The National Examinations Council of Tanzania (NECTA) conducts various examinations, each with its own format. Here are some details about the examination formats:

Primary School Leaving Examination (PSLE)

This exam is for students completing primary education.

The format includes subjects like Mathematics, Science, Social Studies, and Languages.

Official NECTA page.

Download: Primary School Leaving Examination (PSLE) format PDF

Certificate of Secondary Education Examination (CSEE)

Taken by secondary school students.

Subjects include Mathematics, English, Kiswahili, and various other elective subjects.

Download: Certificate of Secondary Education Examination (CSEE) format PDF

Diploma in Secondary Education Examination (DSEE)

For candidates pursuing a diploma in secondary education.

Each subject has a specific examination format, which you can find on the DSEE examination formats page.

Download: Diploma in Secondary Education Examination (DSEE) format PDF

Advanced Certificate of Secondary Education Examination (ACSEE)

Taken by students completing advanced secondary education.

The format covers various subjects, and you can explore the details in the ACSEE examination format booklet.

Download: Advanced Certificate of Secondary Education Examination (ACSEE) format PDF

     OTHER USEFUL FORMAT LINKS     

• Fomatiza mitihani ya ualimu elimu maalumu ngazi ya cheti (daraja la A) 2023
• Mwongozo wa upimaji katika shule za msingi 2022
• Diploma in secondary education examination (DSEE)  2022
• Diploma in secondary education in special needs education (DSE-SNE) examination
• Form two national assessment (FTNA)
• Standard four national assessment (SFNA)
• Darasa la nne
• Fomati ya mtihani wa kumaliza elimu ya msingi (PSLE)
• Primary school leaving examination (PSLE)
• Grade a teachers certificate examination (GATCE)  2022

As we near the culmination of Term One, I want to take a moment to commend each and every one of you for your hard work, dedication, and resilience throughout this term. It's been a journey filled with challenges and triumphs, and your perseverance has not gone unnoticed.

With the end of the term comes a crucial milestone: the Term One Examinations. These assessments serve as an opportunity for you to demonstrate the knowledge and skills you've acquired/shared over the past few months. While exams can be daunting, remember that they are also a chance to showcase your strengths and abilities.

To students: As you prepare for your exams, remember to approach your studies with diligence and determination. Review your notes, ask questions, and seek support from your teachers and peers if needed. Stay focused, stay positive, and believe in your capabilities. You've worked hard, and now is the time to shine.

To teachers: Your guidance and support have been invaluable in shaping the academic journey of our students. As they prepare for their exams, continue to provide them with the encouragement and resources they need to succeed. Your dedication to their learning inspires us all, and we are grateful for your unwavering commitment.

As we enter this crucial period, let's remember the importance of balance. Take breaks when needed, prioritize self-care, and approach the exams with a calm and confident mindset. Remember, your worth is not determined by your exam scores, but by the effort and dedication you put forth every day.

I have full confidence in each and every one of you. Together, we will navigate through these exams with resilience and determination. Let's finish this term strong!

Best wishes,

ADMIN

www.jihudumieschool.com

Wanafunzi na Walimu Wapendwa,

Kufikia mwisho wa Muhula wa Kwanza, ningependa kuchukua muda kidogo kuwapongeza kila mmoja wenu kwa juhudi zenu kubwa, uaminifu, na uimara wenu katika kipindi hiki. Imekuwa safari iliyojaa changamoto na ushindi, na bidii yenu imeonekana.

Mwisho wa Muhula huja na hatua muhimu sana: Mitihani ya Muhula wa Kwanza. Mitihani hii ni fursa kwenu kuonyesha maarifa na ujuzi mliopata/kutoa katika miezi michache iliyopita. Ingawa mitihani inaweza kuwa na wasiwasi, kumbukeni kwamba ni nafasi pia ya kuonyesha umahiri wenu na uwezo wenu.

Kwa wanafunzi: Japo mnajiandaa kwa mitihani yenu, kumbukeni kusoma masomo yenu kwa bidii sana. Hakiki notisi zako, ulizeni maswali, na tafuteni msaada kutoka kwa walimu na wenzenu endapo inahitajika. Endeleeni kuwa na malengo, kuwa na mtazamo chanya, na kuamini katika uwezo wenu. 

Kwa walimu: Mwongozo na msaada wenu umekuwa muhimu katika kuleta sura ya kitaaluma ya wanafunzi wetu. Wanapojiandaa kwa mitihani yao, endeleeni kuwapa moyo na rasilimali wanazohitaji ili kufanikiwa. Azma yenu katika kuelimisha inatuhamasisha sisi sote, na tunashukuru kwa azma yenu isiyoyumba.

Tukiingia katika kipindi hiki muhimu, tukumbuke umuhimu wa kulipa kila somo usawa. Jipimeni wakati inapohitajika, wekeeni kipaumbele huduma ya kibinafsi (kila mmoja anajua anapohitaji kuongeza nguvu zaidi), na elekezeni mitihani kwa mtazamo wa utulivu na ujasiri. Kumbukeni, thamani yenu haiamuliwi na alama zenu za mtihani, bali na jitihada na uaminifu mnaoweka kila siku.

Nina imani kamili katika kila mmoja wenu. Pamoja, tutavuka mitihani hii kwa ushindi. Hadi Muhula Ujao, Mwenyenzi Mungu, awatunze wote.

Salamu,

ADM

www.jihudumieschool.com

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In simpler terms, linear programming helps solve problems where you want to optimize (maximize or minimize) a linear function of several variables, given certain constraints that these variables must satisfy. These constraints could represent limitations on resources, capacities, or other factors.

Linear programming finds applications in various fields such as economics, business management, engineering, and operations research. It's particularly useful in problems involving resource allocation, production planning, transportation, and scheduling.

  DOWNLOAD ALL THESE QUESTIONS AT THE END OF THIS PAGE  

          QUESTIONS           

1.  A dietician wants to create a meal plan that meets the daily nutritional requirements for vitamins A and C. She has two options: granola bars and protein shakes. Each granola bar provides 5 units of vitamin A and 2 units of vitamin C, while each protein shake provides 3 units of vitamin A and 4 units of vitamin C. A granola bar costs TZS 1 and a protein shake costs TZS 2. The dietician wants to minimize the cost of the meal plan while ensuring she meets the minimum daily requirements of 20 units of vitamin A and 30 units of vitamin C.

2.    A recycling plant sorts aluminum cans and plastic bottles. Processing a can yields a profit of 3 cents while processing a bottle yields 5 cents. However, the plant has limited space for processing each material. They can only process a maximum of 1000 cans and 800 bottles per day. Additionally, the sorting machines have limitations. It takes 1 minute to process a can and 2 minutes to process a bottle. The plant has a total of 1200 minutes of processing time available per day.

3.    A movie theater sells popcorn and nachos. Each bag of popcorn has a profit of TZS 1.50 and requires 10 minutes of preparation time. Each order of nachos has a profit of TZS 2.00 and takes 15 minutes to prepare. The theater has two employees dedicated to preparing concessions, and each can work for a maximum of 60 minutes per shift. The manager wants to maximize the total profit from concessions.

4.    A wildlife refuge manager wants to plant a variety of trees to provide food and shelter for different animal species. They have two options: oak trees and maple trees. Each oak tree provides 5 units of food and 3 units of shelter, while each maple tree provides 3 units of food and 4 units of shelter. The refuge has limited space, and they can only plant a maximum of 100 trees. Additionally, the manager wants to ensure at least 200 units of food and 250 units of shelter are available for the animals.

5.    A delivery service uses vans and trucks. Each van can hold 20 packages and costs TZS 3 per delivery, while each truck can hold 50 packages and costs TZS 5 per delivery. The service needs to deliver at least 100 packages but has a daily budget of TZS 150. How many vans and trucks should they use to minimize costs while meeting delivery needs?

6.    A furniture company builds chairs and tables. Each chair requires 2 hours of woodworking and 1 hour of finishing, while each table requires 3 hours of woodworking and 2 hours of finishing. The company has 100 hours of woodworking and 60 hours of finishing available per week. How many chairs and tables should they produce to maximize profit if each chair earns TZS 20 and each table earns TZS 30?

7.    A person with dietary restrictions needs to consume a certain amount of protein and carbohydrates daily. They can achieve this through two food options: shakes and bars. Each shake provides 10 grams of protein and 20 grams of carbohydrates, while each bar provides 20 grams of protein and 10 grams of carbohydrates. They need at least 100 grams of protein and 150 grams of carbohydrates daily. How many shakes and bars should they consume to minimize cost if each shake costs TZS 2 and each bar costs TZS 1?

8.    A coffee roaster wants to create a new coffee blend by mixing two types of beans: Arabica and Robusta. Arabica beans cost TZS 4 per pound and have a caffeine content of 1.2%, while Robusta beans cost TZS 2 per pound and have a caffeine content of 2.4%. The roaster wants to create a 10-pound blend with a caffeine content between 1.5% and 1.8%. How many pounds of each bean type should be used?

9.    A travel agency offers two vacation packages: a beach trip and a mountain adventure. The beach trip generates a profit of TZS 100 per person and requires 2 days, while the mountain adventure generates a profit of TZS 150 per person and requires 3 days. The agency has 10 guides available for a total of 20 days. How many people should they send on each trip to maximize profit?

10.                  A farmer has land available to plant corn and soybeans. Planting one acre of corn costs TZS 100 and yields a profit of TZS 150,while planting one acre of soybeans costs TZS 80 and yields a profit of TZS 120. The farmer has a budget of TZS 12,000 and wants to plant a total of 100 acres. How many acres of each crop should be planted to maximize profit?

11.                  A magazine publisher offers two subscription options: print and online. A print subscription costs TZS 20 per year and requires TZS 5 for printing and distribution, while an online subscription costs TZS 10 per year. The publisher has a printing budget of TZS 10,000 and wants to have at least 2,000 total subscribers. How many of each type of subscription should they offer to maximize profit?

12.                  A factory has two machines available for production. Machine A can produce widget A in 2 minutes and widget B in 3 minutes. Machine B can produce widget A in 1 minute and widget B in 4 minutes. There are orders for 100 units of widget A and 80 units of widget B. How much time should each machine spend on each widget to minimize total production time?

13.                  A company wants to create a vitamin supplement mix by combining two powders: powder X and powder Y. Powder X contains 2 mg of vitamin A and 3 mg of vitamin C per gram, while powder Y contains 4 mg of vitamin A and 1 mg of vitamin C per gram. They want the final mix to contain at least 100 mg of vitamin A and 80 mg of vitamin C.Additionally, powder X costs TZS 1 per gram and powder Y costs TZS 2 per gram. How many grams of each powder should be used to minimize cost?

14.                  An investor wants to allocate their portfolio between stocks and bonds. Stocks have a higher expected return of 10% but also carry a higher risk. Bonds have a lower expected return of 5% but are considered safer. The investor wants at least an 8% overall return on their investment and wants to invest a total of TZS 100,000. How much should they invest in each option to achieve their desired return while staying within their budget?

15.                  Recycling Center Sorting: A recycling center sorts plastic bottles and aluminum cans. Sorting a plastic bottle takes 2 minutes and yields a profit of 4 cents, while sorting an aluminum can takes 1 minute and yields a profit of 3 cents. The center has a total of 120 minutes of sorting time available and wants to maximize their profit. However, due to limited space, they can only process a maximum of 800 bottles and 1000 cans per day.

16.                  Running Shoe Design: A shoe company designs running shoes with different levels of cushioning and responsiveness.Shoe A prioritizes cushioning and takes 4 hours to produce, while shoe B prioritizes responsiveness and takes 3 hours to produce. The company has 100 hours of production time available per day. They want to create at least 50 pairs of each shoe type but also want to maximize the total responsiveness score for their daily production. (Responsiveness score is assigned based on shoe design).

17.                  A clothing manufacturer produces shirts and pants. Each shirt takes 1 hour of cutting and 2 hours of sewing, while each pair of pants takes 2 hours of cutting and 3 hours of sewing. The company has 100 hours of cutting time and 120 hours of sewing time available per day. They want to maximize their profit if each shirt earns TZS 10 and each pair of pants earns TZS 15.

18.                  A furniture factory produces tables and chairs. Each table requires 4 units of wood and 2 units of paint, while each chair requires 2 units of wood and 3 units of paint. The factory has a limited supply of 100 units of wood and 80 units of paint. They want to maximize their profit if each table earns TZS 50 and each chair earns TZS 30.

19.                  A bakery produces cookies and muffins. Each cookie requires 0.5 kg of flour and 0.2 kg of sugar, while each muffin requires 0.3 kg of flour and 0.4 kg of sugar. The bakery has 50 kg of flour and 40 kg of sugar available. They want to minimize the amount of unused flour and sugar while producing at least 100 units of baked goods (cookies + muffins).

20.                  A car manufacturer needs to produce a certain number of sedans and SUVs. Each sedan requires 200 units of steel and 100 units of aluminum, while each SUV requires 300 units of steel and 150 units of aluminum. The manufacturer has a total of 10,000 units of steel and 8,000 units of aluminum available. They need to produce at least 50 sedans and 40 SUVs. How many of each should be produced to minimize leftover materials?

21.                  A company produces two types of electronic devices: laptops and tablets. Each laptop requires 5 hours of assembly and 2 hours of testing, while each tablet requires 3 hours of assembly and 1 hour of testing. The company has 100 hours of assembly time and 60 hours of testing time available per week. They want to maximize their profit if each laptop earns TZS 200 and each tablet earns TZS 100.

22.                  A hospital needs to allocate nurses to two departments: emergency and surgery. Each nurse assigned to the emergency department can handle 5 patients per day, while each nurse assigned to surgery can handle 3 patients per day. The hospital has 20 nurses available and needs to handle at least 80 patients per day (40 in emergency and 40 in surgery). How many nurses should be assigned to each department to minimize idle staff time?

23.                  A construction company has two cranes available for lifting materials. Crane A can lift loads up to 5 tons in 1 hour,while Crane B can lift loads up to 3 tons in 1 hour. They need to lift a total of 20 tons of materials within 4 hours.How much time should each crane be used to minimize total lifting time?

24.                  A city needs to allocate water from two reservoirs to meet daily demand. Reservoir A can supply 1 million gallons per day, while Reservoir B can supply 0.8 million gallons per day. The city has a daily water demand of 1.5 million gallons. Additionally, due to maintenance, Reservoir A can only be used for a maximum of 2 days. How much water should be drawn from each reservoir to meet the demand while minimizing the use of Reservoir A?

25.                  A farmer has land available to plant corn and wheat. Planting one acre of corn costs TZS 120 and yields a profit of TZS 180, while planting one acre of wheat costs TZS 100 and yields a profit of TZS 150. The farmer has a budget of TZS 15,000 and wants to plant a total of 120 acres. How many acres of each crop should be planted to maximize profit?

26.                  A company has two warehouses located in different cities. Warehouse A has a storage capacity of 1000 units, while Warehouse B has a capacity of 800 units. The company needs to ship a total of 1200 units of product to two retail stores. Store A requires 600 units, and Store B requires 800 units. How many units should be shipped from each warehouse to minimize transportation costs (consider distance factors)?

27.                  A fitness trainer wants to create a personalized meal plan for a client using two protein supplements: whey protein and casein protein. Whey protein is faster absorbing and costs TZS 2 per serving, while casein protein is slower absorbing and costs TZS 1.50 per serving. The client needs at least 100 grams of protein per day, with at least 30 grams coming from a fast-absorbing source (whey protein). How many servings of each protein should be included in the plan to minimize cost?

28.                  A web design agency has two teams working on different aspects of a client's website. Team A specializes in front-end development and takes 2 hours per page, while Team B specializes in back-end development and takes 3 hours per page. The website needs a total of 10 pages developed, with at least 4 pages requiring back-end development. How many pages should be assigned to each team to minimize the total development time?

29.                  A foundry needs to create a metal alloy for a specific project. They can use two types of metal: alloy X and alloy Y. Alloy X is stronger but more expensive at TZS 5 per kilogram, while alloy Y is weaker but cheaper at TZS 3 per kilogram. The final alloy needs to have a minimum tensile strength of 100 MPa. Additionally, the weight of the alloy needs to be at least 200 kilograms. How many kilograms of each alloy should be used to minimize cost while meeting the strength and weight requirements?

30.                  A conservation group wants to restore a wetland habitat by planting two types of native plants: reeds and bulrushes. Reeds help filter water and cost TZS 2 per plant, while bulrushes provide shelter for aquatic animals and cost TZS 1 per plant. The group needs to plant at least 1000 plants and wants to maximize the total water filtration capacity of the restored habitat. (Water filtration capacity is assigned based on plant type).

31.                  A newspaper delivery company wants to optimize its delivery routes. They have two options: using delivery trucks or hiring freelance cyclists. Trucks can deliver to 50 houses per hour but have a fixed cost of TZS 20 per route. Cyclists can deliver to 20 houses per hour but only have a cost of TZS 2 per house delivered. The company needs to deliver to at least 1000 houses and wants to minimize the total delivery cost.

32.                  A movie theater wants to create a new snack mix by combining popcorn and pretzels.Popcorn has a higher profit margin but is also higher in calories, while pretzels are lower in calories but have a lower profit margin. The theater wants to create a mix that is at least 50% popcorn by volume but also wants to keep the total calorie count per serving below 300. How many ounces of each snack should be included in the mix to maximize profit?

33.                  A power company wants to generate electricity using two sources: solar and wind power. Solar power plants are more expensive to build but have lower operating costs, while wind power plants are cheaper to build but have higher operating costs. The company needs to generate a minimum of 100 megawatts of electricity and wants to minimize the total cost of production (including building and operating costs).

34.                  An airline wants to determine the optimal prices for economy and business class tickets on a specific route. The airline has a limited number of seats available in each class and wants to maximize their total revenue.They also need to consider historical data on demand and pricing for both classes to ensure they remain competitive.

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