THE FIGURE BELOW SHOWS A RECTANGULAR BASED RIGHT PYRAMID, USE IT TO ANSWERS QUESTIONS THAT FOLLOW:2/1/2023 QUESTIONS
Two inlet taps P and Q opened at the same time can fill a tank in 2 1/2 h. The two taps were opened together at the same time and after 1 hour 10 minutes tap Q was closed and P continued alone and filled the tank after a further 4 hours. Find:
a) The fraction of the tank filled by both taps for 1 hour. (1 marks)
b) The fraction of the tank filled by tap P after Q was closed. (2 marks) c) The time which each tap working alone would have taken to fill the tank. (7 marks) ANSWERS
A piece of wire, 18 cm long is cut into two parts. The first part is bent to form the four sides of a rectangle having length x cm and breath 1 cm.
a). State two expressions in terms of x only for the perimeter of the square and the rectangle. (2 marks)
If A =8 cm^{2}, Solve the equation in (b) above for x, hence find the possible dimensions of the two pieces of wire. (6 marks)
If the bucket above has a hole and 1.1 cm^{3} of water leaks out every 5 seconds and collects in a cylindrical can of base radius and height 10 cm and 25 cm respectively. Calculate how long it takes to fill the cylindrical can. (4 marks)
A cylinder of radius 15 cm and height 24 cm is filled with water. A solid hemisphere of radius 7cm is submerged into the cylinder and removed. Find the change in height of water level in the cylinder. (4 marks)
A wall clock that gains 20 seconds after every hour was set to read the correct time on Tuesday at 03 25. Determine the time the wall clock will read on Thursday 03 25 h. (3 marks)
A dealer sells a mobile phone at a profit of 25%. The customer sells it to a friend at ksh 60,000, making a profit of 20 %. Find the cost prize of the mobile phone. (3 marks)
A threedigit number is such that twice the hundreds digit is more than the tens digit by 2.the unit digit is thrice the hundred digit. When the digits are reversed, the number is increased by 594.Find the number.
RATES, RATIO, PROPORTION AND PERCENTAGE  RATES  FORM 1 LEVEL  PAPER 2 QUESTIONS  SECTION AA dam containing 4158mcubed of water is to be drained. A pump is connected to a pipe of radius 3.5cm and the machine operates for 8 hours per day. Water flows through the pipe at the rate of 1.5m per second. Find the number of days it takes to drain the dam. (3mks)
RATES, RATIO, PROPORTION AND PERCENTAGE  RATES  FORM 3  PAPER 2 QUESTIONS  SECTION AAtieno is now four times as old as her daughter and six times as old as her son. Twelve years from now, the sum of the ages of her daughter and son will differ from her age by 9 years. What is Atieno’s present age? (3mks)
Two grades of coffee one costing sh.42 per kilogram and the other costing sh.47 per kilogram are to be mixed in order to produce a blend worth sh.46 per kilogram in what proportion should they be mixed. (3mks)Worked Answer:A map has a scale of 1 : 2500 and on it is square plot of land which has an area of 4cm². Calculate the actual area in hectares of the land. (3mks)Worked Answer:(a) A small field was surveyed and the measurements recorded in a surveyor’s field book as in the table below. (i) Using a scale of 1cm to 10m make an accurate drawing of the map of the field. (4mks)(ii) Find the area of the field. (3mks)(iii) Assuming that the baseline in (a) runs in a northern direction give the position of D relative to A using bearing and distance. (3mks)
Four points B, C, Q and D lie on the same plane. Point B is 42km due southwest point Q. Point C is 50 km on a bearing of S60^{o}E from Q. Point D is equidistant from B, Q and C.(a) Using the scale: 1cm represents 10km, construct a diagram showing the positions of B, C, Q and D. (5mks)(b) Determine the

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