October 17, 2015 KCSE Exams
SECTION 1 (50 marks)
Answer all the questions in this section in the space provided.
1 In this question, show all the steps in your calculation,giving the answer at each stage.use
logarithms correct to 4 decimal places, to evaluate
2 Make h the subject of the formula
3 Line AB given below is one side of triangle ABC.using a ruler and a pair of compasses only:
(i) Complete the triangle ABC such that BC=5cm and angle ABC=45degree. (1 mark)
(ii) On the same diagram construct a circle touching sides AC,BA produced and BC produced. (2 marks)
4 The position vectors of points A and B are
Find the position vector of point P. (3 marks)
5 Te top of a table is a regular hexagon.each side of the hexagon measures 50.0cm.find the
maximum percentage error in calculating the perimeters of the top of the table. (3 marks)
6 A student at the certain college has a 60% chances of passing examination at the first attempt.each
time a student fails and repeat the examination, his chances of passing are increased by 15%.
Calculate the probability that a student in the college passes an examination at the second or at the
thisrd attempt. (3 marks)
7 An aeroplane flies at an everage speed of 500 Knots due east from a point
to another point Q.it takes 2 ¼ hours to reach point Q.
(i) The distance in nautical miles it travelled: (1 mark)
(ii) The longitude of point Q to 2 decimal places. (2 marks)
8 (a) Expand and simplify the expression
(b) Use the expansion in (a) above to find the value of 145. (2 marks)
9 In the figure below angle BAC and ADC are equal.Angle ACD is a right angle.the ratio of the sides
Given that the area of triangle ABC is 24 cm2, find the area of triangle ACD. (3 marks)
10 Point A(2,2) and B(4,3) are mapped onto B(4,15) respectively by a transformation T.
Find the matrix of T. (4 marks)
11 The equation of the circle is given by
Determine the coordinates of the center of the circle. (3 marks)
12 Solve for y in the equation
13 Without using a calculator or mathematical tables, express
14 The figure below represent a triangular prism.the faces ABCD, ADEF and ABEF are rectangles.
AB=8cm, BC=14cm, BF=7cm and AF=7cm.
Calculate the angle between faces BCEF and ABCD. (3 marks)
15 A particle moves in a straight line from a fixed point .its velocity s after t second is given
Calculate the distance travelled by the particle during the third second. (3 marks)
16 find in radians, the value of x in the interval
(leave the answer in terms of ?) (4 marks)
SECTION II (50 marks)
Answer any five questions in this section.
17 A trader deals in two type of rices : type A cost Ksh 400 per bag and type B costs
Ksh 350 per bag.
(a) trader mixes 30 bags of type A with 50 bags of type B.If he sells the mixtures at a profit of
20% Calculate the selling price of one bag of mixture. (4 marks)
(b) The trader now mixes Type A with type B in the ratio x:y respectively.if the cost of mixure is
Ksh 383.50 per bag, find the ratio x:y. (4 marks)
(c) The trader mixes one bag of mixure in part (a) with one bag of te mixure in part (b) above.
Calculate the ratio of type A rice to type B rice in this mixures (2 marks)
18 Three variable p, q and r are such that p varies directly as q and inversely as the square of r.
(a) When p=9, q=12, and r =2.
Find p when q=15 and r=5. (4 marks)
(b) express q in terms of p and r. (1 marks)
(c) if p is increased by 20% and r is decreased by 10% find:
(i) A simplified expression for the change in Q in terms of p and r; (3 marks)
(ii) The percentage change in q. (2 marks)
19 Complete the table below, giving the values correct to 2 decimal places.
on the same axes.use a scale of 1cm to represent 30degree on the x-axis and 2cm to represent 1 unit on the
y-axis. (5 marks)
(c) Use the graph in (b) above to solve equation 3cosx-sin2x=2. (2 marks)
(d) State the amplitude of y=3cosx-2. (1 mark)
20 In the figure below DA is a diameter of the circle ABCD center O, radius 10cm.TCS is a tangent to
the circle at C, AB=BC and angle DAC=38degree.
(a) Find the size of the angle:
(i) ACS; (2 marks)
(ii) BCA. (2 marks)
(b) Calculate the length of:
(i) AC; (2 marks)
(ii) AB. (4 marks)
21 Two policemen were together at a road junction. each had a walkie talkie. the maximum distance at
which one could communicate with other was 2.5 km.
One of the police man walked due east at 3.2 km/h while the other walked due north at 2.4km/h.
the policeman who headed east travelled for x km while the one who headed north travelled for y km
before they were unable to communicate.
(a) draw a sketch to represent the relative position of the policeman. (1 mark)
(b) (i) From the information above from two simultaneous equation in x and y. (2 marks)
(ii) Find the values of x and y. (5 marks)
(iii) Calculate the time taken before the policemen were unable to communicate. (2 marks)
22 The table below show the distribution of marks scored by 60 pupils in a test.
(a) on the grid provided, draw an ogive that represent the above information. (4 marks)
(b) Use the graph to estimate the interquartile range of this information. (3 marks)
(c) In order to pass the test, a pupil had to score more than 48 marks.calculate the percentage
of pupils who passed the test. (3 marks)
23 Halima deposited Ksh 109375 in a financial institution which paid simple interest at the rate of
8% P.a.at the end of two years, she withdraw the money.she then invested the money in shares.the value of shares depreciated at 4% p.a during the first year of investment in the next three years, the value of the shares appreciated at the rate of 6% every four month.
(a) Calculate the amount Halima invested in shares. (3 marks)
(b) Calculate the value of halima’s shares:
(i) at the end of the first year; (2 marks)
(ii) at the end of the fourth year,to the nearest shilling. (3 marks)
(c) Calculate Halima’s gain from the shares as a percentage. (2 marks)
24 The table belows show values of x and some values of y for the curve
in the range
(a) Complete the table by filling in the missing values of y.
(b) On the grid provided, draw the graph
Use the scale; horizontal axis 2cm for 1 unit and vertical axis 2cm for 5 unit. (3 marks)
(c) By drawing a suitable straight line, on the same grid as (b) above, solve the equation: