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- The figure below shows triangle OPQ in which OP = P and OQ = p. M and N are points on OQ and OP respectively...(Solved)
The figure below shows triangle OPQ in which OP = P and OQ = p. M and N are points on OQ and OP respectively such
that ON:NP = 1:3 and OM:MQ = 2:1
(a) Express the following vectors in terms of p and q
(i) PM
(ii) QN
(iii) PQ
(b) Lines PM and QN intersect at X such that PX = hPM and QX = kQN. Express OX in two different ways and hence
find the value of h and k.
(c) OX produced meets PQ at Y such that PY :YQ = 3:2. Using the ratio theorem or otherwise, find OY in terms of P and q
Date posted: May 6, 2019. Answers (1)
- The number 5.81 contains an integral part and a recurring decimal. Convert the number into an improper fraction and hence into a mixed number(Solved)
The number 5.81 contains an integral part and a recurring decimal. Convert the number into an improper fraction and hence into a mixed number
Date posted: May 6, 2019. Answers (1)
- Find the value of m and n in the figure below.(Solved)
Find the value of m and n in the figure below.
Date posted: May 6, 2019. Answers (1)
- Solve the simultaneous inequality below.(Solved)
Solve the simultaneous inequality below.
2x – 5≤ 10 – 3x < x + 18.
Date posted: May 6, 2019. Answers (1)
- Sales lady sold goods whose marked price was Sh. 340,000 at a discount of 3%. She was paid Sh. 16,490 as a commission for this...(Solved)
Sales lady sold goods whose marked price was Sh. 340,000 at a discount of 3%. She was paid Sh. 16,490 as a commission for this sale. Calculate the percentage rate of commission she was paid.
Date posted: May 6, 2019. Answers (1)
- A solid consists of three discs each of 1.5cm thick with diameter of 4cm, 6cm and 8cm respectively. A central hole 2cm
in a diameter is...(Solved)
A solid consists of three discs each of 1.5cm thick with diameter of 4cm, 6cm and 8cm respectively. A central hole 2cm
in a diameter is drilled out as shown below. If the density of the material used is 2.8cm3, calculate it mass to 1 decimal place.
Date posted: May 6, 2019. Answers (1)
- Given that tan x =5/13,find the value of the following without using mathematics tables or a calculator:(Solved)
Given that tan x =5/13,find the value of the following without using mathematics tables or a calculator:
(a) Cost x
(b) Sin2(90 – x)
Date posted: May 6, 2019. Answers (1)
- Mutai imports rice from the United States at initial cost of 500 US Dollars per tonne. He then pays 20% of this amount
as shipping costs...(Solved)
Mutai imports rice from the United States at initial cost of 500 US Dollars per tonne. He then pays 20% of this amount
as shipping costs and 10% of the same amount as custom duty. When the rice reaches Mombasa he has to pay 5% of the initial cost to transport it to Nairobi. Given that on the day of this transaction the exchange rate was 1US Dollar =KSh. 76.60. Calculate the total cost of importing one tonne of rice up to Nairobi in Kenya Shillings.
Date posted: May 6, 2019. Answers (1)
- Given that Log3 = 0.4771 and log 5 = 0.6990, evaluate the following without using logarithm table or calculator.(Solved)
Given that Log3 = 0.4771 and log 5 = 0.6990, evaluate the following without using logarithm table or calculator.
(a) Log 135
(b) Log 1125
Date posted: May 6, 2019. Answers (1)
- Mr. Wanyama has a plot that is in a triangular form. The plot measures 170m, 190m and 210m, but the altitudes of the plot as...(Solved)
Mr. Wanyama has a plot that is in a triangular form. The plot measures 170m, 190m and 210m, but the altitudes of the plot as well as the angles are not know. Find the area of the plot in hectares.
Date posted: May 6, 2019. Answers (1)
- (a) Find the greatest common divisor of the term 9x3y2 and 4xy4.(Solved)
(a) Find the greatest common divisor of the term 9x3y2 and 4xy4.
(b) Hence factorise completely the expression 9x3y2 – 4xy4.
Date posted: May 6, 2019. Answers (1)
- In a Chemistry experiment, a boy mixed some acid solution of 45% concentration with an acid solution of 25% concentration. In what proportion should the...(Solved)
In a Chemistry experiment, a boy mixed some acid solution of 45% concentration with an acid solution of 25% concentration. In what proportion should the two acids be mixed in order to get 100cm3 of solution of 30% concentration?
Date posted: May 6, 2019. Answers (1)
- A farmer has a piece of land measuring 840m by 396m. He divides it into square plots of equal size. Find the maximum
area of one...(Solved)
A farmer has a piece of land measuring 840m by 396m. He divides it into square plots of equal size. Find the maximum
area of one plot.
Date posted: May 6, 2019. Answers (1)
- Simplify the expression.(Solved)
Simplify the expression.
Date posted: May 6, 2019. Answers (1)
- Evaluate the following;(Solved)
Evaluate the following;
Date posted: May 6, 2019. Answers (1)
- Given the equations: y=4 -x2 and y=x2-2x;(Solved)
Given the equations: y=4 -x2 and y=x2-2x;
a) Find the co-ordinates of the points where the two curves meet. (2 marks)
b) Find the co-ordinates of points where y=4 -x2 meet:
(i) The x-axis.
(ii) The y-axis
c) Find the co-ordinates of the points where y=x2– 2x meet;
(i) The x-axis
(ii) The y-axis
d) Sketch the two curves above on the same axes
e) Find the area enclosed between the curves y=4-x2 and y=x2 – 2x.
Date posted: May 6, 2019. Answers (1)
- Compete the table below(Solved)
Compete the table below
b) On the same axes draw the graphs of y= sin(x+30)o and y= 2cos(x+30)o.
c) Use your graphs to solve the equation 2cos(x+30)o – sin(x+30)o = 0
d) State the amplitude of each wave.
Date posted: May 6, 2019. Answers (1)
- The position of two towns P and Q are given to the nearest degrees as P(45oN, 110oW) and Q (45oN, 70oE) Take ??=3.142, Radius of...(Solved)
The position of two towns P and Q are given to the nearest degrees as P(45oN, 110oW) and Q (45oN, 70oE) Take 𝜋=3.142, Radius of the earth R = 6370km. Find
a) The distance between the two towns along the parallel of latitude in km.
b) The distance between the towns along a parallel of latitude in nautical miles.
c) A plane flew from P to Q taking the shortest distance possible. It took the plane 15 hours to move from P and Q.
Calculate it’s speed in knots
Date posted: May 6, 2019. Answers (1)
- In the figure below, E is the midpoint of AB, OD:DB=2:3 and F is the point of intersection of OE and AD.(Solved)
In the figure below, E is the midpoint of AB, OD:DB=2:3 and F is the point of intersection of OE and AD.
a) Given that OA = a and OB = b , express in terms of a and b
i) OE
ii) AD
b) Given further that AF = tAD and OF = sOE where s and t are scalars, find the values of s and t.
c) Show that O, F and E are collinear.
Date posted: May 6, 2019. Answers (1)
- a) PQRS is a quadrilateral with vertices p(1, 4) Q(2, 1), R(2, 3) and S(6, 4). On the grid provided plot the quadrilateral(Solved)
a) PQRS is a quadrilateral with vertices p(1, 4) Q(2, 1), R(2, 3) and S(6, 4). On the grid provided plot the quadrilateral
b) Draw P1Q1R1S1 the image of PQRS under a positive quarter turn about the origin and write down its co-ordinates.
c) Draw P11Q11R11S11 the image of P1Q1R1S1 under the transformation whose matrix is 
and write down its co-ordinates.
d) Determine the matrix T of a single transformation that maps PQRS onto P11Q11R11S11
Date posted: May 6, 2019. Answers (1)