Form 4 Mathematics
A workshop makes cupboards and tables using two artisans A and B every cupboard made requires 3 days of work by artisan A and 2 days of work by artisan B. Every table made requires 2 days of work by artisan A and 2 days of work by artisan B.
In one month artisan A worked in less than 24 while artisan B Worked for Not More Than 18 Days. The workshop made x cupboards and y tables in that month. (a) Write all the inequalities which must be satisfied by x and y. (b) Represent the inequalities in (a) on the grid provided. (c) The workshop makes a profit of Ksh 6 000 on each cupboard and Ksh4 000 on each table. Find the number of cupboards and the number of tables that must be made for maximum profit and hence determine the maximum profit.
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Form 4 MathematicsDiet expert makes up a food production for sale by mixing two ingredients N and S. One kilogram of N contains 25 units of protein and 30 units of vitamins. One kilogram of S contains 50 units of protein and 45 units of vitamins. If one bag of the mixture contains x kg of N and y kg of S. (a) Write down all the inequalities, in terms of x and representing the information above ( 2 marks)
Answer
Form 4 Mathematics
A hotel buys beef and mutton daily. The amount of beef bought must be at least 30kg and that of mutton at least 20 kg. The total mass of beef and mutton bought should not exceed 100 kg. The beef is bought at Ksh 360 per kg and the mutton at Ksh 480 per kg.
The amount of money spent on both beef and mutton should not exceed Ksh 43 200 per day. Let x represent the number of kilograms of beef and y the number of kilograms of mutton. (a) Write the inequalities that represent the above information. (b) On the grid provided, draw the inequalities in (a) above. (c) The hotel makes a profit of ksh 50 on each kg of beef and ksh 60 on each kg of mutton. Determine the maximum profit the hotel can make
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Form 4 Mathematics
A trader stocks two brands of rice A and B. The rice is packed in packets of the same size. The trader intends to order fresh supplies but his store can accommodate a maximum of 500 packets. He orders at least twice as many packets of A as of B.
He requires at least 50 packets of B and more than 250 packets of A. If he orders x packets of A and y packets of B, (a) Write the inequalities in terms of x and y which satisfy the above information. (b) On the grid provided represent the inequalities in part (a) above (c) The trader makes a profit of Ksh 12 on a packet of type A rice and Ksh 8 on a packet of type B rice. Determine the maximum profit the trader can make.
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Form 2 Mathematics
The diagram below shows a region R bounded by three lines L1 L2 L3
Form the three inequalities that satisfy the given region R.
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Form 2 Mathematics
A school decided to buy at least 32 bags of maize and beans. The number of bags of beans were Lo be at least 6. A bag of maize costs Ksh 2500 and a bag of beans costs Ksh 3 500, The school had Ksh 100 000 to purchase the maize and beans. Write down all the inequalities that satisfy the above information,
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Form 2 Mathematics
A school decided to buy at least 32 bags of maize and beans. The number of bags of maize were to be more than 20 and the number of bags of beans were to
be at least 6. A bag of maize costs Ksh 2500 and a bag of beans costs Ksh 3500. The school had Ksh 100 000 to purchase the maize and beans. Write down all the inequalities that satisfy the above information.
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The dimensions of a rectangular floor of a proposed building are such that!
• the length is greater than the width but at most twice the width; • the sum of the width and the length is, more than 8 metres but less than 20 metres. If'x represents the width and y the length. (a) write inequalities to represent the above information. (b) (i) Represent the inequalities in part (a) above on the grid provided. (ii) Using the integral values of x and y, find the maximum possible area of the floor.
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Form 4 Mathematics
Omondi makes two types of shoes: A and B. He takes 3 hours to make one pair of type A and 4 hours to make one pair of type B. He works for a maximum of 120 hours to x pairs of type A and Y pairs of type B.It costs him sh 400 to make a pair of type A and sh 150 to make a pair of type B.
His total cost does not exceed sh 9000. He must make 8 pairs of type A and more than 12 pairs of type B.
aNSWER
Form 4 Mathematics
A mixed school can accommodate a maximum of 440 students. The number of girls must be at least 120 while the number of boys must exceed 150. Taking x to represent the number of boys and y the number of girls, write down all he inequalities representing the information above.
Answer
Form 4 Mathematics
A building contractor has two lorries, P and Q, used to transport at least 42 tonnes of sand to a building site. Lorry P carries 4 tonnes of sand per trip while lorry Q
carries 6 tonnes of sand per trip. Lorry P uses 2 litres of fuel per trip while lorry Q uses 4 litres of fuel per trip. The two lorries are to use less than 32 litres of fuel. The number of trips made by lorry P should be less than 3 times the number of trips made by lorry Q. Lorry P should make more than 4 trips. (a) Taking x to represent the number of trips made by lorry P and y to represent the number of trips made by lorry Q, write the inequalities that represent the above information. (b) On the grid provided, draw the inequalities and shade the unwanted regions. (c) Use the graph drawn in (b) above to determine the number of trips made by lorry P and by lorry Q to deliver the greatest amount of sand.
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Form 4 Mathematics
A company is considering installing two types of machines. A and B. The information about each type of machine is given in the table below.
The company decided to install x machines of types A and y machines of type B(a) Write down the inequalities that express the following conditions
I. The number of operators available is 40 II. The floor space available is 80m2 III. The company is to install not less than 3 type of A machine IV. The number of type B machines must be more than one third the number of type A machines (b) On the grid provided, draw the inequalities in part ( a) above and shade the unwanted region (c) Draw a search line and use it to determine the number of machines of each type that should be installed to maximize the daily profit.
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Form 4 Mathematics
Mwanjoki flying company operates a flying service. It has two types of aeroplanes. The smaller one uses 180 litres of fuel per hour while the bigger one uses 300 litres per hour.
The fuel available per week is 18,000 litres. The company is allowed 80 flying hours per week while the smaller aeroplane must be flown for y hours per week. (a) Write down all the inequalities representing the above information (b) On the grid provided on page 21, draw all the inequalities in a) above by shading the unwanted regions (c) The profits on the smaller aeroplane is Kshs 4000 per hour while that on the bigger one is Kshs 6000 per hour Use the graph drawn in (b) above to determine the maximum profit that the company made per week.
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Form 4 Mathematics
Bot juice Company has two types of machines, A and B, for juice production. Type A machine can produce 800 litres per day while type B machine produces 1,600 litres per day.
Type A machine needs 4 operators and type B machine needs 7 operators. At least 8,000 litres must be produced daily and the total number of operators should not exceed 41. There should be 2 more machines of each type. Let x be the number of machines of type A and Y the number of machines for type B,
Answer
Form 4 MathematicsThe diagram below shows the graph of: Y ≥ 3/10x – 3/2, 5x + 6y = 30 and x = 2 
By shading the unwanted region, determine and label the region R that satisfies the three inequalities. Y ≥ 3/10x – 3/2 , + 6y ≥ 30 and x ≥ 2
aNSWER
Form 4 Mathematics
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 cost Kshs 16,000 to stage a show and the theater 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.
Answer
 An institute offers two types of courses technical and business courses. The institute has a capacity of 500 students. There must be more business students than technical students but at least 200 students must take technical courses. Let x represent the number of technical students and y the number of business students.
A school has to take 384 people for a tour. There are two types of buses available, type X and type Y. Type X can carry 64 passengers and type Y can carry 48 passengers. They have to use at least 7 buses.
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