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- A small scale farmer wishes to buy some sheep and goats for rearing. A sheep costs sh.400 and a goat costs sh.300.(Solved)
A small scale farmer wishes to buy some sheep and goats for rearing. A sheep costs sh.400 and a goat costs sh.300. The farmer has enough space for only 20 animals and may spend at most sh.6800. The number of goats should not exceed twice the number of sheep.
a) By letting x and y to represent the number of sheep and goats he can buy respectively, write down all inequalities from the above information.
b) Represent the inequalities on the grid provided.
c) From your graph; find the maximum number of animals he can buy at the lowest cost.
Date posted: September 13, 2019. Answers (1)
- The probability that it will rain on a certain morning is 1/3.(Solved)
The probability that it will rain on a certain morning is 1/3. If it rains, the probability that Sagero misses the bus is 3/4. If it does not rain, the probability that he catches the bus is 5/6.
a) Represent the above information in a tree diagram.
b) Calculate the probability that on a given morning
i) it rains and he catches the bus.
ii) it rains and he misses the bus.
iii) he misses the bus.
iv) it does not rain and he misses the bus.
Date posted: September 13, 2019. Answers (1)
- A particle P moves in a straight line so that its velocity Vm/s at time t seconds where(Solved)
A particle P moves in a straight line so that its velocity Vm/s at time t seconds where t> or equal to 0 is given by V=28+t-2t2
Find;
a) The time when P is instantaneously at rest.
b) The speed of P at the instant when the acceleration of P is zero
c) Given that P passes through point O of the line when t=0
i) Find the distance of P from O when P is instantaneously at rest
ii) Find the distance covered by the particle during the 3rd second
Date posted: September 13, 2019. Answers (1)
- The table below shows the masses in kg of some form three students in a school.(Solved)
The table below shows the masses in kg of some form three students in a school.
a)
i) State the median class.
ii) Using an assumed mean of 54.5, calculate the mean mass.
b) Calculate the standard deviation of the data, give your answer correct to 2 decimal places.
Date posted: September 13, 2019. Answers (1)
- i) On the grid (graph paper) plot and draw triangle ABC where A(4,3),B(4,6) and C(7,6) .(Solved)
a) i) On the grid (graph paper) plot and draw triangle ABC where A(4,3),B(4,6) and C(7,6)
ii) Triangle ABC is given a rotation of +900 about (0,0) to map onto AIBICI.Plot AIBICI and state its coordinates.
iii) Triangle AIBICI is transformed by the matrix 
to map onto A11B11C11. Plot A11B11C11 and state its co-ordinates.
b) A11B11C11 is further transformed by a reflection on the line x=0 to map onto A111B111C111. Plot A111B111C111. What single transformation will map A111B111C111 onto triangle ABC?
Date posted: September 13, 2019. Answers (1)
- Using a ruler and a pair of compasses only.
a) Construct a ?ABC in which AB =7.4cm, AC=8.2cm and angle BAC=450(Solved)
Using a ruler and a pair of compasses only.
a) Construct a ΔABC in which AB =7.4cm, AC=8.2cm and angle BAC=450
b) On the same diagram, construct ΔACD such that D, and B are on the opposite sides of line AC, D is equidistant from A and C and BD=8.5cm. Measure AD.
c) Draw locus of Q which passes through C and is parallel to BD.
d) The normal from C meets BD at N. Mark the points M1 and M2 on the locus of Q such that M1N=M2N=4.1cm. Measure the lengths M1M2 and CN.
Date posted: September 13, 2019. Answers (1)
- In the figure below, E is the midpoint of BC,AD:DC=3:2 and AE intersect with BD at F.(Solved)
In the figure below, E is the midpoint of BC,AD:DC=3:2 and AE intersect with BD at F.
a) Given that AB=b and AC=c, express in terms of b and c
(i)AE
(ii)BD
b) If BF= t BD and AF= sAE , where t and s are scalars, find the values of t and s.
c) What is the ratio in which F divides AE
Date posted: September 13, 2019. Answers (1)
- The table below shows income tax rates.(Solved)
The table below shows income tax rates.
Agnes earns a monthly salary of Ksh. 20,000 per month, Her house allowance is Ksh. 15000P.M. She is entitled to a personal relief of Ksh. 1260P.M. Her deductions are NHIF sh.960, cooperative loan sh. 3500 and service charge of Ksh.400 per month.
Calculate
a) the taxable income.
b) the tax charged on Agnes earning.
c) the tax paid.
d) the net salary.
Date posted: September 13, 2019. Answers (1)
- The distance between two places P(theta0 S,350 E) and (theta0 S, 1450 W)(Solved)
The distance between two places P(theta0 S,350 E) and (theta0 S, 1450 W),on the earth via South Pole is 3240nm. Find
a) the value of theta0.
b) the distance between P and Q along the parallel of latitude in nautical miles.
Date posted: September 13, 2019. Answers (1)
- Find the equation of a circle whose diameter has the end points (-2,6) and 6,2)(Solved)
Find the equation of a circle whose diameter has the end points (-2,6) and 6,2)
Date posted: September 13, 2019. Answers (1)
- The figure below is a square –based pyramid with vertex V. (Solved)
The figure below is a square –based pyramid with vertex V. Point O is the intersection of diagonals AC and BC. VA=VB=VC=VD=12cm and AB=BC=4cm
a) Name the projection of line VA on plane ABCD.
b) Find the angle between line VB and the plane ABCD
Date posted: September 13, 2019. Answers (1)
- Simplify without using mathematical tables or calculator.(Solved)
Simplify without using mathematical tables or calculator.
Date posted: September 13, 2019. Answers (1)
- Mrs. Ondiek invested Ksh. 63560 in a bank where the interest was compounded quarterly at the rate of 12% per month. (Solved)
Mrs. Ondiek invested Ksh. 63560 in a bank where the interest was compounded quarterly at the rate of 12% per month. Determine the amount of money she had after 2 ½ years.
Date posted: September 13, 2019. Answers (1)
- Expand up to a term in x3
(Solved)
a) Expand 
up to a term in x3
b) Use the expansion in(a)above to find the value of (0.9)8
Date posted: September 13, 2019. Answers (1)
- Determine the semi-interquartile range for the given set of data.
40,20,30,42,10,18,26,32(Solved)
Determine the semi-interquartile range for the given set of data.
40,20,30,42,10,18,26,32
Date posted: September 13, 2019. Answers (1)
- Calculate the relative error in 7.9 ÷ 4.3(Solved)
Calculate the relative error in 7.9 ÷ 4.3
Date posted: September 13, 2019. Answers (1)
- In the diagram below, CD is a tangent to the circle at point D. If BC=7cm and CD=9cm(Solved)
In the diagram below, CD is a tangent to the circle at point D. If BC=7cm and CD=9cm, calculate the length of the chord AB.
Date posted: September 13, 2019. Answers (1)
- Solve the equation 3Sin x=2Cos2x(Solved)
Solve the equation 3Sin x=2Cos2x where 
Date posted: September 13, 2019. Answers (1)
- Solve for x in the equation below
logx 4+ log4 x= 2 (Solved)
Solve for x in the equation below
logx 4+ log4 x= 2
Date posted: September 13, 2019. Answers (1)
- In the figure below, the tangents DC and BC meet at point C, angle BCD=500 while angle ABE=700(Solved)
In the figure below, the tangents DC and BC meet at point C, angle BCD=500 while angle ABE=700
Calculate the sizes of angles
i) angle CBD
ii) angle CDE
Date posted: September 13, 2019. Answers (1)