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In the figure below OA = a, OB = b, OA : AE = 2 : 3 and OB : OC = 1 : 2
a) Express AC and BE in terms of a and b
i) AC
ii) BE
b) If DC = kAC and BD = mBE where k and m are scalars.
By expressing DC in two ways, determine the values of k and m.
c) Find the ratio of BD : DE
Date posted:
November 5, 2019
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A house is to be sold either on a cash basis or through a loan. The cash price is Kshs. 750,000. The loan conditions are as follows: there is to be a down payment of 10% of the cash price and the rest of the money to be paid through a loan of 10% per annum compound interest.
A customer decided to buy the house through a loan.
a) i) Calculate the amount of money loaned to the customer.
ii) The customer paid the loan in 3 years.
Calculate the total amount paid for the house.
b) Find how long the customer would have taken to fully pay for the house if she paid a total of Kshs 891,750.
Date posted:
November 5, 2019
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A cylindrical water tank is of diameter 7 metres and height 2.8 metres.
a) Find the capacity of the water tank in litres.
b) Six members of a family use 15 litres each per day. Each day 80 litres are used for cooking and washing and a further 60 litres are wasted.
Find the number of complete days a full tank of water would last the family.
c) members of the family were absent for 90 days. During the 90 days, wastage was reduced by 20% but cooking and washing remained the same. Calculate the number of days a full tank would now last the family.
Date posted:
November 5, 2019
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Divide line AB such that AP = 2/5 AB
Date posted:
November 5, 2019
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Use the matrix method to find the co-ordinates of the points of intersection of the line
3x - 4y = 1 and y + 7x = 23
Date posted:
November 5, 2019
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In the figure below the lines AB and CD are parallel. AD and CB intersect at X. AB = 6cm, CD = 9cm and DX = 3 cm.
a) Calculate the length of AX.
b) The area of ΔABX is 6cm2. Calculate the area of ΔCXD.
Date posted:
November 5, 2019
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Without using a calculator evaluate
Date posted:
November 5, 2019
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Find the value of
Date posted:
November 5, 2019
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Simplify the expression
Date posted:
November 5, 2019
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Given Sin (90 – a) = 1/2 , find without using tables or calculators the value of Cos a.
Date posted:
November 5, 2019
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Solve the equation below.
Date posted:
November 5, 2019
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Use logarithms to evaluate
Date posted:
November 5, 2019
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The sketch below represents the curve y=x2+5 and a straight line PQ which meets the x-axis and
y-axis at the points (-4, 0) and (0, 8) respectively. The line intersects the curve at point P and Q as
shown.
a) Find the equation of the line in the form y = mx + c
b) Determine the co-ordinates of P and Q
c) Calculate the area of the shaded region
Date posted:
November 2, 2019
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A quantity A varies jointly as the cube of y and inversely as the square root of x. If A = 7 when
y=2 and x=25,
(a) Write an equation convecting A, x and y
(b) Find the value of y to three significant figures, when A=12 and x=36
(c) Find the percentage change in A when y is decreased by 11% and x is increased by 21%.
Date posted:
November 2, 2019
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The first three terms of a G.P. are the first, fourth and tenth terms of an A.P. Given that the first
term is 6 and that all the terms of the G.P. are different, find the common ratio.
Date posted:
November 2, 2019
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Solve for x given logx3 + log3X = 2.
Date posted:
November 2, 2019
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y varies partly as the square root of x and partly varies inversely as the cube of x.
When y=2, x=4 and when y=3, x=1. Express y in terms of x.
Date posted:
November 2, 2019
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A point T divides line AB externally in the ratio 8:2. Given that the position vectors of A and B are 3i - 4l + k and -1 +j -3k respectively. Find the position vector of T in unit vector form.
Date posted:
November 2, 2019
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Solve for x given that 2 sin x = tax x for 00 ≤ x ≤ 3600
Date posted:
November 2, 2019
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Given sin 
find cos (90 - theta) without using mathematical tables or calculators.
Date posted:
November 2, 2019
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Make P the subject of the formula
Date posted:
November 2, 2019
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The figure below shows a transverse pulley systems.
The wheels have radius 15cm and 10cm respectively. If O1X=30cm and XO2 =20cm
Calculate:
(a) AO1C
(b) DO2F
(c) Length AD to 4 decimal places
(d) Length BE
(e) Length of arc ABC and BEF.
(f) The length of the belt
Date posted:
November 2, 2019
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A bus left town A at 5:20am to town B 610km away at an average speed of 60km/hr. After 3 hrs 10 minutes, a van left town B and travelled towards A at an average speed of 80km/hr.
(a) (i) At what time did they meet
(ii) How far from A was the meeting point
b) A car left town B at 9:00am and travelled towards A at an average speed of 100km/hr.
Determine
(i) The time the car caught up with the van
(ii) The distance the car travelled to catch up with the van.
Date posted:
November 2, 2019
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A triangle has vertices P(1,2) Q(3,5) and R(5,3)
a) Draw triangle PQR and its image P1Q1R1 under a translation vector 
b) Draw triangle PII QII RII , the image of triangle PI QI RI under a rotation of half turn about the origin
c) Triangle PIII QIII RIII is the image of triangle PII QII RII under reflection in the line y=x.
Draw triangle PIII QIII RIII and state its co-ordinates.
d) Triangle PIII QIII RIII is reflected in the line x=0. State the co-ordinates of its image
Date posted:
November 2, 2019
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Find the equation of the normal to the curve y=x2 – 4x + 5 at the point (4,5)
Date posted:
November 1, 2019
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Juma needs to import a car from Japan whose cost is US $ 5000 outside Kenya. He intends to buy the car through an agent who deals in Japanese yen. The agent will charge him 20% commission on the price of the car and a further 80325 Japanese yen for shipment of the car. How many Kshs will he need to send to the agent to get the car given that
1 US $ = 105.00 Japanese yen
1 US $ = KShs 63.00
Date posted:
November 1, 2019
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ABCD is a parallelogram. DAB=124o. The bisectors of angle BCD and angle ADC meet at x. Find angle DXC (Reflex)
Date posted:
November 1, 2019
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Find the inequalities that defines the region marked R in the diagram below.
Date posted:
November 1, 2019
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(a) Construct triangle PQR where PQ = 6cm, QR = 9cm and PR = 8cm.
(b)Drop a perpendicular from P to meet QR at M. Measure PM hence calculate the area of
triangle PQR
Date posted:
November 1, 2019
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Evaluate 
Date posted:
November 1, 2019