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)
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)
State the inequalities that satisfy the region defined by R. (3marks)Without using a calculator, solve for x in the equation ã€–0.5ã€—^xÃ—ã€–0.125ã€—^(1x)=3211/12/2022
Without using a calculator, solve for x in the equation
\[\LARGE 0.5^{X}\times 0.125^{1X}=32\]
In the figure below, EAF and EDG are tangents to the circle. AB is parallel to DC, angle FAB = 46° and angle AED = 110°.Find the values of angles P and q. (3mks)Worked Answer:
A bus left Nairobi at 7.00 am and traveled towards Eldoret at an average speed of 80Km/hr.22/11/2021 Paper 1, Section B A bus left Nairobi at 7.00 am and traveled towards Eldoret at an average speed of 80Km/hr. At 7.45 a.m a car left Eldoret towards Nairobi at an average speed of 120Km/hr. The distance between Nairobi and Eldoret is 300 km. Calculate:(a) The time the bus arrived at Eldoret. (2mks)(b) The time of the day the two met. (4mks)
(c) The distance of the bus from Eldoret when the car arrived in Nairobi. (2mks)(d) The distance from Nairobi when the two met. (2mks)
A straight line L1 has a gradient ˉ½ and passes through point P (1, 3). Another line L2 passes through the points Q (1, 3) and R (4, 5). Find.(a) The equation of L1. (2mks)(b) The gradient of L2. (1mk)
(c) The equation of L2. (2mks)(d) The equation of a line passing through a point S (0, 5) and is perpendicular to L2. (3mks)(e) The equation of a line through R parallel to L1. (2mks)
A line passes through the point (1, 2) and has gradient ½. Write down its equation in the form ax + by = c (3mks)A chord PQ of length 15cm subtends an angle of 65º at the circumference centre O. Find the radius of the circle. (3mks)Worked Solution
The figure below is a velocity time graph for a car.(a) Find the total distance traveled by the car.(b) Calculate the deceleration of the car.
The table below shows the number of goals scored in 40 soccer matches during a certain season.19/11/2021 The table below shows the number of goals scored in 40 soccer matches during a certain season.Calculate the mean number of goals scored per match. (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: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: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) 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:

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