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) ANSWERSThe coordinates of two points A and B are (2, 3) and (4, 5) and R is the midpoint of AB.2/1/2023 questions
The coordinates of two points A and B are (2, 3) and (4, 5) and R is the midpoint of AB.
a) Determine the coordinates of R. (2 marks)
b) Find the equation of a straight line joining A and B, expressing it in the form y=mx+c where m and c are constants. (3 marks) c) The straight line L_(1 ) which is a perpendicular bisector of AB meets the Xaxis at T. Find the coordinates of T. (3 marks) d) If the straight line L_(1 )is parallel to a line that passes through the point (1, 6) and (a, 8), find a. (2 marks) answersQUESTIONS
A Business man is paid a commission of 5% on sales of goods worth over ksh 100,000. He is paid a monthly salary of ksh 15,000 but 2% of his total earning is remitted as tax. In a certain month he sold goods worthy khs 500,000.
a) Calculate his monthly net earnings that month. (5marks)
b) The following month, his monthly salary increased by 20%. His commission was increased to 10% but on goods worth over ksh 200,000. If his total earnings that month was ksh 64,800, Calculate the money received from the sale of goods. (5marks) aNSWERS
a) Complete the table of values for the equation y=x^{2}+3x6, given that 6≤x≤4.
b) Using a scale of 1cm to represent 2 units in both axes, draw the graph of y=x^{2}+3x6 . (3 marks)
c) Using the graph drawn above Solve the equation
i) x^{2}+3x6=0 (2 marks) (ii) x^{2}+3x2=0 (3 marks) Answers
The distance between two towns P and Q is 300 km. A bus started at P at 10.30 am and travelled towards town Q at 80 km/h. After 45 minutes a car started at Q and travelled to town P at x km/h. The car met the bus after 1hour 20 minutes.
a) Determine the value of x. (3 marks) b) Find the distance from P where the car met the bus. (2 marks) c) At what time did the car meet the bus? (2 marks) d) If t a shuttle started at P, 1hour after the car left Q for P. Calculate the speed to the nearest km/h at which the shuttle should be driven in order to arrive at Q at the same time with the bus. (3 marks)
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 tower is on a bearing of 030^{o} from a point P and a distance of 100m.From P, the angle of elevation of the top of the tower is 15^{o} and the angle of depression of the foot of the tower is 1^{o}. 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 330^{o}from 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)
(a) A figure whose coordinates are A(2, 2), B(4, 1), C(4, 3) and D(2, 3) undergoes successive transformation ERS; where E, R and S are transformations represented by the matrices,On the grid provided, show the figure ABCD and its final image under the successive transformations ERS. (6mks)
(b) Find the matrix representing the single transformation mapping the image found in (a) above

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