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A theatre has a seating capacity of 250 people. The charges are Kshs. 100 for an ordinary seat and Kshs. 160 for a special seat. It costs Kshs. 16,000 to stage a show and the theatre must make a profit. There are never more than 200 ordinary seats and for a show to take place at least 50 ordinary seats must be occupied. The number of special seats is always less than twice the number of ordinary seats. Taking x to be the number of ordinary seats and y the number of special seats:-
(a) Write down all the inequalities representing the above information.
(b) On the grid provided, draw the graph to show the inequalities.
(c) Determine the number of seats each type that should be booked in order to maximize the profit.
(d) Determine the maximum profits.
Date posted:
August 19, 2019
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A curve is represented by the function below
(a) Find 
(b) Determine the values of y at the turning points of the curve 
(c) In the space provide below sketch the curve in (b) above.
Date posted:
August 19, 2019
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Onyango and Juma live 200km apart. One day, Onyango left his house at 7.00am and travelled toward’s Juma’s house at an average speed of 30km/hr. Juma left his house at 7.30am on the same day and travelled towards Onyango’s at an average speed of 40km/hr.
(a) Determine:-
(i) The time they met.
(ii) The distance from Onyango’s house where the two met.
(iii) How far was Onyango from Juma’s house when they met?
(b) The two took 15 minutes at the meeting point and then travelled to Juma’s house at an average speed of 20km/hr. Find the time he arrived at Juma’s house.
Date posted:
August 19, 2019
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A ship B is on bearing of 0800 from port A and at a distance of 95km. Another ship is stationed at port D which is on a bearing of 2000 from A and a distance of 124km from B. A ship leaves B and moves directly to island P which is on a bearing of 1400 from A.
(a) Using a scale of 1cm to represent 10km, make a scale drawing to show the relative positions of A, B, D and P.
(b) Hence find:-
(i) The distance from A to D.
(ii) The bearing of D from B.
(iii) The bearing of P from D.
(iv) The distance from P to D.
Date posted:
August 19, 2019
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Two rectangles A and B each has an area of 240m2. The length of rectangle A is y m and the length of rectangle B is 4 m longer.
(a) Write down the expression for width in terms of y for
(i)Rectangle A.
(ii) Rectangle B
(b) The widths of the rectangle differ by 3. form an equation in y duly simplified.
(c) Solve the equation in (b) above and hence find the difference between the perimeters of the rectangles.
Date posted:
August 19, 2019
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Using a ruler and a pair of compasses only, construct a triangle ABC such that AB=6cm; BC= 7cm and ∠ABC = 76½o. Locate the region covered by the locus R, such that:
(a) AR ≥ ‘BR’
(b) ∠CAR ≤ ∠BAR
(c) AR ≤ 4.5cm
Date posted:
August 19, 2019
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Five members of ‘SILK’, a self supporting enterprise Jane, Jepchoge, Esther, Mama Charo and Chepkoech were given a certain amount of money to share amongst themselves. Jane got 3/8 of the total amount while Jepchoge got 2/5 of the remainder. The remaining amount was shared equally among Esther, Mama Charo and Chepkoech each of which received Kshs. 6,000;
(a) How much was shared among the five business women?
(b) How much did Jepchoge get?
(c) Jane, Jepchoge and Chepkoech invested their money and earned a profit of Kshs. 12,000. A third of the profit was left to maintain the business and the rest was shared according to their investments. Find how much each got.
Date posted:
August 19, 2019
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Msamaria bus leaves Butere for Nairobi at 7.00 am at an average speed of 80Km/h. Kukhu bus leaves Nairobi towards Butere at 7.30 am on the same day at an average speed of 60km/h. the distance from Nairobi to butere is 450km. after traveling for one and half hours; Kukhu bus developed a mechanical problem which took 45 minutes to repair before continuing at its speed in the same direction.
(a) Determine the time when the two buses met.
(b) Calculate the distance from Nairobi at the time of the two buses meeting.
(c) For how long did the Msamaria bus stay in Nairobi before Kukhu bus arrving at Butere.
Date posted:
August 19, 2019
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A school requires to transport 800 bags of cement from Athi river Portland to butere 500km away. The school can not opt to use a container freight charging shs 3000 for every 25km or pay shs 50 per bag using a lorry to Butere: Which option is cheaper and by how much.
Date posted:
August 19, 2019
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Atieno started a business with a capital of shs. 12,000. Jane joined her after 4 months with a capital of shs. 10,000. Awinja joined them after 10 months with a capital of shs. 8,000. if they made a profit of shs. 16,500 at the end of 15 months; find the share of Jane if they shared all the profit in the ratio of their capital and time in business.
Date posted:
August 19, 2019
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Below is a triangular Prism ABCDEF. A tight string stretches from F to D through R on BC.By drawing accurate net of the solid determine the shortest possible length of the string.
Date posted:
August 19, 2019
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A metallic sphere is immersed in water in a cylindrical container. This causes a rise in the level of water by 7.5cm if the cylinder has a base radius of 7cm. Find the radius of the sphere to 2 d.p
Date posted:
August 19, 2019
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Find the greatest integral value of x which satisfies.
Date posted:
August 19, 2019
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A salesman gets commission of 2% on sales up to shs. 100,000. He gets additional commission of 1½ % on sales above this. He sold goods and allowed a discount of 2%. If he received a commission of Sh. 5792 calculate the sales made.
Date posted:
August 19, 2019
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A parallelogram ABCD has the coordinates A (3,-2) B (2,3) and C ( -4,-2). Using vector method find the co-ordinates of point D.
Date posted:
August 19, 2019
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Solve for x in the following without using a calculator or mathematical tables.
9x( 27(x-1)) = tan 30o
Date posted:
August 19, 2019
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An aircraft takes off from airport A ( 30oS, 45oE) at 11.30 am at a speed of 60 knots to another airport B ( 30oS, 30oE). Calculate the time the aircraft arrived at B.
Date posted:
August 19, 2019
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Simplify completely:
Date posted:
August 19, 2019
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Evaluate the following
Date posted:
August 19, 2019
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Using ruler and a pair of compasses only:
(a) Construct triangle ABC in which BC = 8cm and angle ABC = 1050 and angle BAC = 450.
(b) Drop a perpendicular from A to meet line BC at P. Determine the area of triangle ABC.
Date posted:
August 19, 2019
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(a) Using a ruler and compasses only, construct triangle PQR in which QR=5cm,PR = 7cm and angle PRQ = 105o
(b) Measure PQ and Angle PQR
(c) From P drop a perpendicular to meet QR produced at S
(d) Mark a point T on SP produced such that the area of triangle TQR is half the area of triangle PQR.
(e) Complete the TQR and measure angle QRT
(f) measure ST and angle QTR
Date posted:
August 19, 2019
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Four strings measuring 12cm, 18cm, 24cm and 36cm are cut into pieces of equal length so that exact number of pieces are obtained from each string without wastage. Find the longest length of each string.
Date posted:
August 19, 2019
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Use tables to evaluate:-
Date posted:
August 19, 2019
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The points P(-6, 4) and Q (2,2) are the end points of the diameter of a circle.
(i) Find the coordinates of the centre of the circle.
(ii) Hence find the equation of the circle giving your answer in the form
ax2 + by2 + cx + dy + k = 0
Date posted:
August 19, 2019
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Three businessmen Onyango,Abdul and Mwangi decided to buy bus. The marked price of the bus was sh. 6,800,000. The dealers agreed that the three men could pay a deposit of 60% of the money and the rest to be paid within one year. Onyango, Abdul and Mwangi raised the deposit in the ration 3: 2 :5 respectively.
The balances was to be paid to the dealer from the proceeds from the bus in the same ratio as the deposits. The three men shared the proceeds from the bus in the ratio as the deposits. During the year the bus realized sh. 6,080,000
(a)How much of the deposit did Abdul contribute?
(b)How much of the remaining amount did Mwangi pay at the end of the year ?
(c)After paying the remaining amount at the end of the year, how much money was Onyango left with?
Date posted:
August 19, 2019
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On the figure below, Lm is parallel to PQ. Angle MLR = 300 and angle RPQ = 700. Find the value of x.
Date posted:
August 19, 2019
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The marked price of a modern camera is Kes 24,000. A trader sold it to a customer at a 10% discount. If the trader still made a profit of 20% on the cost price, what was its cost price?
Date posted:
August 19, 2019
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If sin Ф = 15/17 and Ф is acute, find without using calculators or mathematical tables cos Ф + tan Ф.
Date posted:
August 19, 2019
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The figure below is a semi-cylindrical solid of length 18cm and radius 3.5cm as shown.
(a) Draw the labeled net of the solid.
(b) Find the surface area of the solid.
Date posted:
August 19, 2019
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a) Some articles are on sale at two different prices, the dealer being Ksh. 30 per dozen more than the cheaper ones. for kshs . 50, Mary get 9 articles more when she buy cheaper ones than when she by dealer ones. If the dealer articles cost Ksh. X per dozen,
(i) Write the terms of X the number of articles that Mary can buy in both cases.
(ii) Find the cost per dozen of each type of articles.
(b) Mary bought the cheaper articles and sold 3 dozens at a profit of 25 % what was the selling price of each article.
Date posted:
August 19, 2019