A particle P moves in a straight line such that t seconds after passing a fixed point Q, its velocity is given by the equation
a) The values of t when p is instantaneously at rest (2mks)b) An expression for the distance moved by P after t seconds (2mks)c) The total distance traveled by P in the first 3 seconds after passing point O. (3mks)d) The distance of P from O when acceleration is zero
a) An arithmetic progression is such that the first term is 5, the last is 135 and the sum of progression is 975.
i) The number of terms in the series (7mks)ii) The common difference of the progression (2mks)b) The sum of the first three terms of a geometric progression is 27 and the first term is 36. determine the common ratio and the value of the fourth term (4mks)
Worked Solution:
A tailor bought a number of suits at a cost of sh. 57,600 from Ken – suit wholesalers. Had he bought the same number of suits from Umoja wholesalers, it would have cost him sh. 480 less per suit. This would have enabled him to buy 4 extra suits for the same amount of money.a) Find the number of suits the tailor bought (4mks)b) The tailor later sold each suit for sh 720 more than he had paid for it. Determine the percentage profit he made?
Worked Solution:John bought 3 brands of tea A, B and C. The cost of the three brands was sh. 25, sh. 30 and sh. 45 per kilogram respectively. He mixed the three brands in the ratio 5 : 2 : 1 respectively. After selling the mixture he made a profit of 20%.a) How much profit did he make per kilogram of the mixture? (4mks)b) After one year the cost price of each brand was increased by 12%.i) For how much did he sell one kilogram of the mixture to make 20% profit%, give your answer to the nearest 5cts (3mks)ii) What would have been his percentage profit if he sold one kilogram of the mixture at sh. 40.25? (3mks)
Worked Solution:In the figure below AB and AC are tangents to the circle center O at B and C respectively, the angle AOC = 60^{0}Calculate;a) The length of AC (2mks)b) The area of triangle OAC (2mks)c) The area of minor sector COD (2mks)d) The area of the shaded region (4mks)
Worked Solution:a) Construct triangle ABC such that AB = 8cm, BC = 6cm and angle ABC = 300 (3mks)b) Measure the length of AC (1mk)c) Draw a circle that touches the vertices A, B and C (2mks)d) Measure the radius of the circle (1mk)c) Hence or otherwise, calculate the area of the circle outside triangle (3mks)
Worked Solution:Draw the graph ofb) Using a suitable line solve2x^{2} – 3x – 50 = 0 (5mks)
Worked solution:A bucket is in the shape of a frustrum with base radius 12cm and top radius 16cm. the slant height of the bucket is 30cm as shown below. The bucket is full of water.a) Calculate the volume of the water. (Take = 3.142) (6mks)b) All the water is poured into a cylindrical container of circular radius 12cm. If the cylinder has height 45cm, calculate the surface area of the cylinder which is not in contact with water (4mks)
Worked Solution:From a point 20m away on a level ground the angle of elevation to the lower window line is 27^{0} and the angle of elevation to the top of the window is 32^{0}. calculate the height of the window (3mks)Worked Answer:The sides of a parallelogram are 4cm by 5cm and its area is 12cm square. calculate its angles.24/10/2021 The sides of a parallelogram are 4cm by 5cm and its area is 12cm^{2}. calculate its angles (3mks)Worked Answer:A Kenyan tourist left Germany for Kenya through Switzerland. While in Switzerland he bought a watch worth 52 Deutsche marks.Find the value of the watch in:a) Swiss Francsb) Kenya shillings (3mks) Use the exchange rates below1 Swiss Franc = 1.28 Deutsche marks1 Swiss Franc = 45.21 Kenya shillings Worked Answer:
The figure above is a triangular prism of uniform cross – section in which AF = 4cm, AB = 5cm and BC = 8cm.a) If a triangle BAF = 30^{0}, calculate the surface area of the prism (3mks)b) Draw a clearly labelled net of the prisms (1mk)Worked Answer:A man imported a vehicle at sh 600,000 and sold it at sh. 1, 080,000. find his percentage profit if he spent sh 60,000 for clearing the vehicle from the port and a further sh. 40,000 for shipping. (3mks)Worked Example:
The exterior angle of regular polygon is an eighth of the interior angle. How many sides does the regular polygon have? (3mks)Worked Answer:
During a certain ceremony goats and chicken were slaughtered. The number of heads (for both chicken and goats) was 45. The total number of legs was 100. Determine the exact number of goats and chicken slaughtered. (3mks) Worked Answer:
a) Find the total distance traveled by the car (2mks)b) Calculate the deceleration of the car (2mks)Worked Answers:
Two similar cans have different heights 8cm and other one 10cm. If the surface area of the larger can is 480cm^{3}, find the surface area of the smaller can (3mks)Worked Answer:
The position vectors of A and B arerespectively. Find the coordinates of M which divides AB in the ration 1: 2 (3mks)Worked Answer:The gradient of a line L through points A(2x, 4) and B(1, x) is 1/7. find the equation of a line perpendicular to L through B (3mks)
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