KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Form 3 Mathematics
A house is to be sold either on cash basis or through a loan. The cash price is sh.750,000. The loan conditions area s follows: there is to be down payment of 10% of the cash price and the rest of the money is to be paid through a loan at 10% per annum compound interest.
A customer decided to but the house through a loan.
Related Questions and Answers on Commercial Arithmetic II
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Form 4 MathematicsForm 2 Mathematics
In the figure below (not drawn to scale), AB = 8cm, AC= 6cm, AD= 7cm, CD= 2.82 cm and angle CAB =500
Calculate, to 2 decimal places
a) The length BC, b) The size of angle ABC, c) The size of angle CAD, d) The area of triangle ACD b) Express vector NM in terms of OB
OP = OM + 2 MN, find the coordinates of P.
Form 3 Mathematics
The table below shows values of x and some values of y for the curvey = x +3+3x2+-4x-12 in the range -4 ≤ x ≤ 2.
a) Complete the table by filling in the missing values of y.
b) On the grid provided, draw the graph y=x3 + 3x2+ -4x – 12 for -4 ≤ x ≤ 2.Use the scale. Horizontal axis 2cm for I unit and vertical axis 2cm for 5 units.
c) By drawing a suitable straight line on the same grid as the curve, solve the equation x3+3x2-5x-6=0 Form 1 Mathematics
Halima deposited Ksh. 109375 in a financial institution which paid simple interest at the rate of 8% p.a. At the end of 2 years, she withdrew all the money. She then invested the money in share. The value of the shares depreciated at 4% p.a. during the first year of investment. In the next 3 years, the value of the shares appreciated at the rate of 6% every four months
a) Calculate the amount Halima invested in shares. b) Calculate the value of Halima's shares. (i) At the end of the first year; (ii) At the end of the fourth year, to the nearest shilling. c) Calculate Halima„s gain from the share as a percentage. (ii) Find the values of x and y. (iii) Calculate the time taken before the policemen were unable to communicate. Form 4 MathematicsForm 2 Mathematics
Two policemen were together at a road junction. Each had a walkie talkie. The maximum distance at which one could communicate with the other was 2.5 km.
One of the policemen walked due East at 3.2 km/h while the other walked due North at 2.4 km/h the policeman who headed East traveled for x km while the one who headed North traveled for y km before they were unable to communicate. (a) Draw a sketch to represent the relative positions of the policemen. (b) (i) From the information above form two simultaneous equations in x and y. Form 2 MathematicsForm 4 Mathematics
a) complete the table below, giving the values correct to 2 decimal places.
b) On the grid provided, draw the graphs of y=sin 2x and y=3cosx-2 for 00 ≤ x ≤3600 on the same axes.
Use a scale of 1 cm to represent 300 on the x-axis and 2cm to represent 1 unit on the y-axis. c) Use the graph in (b) above to solve the equation 3 Cos x – sin 2x = 2. d) State the amplitude of y=3cosx-2. Form 1 Mathematics
a) A trader deals in two types of rice; type A and with 50 bags of type B. If
he sells the mixture at a profit of 20%, calculate the selling price of one bag of the mixture. b) The trader now mixes type A with type B in the ratio x: y respectively. If the cost of the mixture is Ksh 383.50 per bag, find the ratio x: y. c) The trader mixes one bag of the mixture in part (a) with one bag of the mixture in part (b). Calculate the ratio of type A rice to type B rice in this mixture. Form 4 Mathematics
The distance s metres from a fixed point O, covered by a particle after t seconds is given by the equation;
S =t3 -6t2 + 9t + 5. a) Calculate the gradient to the curve at t=0.5 seconds b) Determine the values of s at the maximum and minimum turning points of the curve. c) On the space provided, sketch the curve of s= t3-6t2+9t + 5. Form 3 Mathematics
A group of people planned to contribute equally towards a water project which needed Ksh 200 000 to complete, However, 40 members of the group without from the project.
As a result, each of the remaining members were to contribute Ksh 2500. a) Find the original number of members in the group. b) Forty five percent of the value of the project was funded by Constituency Development Fund (CDF). Calculate the amount of contribution that would be made by each of the remaining members of the group. c) Member‟s contributions were in terms of labour provided and money contributed. If the ratio of the value of labour to the money contributed was 6:19; calculate the total amount of money contributed by the members. Form 2 Mathematics
The diagram below represents a conical vessel which stands vertically. The which stands vertically,. The vessels contains water to a depth of 30cm. The radius of the surface in the vessel is 21cm. (Take π=22/7).
a) Calculate the volume of the water in the vessels in cm3
b) When a metal sphere is completely submerged in the water, the level of the water in the vessels rises by 6cm. Calculate: (i) The radius of the new water surface in the vessel; (ii) The volume of the metal sphere in cm3 (iii) The radius of the sphere. Form 2 Mathematics
The diagram below shows a triangle ABC with A (3, 4), B (1, 3) and C (2, 1).
a) Draw triangle A'B'C' the image of ABC under a rotation of +900+ about (0, 0).
b) Drawn triangle A"B" the image of A"B'C" under a reflection in the line y=x. c) Draw triangle A"B" C. the image under a rotation of -900 about (0, 0) d) Describe a single transformation that maps triangle ABC"" onto angle A"""B"""C""" e) Write down the equations of the lines of symmetry of the quadrilateral BB"A""A Form 2 Mathematics
The diagram below represents two vertical watch-towers AB and CD on a level ground. P and Q are two points on a straight road BD. The height of the tower AB is 20m road a BD is 200m.
a) A car moves from B towards D. At point P, the angle of depression of the car from point A is 11.3. Calculate the distance BP to 4 significant figures.
b) If the car takes 5 seconds to move from P to Q at an average speed of 36 km/h, calculate the angle of depression of Q from A to 2 decimal places c) Given that QC=50.9m, calculate; (i) The height of CD in meters to 2 decimal places; (ii) The angle of elevation of A from C to the nearest degree. Form 3 MathematicsForm 4 Mathematics
The figure below is a sketch of the curve whose equation is y=x2+x+5.
It cuts the line y=11 at points P and Q.
a) Find the area bounded by the curve = x2+x+5 and the line y=11 using the trapezium rule with 5 strips.
b) Calculate the difference in the area if the mid-ordinate rule with 5 ordinates was used instead of the trapezium rule. Form 1 Mathematics
a) The ratio of Juma's and Akinyi's earnings was 5:3 Juma's earnings rose to Ksh 8400 after an increase of 12%.
Calculate the percentage increase in Akinyi's earnings given that the sum of their new earnings was Ksh. 14100. b) Juma and Akinyi contributed all the new earnings to buy maize at Ksh 1175 per bag. The maize was then sold at Ksh 1762.50 per bag. The two shared all the money from the sales of the maize in the ratio of their contributions. Calculate the amount that Akinyi got. Form 3 MathematicsA minor sector of a circle of radius 28cm includes an angle of 1350 at the center. a) (i) convert 1350 into radians. Hence of otherwise find the area of the sector. ii) Find the length of the minor arc. b) The sector is folded to form a right circular cone. Calculate the : i) Radius of the cone ii) Height of the cone. (Take the value of Ð to be 22/7) (8mks) Form 4 MathematicsA triangle T whose vertices are A (2,3) B(5,3) and C (4,1) is mapped onto triangle T1 whose vertices are A1 (-4,3) B1 (-1,3) and C1 (x,y) by a transformation Find the: (i) Matrix M of the transformation (ii) Coordinates of C1 b) Triangle T2 is the image of triangle T1 under a reflection in the line y = x. Find a single matrix that maps T and T2 (8mks) Form 1 Mathematics
In this question use a ruler and a pair of compasses
Line PQ drawn below is part of a triangle PQR. Construct the triangle PQR in which
a) < QPR = 300 and line PR = 8cm b) On the same diagram construct triangle PRS such that points S and Q are no the opposite sides of PR<PS = PS and QS = 8cm c) A point T is on the a line passing through R and parallel to QS.If <QTS =900, locate possible positions of T and label them T1 and T2, Measure the length of T1T2. Form 2 Mathematics
The figure below represents a right prism whose triangular faces are isosceles. The base and height of each triangular face are 12cm and 8cm respectively. The length of the prism is 20cm.
Calculate the:
Form 3 Mathematics
Two bags A and B contain identical balls except for the colours. Bag A contains 4 red balls and 2 yellow balls. Bag B contains 2 red balls and 3 yellow balls.
(a) If a ball is drawn at random from each bag, find the probability that both balls are of the same colour. (b) If two balls are drawn at random from each bag, one at a time without replacement, find the probability that: (i) The two balls drawn from bag A or bag B are red (ii) All the four balls drawn are red Form 4 Mathematics
The table below shows the values of the length X ( in metres ) of a pendulum and the corresponding values of the period T ( in seconds) of its oscillations obtained in an experiment.
(a) Construct a table of values of log X and corresponding values of log T,
correcting each value to 2 decimal places (b) Given that the relation between the values of log X and log T approximate to a linear law of the form m log X + log a where a and b are constants (i) Use the axes on the grid provided to draw the line of best fit for the graph of log T against log X.
(ii) Use the graph to estimate the values of a and b
(b) Find, to decimal places the length of the pendulum whose period is 1 second Form 4 Mathematics
A company is considering installing two types of machines. A and B. The information about each type of machine is given in the table below.
The company decided to install x machines of types A and y machines of type B(a) Write down the inequalities that express the following conditions
I. The number of operators available is 40 II. The floor space available is 80m2 III. The company is to install not less than 3 type of A machine IV. The number of type B machines must be more than one third the number of type A machines (b) On the grid provided, draw the inequalities in part ( a) above and shade the unwanted region (c) Draw a search line and use it to determine the number of machines of each type that should be installed to maximize the daily profit. |
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