing of 330^{0} from Y. 
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AuthorMaurice A Nyamoti is a Mathematics/ Computer Teacher and has passion to assist students improve grades RSS_FEED
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