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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 the sum of the areas of the square and the rectangle is A cm2, show that
If A =8 cm2, Solve the equation in (b) above for x, hence find the possible dimensions of the two pieces of wire. (6 marks)
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If the bucket above has a hole and 1.1 cm3 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 tower is on a bearing of 030o from a point P and a distance of 100m.From P, the angle of elevation of the top of the tower is 15o and the angle of depression of the foot of the tower is 1o. a). Calculate the height of the tower. (4 marks) b). A point Q is on the same horizontal plane as point P. The tower is on a bearing of 330ofrom Q and a distance of 70 m. Calculate: i) The distance from P to Q. (3 marks) ii) The bearing of P from Q. (3 marks)
The scale of a map is 1: 200.Calculate the actual area of a triangular coffee field whose sides are 6cm, 8cm and 10cm on the map. (3 marks)
State the inequalities that satisfy the region defined by R. (3marks)
State the inequalities that satisfy the region defined by R. (3marks)
ANSWER
The average rate of depreciation in value of a laptop is 10% per annum. After three complete years its valuewas ksh 35,000. Determine its value at the start of the three-year period.(3marks)
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)
The velocity V m/s of a particle in motion is given by V=3t2-2t+5.Calculate the distance travelled by the particle between t= 2 seconds and t = 6 seconds. (3 marks)
Without using a calculator, solve for x in the equation 〖0.5〗^x×〖0.125〗^(1-x)=3211/12/2022
Without using a calculator, solve for x in the equation
\[\LARGE 0.5^{X}\times 0.125^{1-X}=32\]
The mass of maize flour to the nearest 10 grams is 8. 67kg. Determine the percentage error in this measurement. (3marks)
A three-digit 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.
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