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KCSE Mathematics Paper 1 Revision Exercise Set 5

KCSE Mathematics Paper 1 Revision Exercise Set 5

Lessons (17)

• 1.    A trader sold an article at 15% discount to a customer who paid sh 510 for it. What was the marked price of the article.
  2m 9s

• 2.    Simplify #((3x+y)^2-(y-3x)^2)/((x+y)^2-(y-x)^2)#
  6m 9s

• 3.    The figure below shows a rectangle PQRS in which all the dimensions are given in centimeters. Find the value of x and hence calculate the area of the rectangle.
  2m 39s

• 4.    Solve for x in the equation #2^(3x - 2) times 8^(x) = 4^(x + 1)#
  2m 15s

• 5.    a) Given that the position vectors of points P, Q and R are p, q and r respectively and that R is the midpoint of PQ, write down a vector equation that relates p, q and r. b) If p =# ((5),(-8))#and q =# ((7),(4))# , find r and hence state the coordinates of point R.
  6m 19s

• 6.    A lorry which consumes 1 litre of diesel for every 9 km uses 108 litres of diesel for a journey. Find how many litres of diesel a trailer which consumes 1 litre of diesel for every 6 km uses for the same journey.
  1m 47s

• 7.    The distance between towns T and S is 418 km. At 9.45 a.m a truck left town T and travelled towards town S. At the same time a car left town S and travelled towards town T along the same road. Given that the car travels 30 km/h faster than the truck and that the two vehicles meet at 1.33 p.m, find the speed of each vehicle
  5m 29s

• 8.    A coil which is made by winding 500 metres of copper wire of cross-sectional diameter 1.26 mm has the same mass as another coil of copper wire whose cross-sectional diameter is 1.4 mm. Find the length of wire in the second coil.
  7m 25s

• 9.    The sum of the interior angles of an n-sided polygon is 1 440°. Find the value of n and hence deduce the name of the polygon.
  1m 59s

• 10.    The wheel of a bicycle has a diameter of 70 cm and makes 2 revolutions per second. Calculate to one decimal place the speed of the bicycle in km/h.
  5m 22s

• 11.    The straight line whose double intercept equation is #x/a + y/b# = 1 Passes through the points P(-4 ,9) and Q(4, -3). Write down the equation of the line in the form y = mx +c and hence determine the value of a and b.
  6m 55s

• 12.    From the quadratic equation whose root are x = #-5/3# and x = 1
  2m 29s

• 13.    Solve the inequality 4 - #3/2x = 5/3x - 2 3/1#
  4m 9s

• 14.    Two pipes P and Q each running alone can fill a trough in 6 hours and 10 hours respectively. A drainage pipe R can empty the full trough in 15 hours. Pipes P and Q are turned on and left running for 121 hours. The drainage pipe R is then opened and all three-left running. Find how much longer it takes to fill the trough.
  5m 34s

• 15.    The figure shows a water tank which consists of a hemispherical part surmounted on top of a cylindrical part. The two part have the same diameter of 2.1 m and the cylindrical part is 1.5 m high as shown. All the surfaces of tank are made of iron sheet. a) Allowing for a 15% wastage on overlapping, calculate to two decimal place the area of iron sheet required. b) Iron sheet cost sh 400 per square
  11m 12s

• 16.    The table below shows the marks stored by form two students in a mathematics test. a) Complete the table b) State the modal class c) Use the completed table to calculate the mean mark for the students.
  5m 18s

• 17.    A spire stand directly across the street from a building. The angle of depression of the top of the building from the top of the spire is #25.8^0# and the angle of elevation of the top of the spire from the foot of the building is #43.5^0#. given that the distance between the spire and the building is 40 metres, calculate to two decimal places: a)The height of the spire. b)The difference in height
  9m 53s