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The boundaries PQ, QR, RS and SP of a ranch are straight lines such that Q is 16km on a bearing of 040° from P....
(Solved)
The boundaries PQ, QR, RS and SP of a ranch are straight lines such that Q is 16km on a bearing of 040° from P. R is
directly south of Q and East of P and S is 12km on a bearing of 120° from R.
(a) Using a scale of 1cm to represent 2km, show the above information in a scale drawing.
(b) From the scale drawing determine:
(i) the distance in kilometres between P and S.
(ii) the bearing of P from S.
Date posted:
May 10, 2019
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Answers (1)
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(a) On the grid provided, draw the graph of the function y = ½ x² - x + 3 for 0 = x = 6
(Solved)
(a) On the grid provided, draw the graph of the function y = ½ x² - x + 3 for 0 ≤ x ≤ 6
(b) Calculate the mid-ordinates for 5 strips between x = 1 and x = 6 and hence use the mid-ordinate rule to
approximate the area under the curve between x = 1, x = 6, and x-axis.
(c) Assuming that the area determined by integration to be the actual area, calculate the percentage error in using the
mid-ordinate rule.
Date posted:
May 10, 2019
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Answers (1)
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A triangular plot ABC is such that AB = 36m, BC = 40m and AC = 42m.
(Solved)
A triangular plot ABC is such that AB = 36m, BC = 40m and AC = 42m.
( a) Calculate the :-
(i) Area of the plot in hectares.
(ii) The acute angle between the sides AB and BC.
(b) A water tap is to be installed inside the plot such that the tap is at the centre of the circumcircle passing through
the vertices A, B and C. Calculate the distance of the tap from the vertex A.
(c) Find the area outside the plot that would be watered by the sprinkler connected directly to the tap.
Date posted:
May 10, 2019
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Answers (1)
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In the diagram below OA = a, OB = b the points P and Q are such that AP = 2/3 AB, OQ = 1/3...
(Solved)
In the diagram below OA = a, OB = b the points P and Q are such that AP = 2/3 AB, OQ = 1/3 OA

(a) Express OP and BQ in terms of a and b
(b) If OC = hOP and BC = kBQ, Express OC in two different way and hence
(i) Deduce the value of h and k.
(ii) Express vector OC in terms of a and b only.
(iii) State the ratio in which C divides BQ
Date posted:
May 10, 2019
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Answers (1)
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The diagram below represents the cross section of a solid prism of length 8cm
(Solved)
The diagram below represents the cross section of a solid prism of length 8cm

(a) Calculate the volume of the prism.
(b) Given that the density of the prism is 5.75gcm-³, calculate its mass in grams.
(c) A second prism is similar to the first one but it made of a different materials. The volume of the second prism is
246.24cm³.
Calculate the area of the cross-section of the second prism.
(d) Given that the ratio of the mass of the first prism to that of the second is 2.5, find the density of the second prism.
Date posted:
May 10, 2019
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Answers (1)
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Last year, Nafula was four times as old as her son, Kamau. In four years time, the sum of their ages will be 53.
Determine their...
(Solved)
Last year, Nafula was four times as old as her son, Kamau. In four years time, the sum of their ages will be 53.
Determine their present ages
Date posted:
May 10, 2019
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Answers (1)
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A fruit seller bought 144 pineapples at Kshs 100 for every six pineapples. He sold some of them at Kshs 72 for every
three and the...
(Solved)
A fruit seller bought 144 pineapples at Kshs 100 for every six pineapples. He sold some of them at Kshs 72 for every
three and the rest at Kshs 60 for every two. If he make a 65% profit, calculate the number of pineapples sold at Kshs
72 for every three.
Date posted:
May 10, 2019
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Answers (1)
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The figure below shows triangle PQR in which PR = 12cm. T is a point on PR such that TR =4cm. Line ST is parallel...
(Solved)
The figure below shows triangle PQR in which PR = 12cm. T is a point on PR such that TR =4cm. Line ST is parallel to
QR. If the area of triangle PQR is 336cm². Find the area of the quadrilateral STQR.

Date posted:
May 10, 2019
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Answers (1)
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The points P, Q and R lie on a straight line. The position vectors of P and R are 2i+ 6j + 13k and 5i...
(Solved)
The points P, Q and R lie on a straight line. The position vectors of P and R are 2i+ 6j + 13k and 5i – 3j + 4k
respectively. Find
(i) the position vector of Q
(ii) the length of PQ
Date posted:
May 10, 2019
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Answers (1)
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If 4x2 + 8x + (k-3) is a perfect square, find the value of k.
(Solved)
If 4x2 + 8x + (k-3) is a perfect square, find the value of k.
Date posted:
May 10, 2019
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Answers (1)
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The marks scored by a group of pupils in a Mathematics test were as recorded in the table below.
(Solved)
The marks scored by a group of pupils in a Mathematics test were as recorded in the table below.

(a) State the modal class.
(b) Calculate:
(i) the median
(ii) the mean
Date posted:
May 10, 2019
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Answers (1)
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Milk in a cool factory is stored in a rectangular tank whose internal dimensions are 1.7m by 1.4m by 2.2m. On one day
the tank was...
(Solved)
Milk in a cool factory is stored in a rectangular tank whose internal dimensions are 1.7m by 1.4m by 2.2m. On one day
the tank was 75% full of milk.
(a) Calculate the volume of milk in the tank in litres.
(b) The milk is packed in small packets which are in the shape of a right pyramid on an equilateral triangle of side
16cm. The height of each packet is 13.6cm. Each packet is sold at Sh. 30. Calculate:-
(i) the volume of milk in milliliters in each packet to 2 significant figures.
(ii) the exact amount of money that was realized from the sale of all packets of milk.
Date posted:
May 10, 2019
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Answers (1)
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In an n-sided polygon two angles are right angles and each of the remaining angles is 1500.
(Solved)
In an n-sided polygon two angles are right angles and each of the remaining angles is 1500.
(a) Find the value of n and hence the sum of the interior angles of this polygon.
(b) Name the polygon.
(c) Find the area of a regular octagon of sides 4cm giving answer correct to 4 significant figures.
Date posted:
May 10, 2019
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Answers (1)
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Three business partners Mogambi, Ouko and Memba contributed Sh. 600,000, Sh. 400,000 and Sh. 800,000
respectively to start a business of matatu plying Kisii – Kisumu...
(Solved)
Three business partners Mogambi, Ouko and Memba contributed Sh. 600,000, Sh. 400,000 and Sh. 800,000
respectively to start a business of matatu plying Kisii – Kisumu route. The matatu carries 14 passengers with each
paying Sh. 250. The matatu makes 2 round trips everyday and is ever full. Each day Sh. 6000 is used to cover running
costs and wages.
(a) Calculate their profit per day.
(b) The matatu works for 25 days per month and is serviced every month at a cost of Sh. 10,000. Calculate their
monthly profit in June. (1 Month)
(c) The three partners agreed to save 40% of the profit, 24% to be shared in the ratio of their contribution and the
remaining to be shared equally. Calculate Ouko’s share in the month of July.
(d) The matatu developed a mechanical problem and they decided to sell it through an agent who charged a
commission of 5% on the selling price. Each partner received Sh. 475,000 from the agent after he had taken his
commission. Determine the price at which the agent sold the matatu.
Date posted:
May 10, 2019
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Answers (1)
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The length of a rectangle is (3x+1)cm. Its width is 3cm shorter than the length. Given that area of the rectangle is
28cm2, find its length.
(Solved)
The length of a rectangle is (3x+1)cm. Its width is 3cm shorter than the length. Given that area of the rectangle is
28cm2, find its length.
Date posted:
May 10, 2019
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Answers (1)
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A water tank has a capacity of 70 litres. A similar model tank has a capacity of 0.25 litres. If the larger tank has a...
(Solved)
A water tank has a capacity of 70 litres. A similar model tank has a capacity of 0.25 litres. If the larger tank has a height
of 150cm, calculate the height of the model.
Date posted:
May 10, 2019
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Answers (1)
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In chemistry form 4 classes, 1/3 of the class are girls and the rest boys, 4/5 of the boys and 9/10 of the girls are...
(Solved)
In chemistry form 4 classes, 1/3 of the class are girls and the rest boys, 4/5 of the boys and 9/10 of the girls are right handed
while the rest are left handed. The probability that a right-handed student breaks a conical flask in any practical session is
3/10 and the corresponding probability of a left-handed student 4/10 . The probabilities are independent of the students
gender.
a) Represent the above information on a tree diagram with independent probabilities.
b) Determine the probability that student chosen at random form the class is left handed and does not break a conical flask in
simplest form.
c) Determine the probability that a conical flask is broken in any chemistry practical session in simplest
d) Determine the probability that a conical flask is not broken by a right-handed student in the simplest form.
Date posted:
May 9, 2019
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Answers (1)
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The velocity , Vm/s, of the particles projected into space is given by the formula: V = 5t² - 2t² + 9 where t is...
(Solved)
The velocity , Vm/s, of the particles projected into space is given by the formula: V = 5t² - 2t² + 9 where t is time in seconds
elapsed since projection,
Determine
a) The acceleration of the particle when t = 4
b) The value of t which minimises the acceleration.
c) The velocity of the particle when acceleration is minimum
d) The total distance moved by the particle between t = 1 to t = 4 seconds.
Date posted:
May 9, 2019
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Answers (1)
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Use a ruler and a pair of compass only in the constructions below:
(Solved)
Use a ruler and a pair of compass only in the constructions below:
a) Construct a triangle ABC such that AB = 4cm, BC = 5cm and angle ABC = 120°, measure AC.
b) On the same diagram
i) locate P the locus of a point equidistance from the three vertices of the triangle ABC and demonstrate this using a circle.
Measure the radius of the circle.
ii) On the same side of BC as A, construct Q the locus of points such that angle BQC = 120°.
iii) On the side of AC opposite point B construct R the locus of points 4cm from line AC.
iv) Within the circle shade the set of points such that Angle BQC ≥ 120°
Date posted:
May 9, 2019
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Answers (1)
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After how many years would Kshs 15,000 amount to Kshs 24,015.50 at a rate of 16% p.a. compounded quarterly?
(Solved)
After how many years would Kshs 15,000 amount to Kshs 24,015.50 at a rate of 16% p.a. compounded quarterly?
Date posted:
May 9, 2019
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Answers (1)