Form Four Basic Mathematics Past Paper 2024 PDF

THE UNITED REPUBLIC OF TANZANIA PRESIDENT’S OFFICE REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT FORM FOUR SPECIAL SCHOOLS SYNDICATE JOINT EXAMINATION, 2024 Code: 041 BASIC MATHEMATICS Time: 3:00 Hrs. Tuesday 17-S...

THE UNITED REPUBLIC OF TANZANIA PRESIDENT’S OFFICE REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT FORM FOUR SPECIAL SCHOOLS SYNDICATE JOINT EXAMINATION, 2024 Code: 041 BASIC MATHEMATICS Time: 3:00 Hrs. Tuesday 17-September-2024 AM Instructions 1. This paper consists of fourteen (14) compulsory questions. 2. All necessary working and answers for each question must be shown clearly in the answer sheet(s) provided. 3. All writing must be in blue or black ink except drawings, which must be in pencil. 4. Necta Mathematical tables, Geometrical instruments and graph paper may be used where necessary. 5. All communication devices and unauthorized materials are not allowed in the examination room. 6. Write your Examination Number on every page of your answer booklet(s). Page 1 of 6  SECTION A (60 Marks) Answer all questions 1. (a) (i) Determine the common factors of the numbers 36 and 54. (ii) Kibasila was told by his teacher to find the total integers 𝑍 on the interval 3 − 2 < 𝑍 ≤ 2. What correct answer did he get? (b) A customer at MALAIKA restaurant spent one−fifth of the money she had on breakfast. She then spent one−third of what remained on dinner. After all these expenses she found that she has 32,000 Tanzanian shillings remaining. Find the amount of money she had initially. 1 (2𝑥) 1 −𝑥 1 1 𝑥 2. (a) Solve for the value of 𝑥 in equation (9) (3) ÷ 27 − (243) = 0 2 (b) (i) Express the square of the expression in a simplified form. 2+2√3 (ii) If 𝑙𝑜𝑔2 = 0.3010 and 𝑙𝑜𝑔3 = 0.4771, evaluate 𝑙𝑜𝑔1.5 3. (a) Out of 150 failures at Mamboleo secondary school over a period of 5 years, 60% were caused by absenteeism and 30% by low remembering capacity. If 20% were caused by low remembering capacity but not absenteeism, find the number of students whose failures were caused by factors other than the two mentioned. (b) Crest hotel has 30 rooms which are single or double rooms. If a room is 1 chosen at randomly, the probability of choosing a single room is , find the 6 number of double rooms in the hotel. 4. (a) A figure below represents two lines 𝐴𝐵 and 𝑀𝑁 intersecting at point 𝑀. If 𝐴𝑀 = 𝐵𝑀, determine the equation of line 𝑀𝑁 in the form 𝑎𝑥 + 𝑏𝑦 + 𝑐 = 0 given that points 𝐴 and 𝐵 are (4, 8) and (6, 0) respectively. Page 2 of 6  1 (b) (i) Given the position vectors 𝑎 = 3𝑖 + 2𝑗 and 𝑏 = 6𝑖 − 2𝑗. If 𝑐 = 𝑎 − 𝑏, how 2 far is vector 𝑐 from the origin? (ii) The football ground at Dutwa secondary school is 250 metres at a bearing of 0450 from administration block and the library is 200 metres at a bearing of 0900 from football ground. By representing this information on a well labelled diagram, determine the displacement from library to administration block. 5. (a) Find the perimeter of a regular polygon of interior angle of 1440 when inscribed to the circle of a radius of 10 𝑐𝑚. (b) A plot of land with an equilateral triangular shape has a side of 40 metres. Find its area correct to two decimal places. 6. (a) A bottle of soda costs 600 Tanzanian shillings. If 20 Tanzanian shillings is equivalent to 1 Kenyan shilling, find the price of the bottle of soda in Kenyan shillings. (b) 𝑃 varies directly as the square of 𝑁. If the value of 𝑁 is increased by 20%, determine the percentage increase of the value of 𝑃. 7. (a) At Kingalu market in Morogoro, the ratio of men to women is 7:12. If there are present 1380 women, find the number of men in the market. (b) Miss Subira started the business on 16th March,2020 with a capital in cash Tshs. 66,000/=. March. 17 bought goods for cash Tshs. 40,000/= 19 sold goods for cash Tshs. 30,000/= 21 purchases goods for cash Tshs. 25,000/= 22 sold goods for cash Tshs. 20,000/= 24 advertising for cash Tshs. 5,000/= 26 paid rent Tshs. 15, 000/= 27 sold goods on credit to Mr Ngumbuke Tshs. 10,000/= Record and close the above transactions in the cash account. 8. (a) Using the concept of arithmetic progression, find the sum of the first 50 even positive integers. (b) A business person borrows two million shillings from Azania bank at 7% interest rate compounded quarterly, and repays 90,000 shillings at the end of each month. How much does he still owe the bank at the end of two years? Page 3 of 6 9. (a) (i) A tree which is 8 metres high, casts the shadow with length 6 metres long. Find the distance between the end of the shadow to the top of the tree. (ii) Given the expression 13 𝑠𝑖𝑛 𝜃 = 5. If 𝜃 is an obtuse angle, find the value of 𝑐𝑜𝑠 𝜃. (b) Below is the location of the houses of Abdera, Benadetha and Cosmas. How far is Abdera’s house from benadetha’s house? 10. (a) A BODABODA rental man charges Tshs 3,000 a day and Tshs 150 per kilometre for renting a motorcycle. Josiah rents a motorcycle for two days and his bill comes to Tshs 10,800. How many kilometres did he drive? 1 (b) If the values 𝑥 = 1 and 𝑥 = − 4 are only potential solutions of the equation 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 where 𝑎, 𝑏 and 𝑐 are integers, determine the values of 𝑎, 𝑏 and 𝑐. SECTION B (40 Marks) Answer all questions 11. (a) The final scores in a computer science test of 62 candidates were recorded as shown in the table below. scores 65 - 69 70 - 74 75 - 79 80 - 84 85 - 89 90 - 94 No. of candidates 10 12 18 6 9 7 (i) Calculate the median score of the distribution. (ii) Draw the histogram and from it estimate the mode of the distribution. (b) Study the figure below, and hence; Page 4 of 6  (i) Prove that 𝐴𝐵̂ 𝐶 = 𝐶𝐷 ̂𝐸 (ii) Find the value of the angle marked 𝑛. 12. (a) (i) A rectangular pyramid with base PQRS of dimensions 8 cm and 6 cm has a vertex at point W. If each slanting edge has a size of 10 cm, find the angle ̅̅̅̅̅ makes with the plane PQRS. that a line 𝑊𝑅 (ii) Find the volume of the following right prism given that ̅̅̅̅ 𝐴𝐵 = 5 𝑐𝑚, ̅̅̅̅ = 10, ̅̅̅̅ 𝐵𝐶 𝐴𝐸 = ̅̅̅̅ 𝐵𝐹 = 2 𝑐𝑚 and E Aˆ B  60 0. (b) A ship leaves from town 𝑅(400 𝑆, 1720 𝐸) to town 𝑃(400 𝑆, 1780 𝐸) on Friday 06: 30 p.m. when steaming at 15 knots. Find when will it arrive to town 𝑃. 1 3 3 2 13. (a) Given that 𝐴 = ( ) and 𝐵 = ( ). Find the value of 𝐴2 + 3𝐵. −2 0 0 1 (b) A farmer has 83000 Tanzanian shillings for buying planting and growing fertilizers. If he buys 2 bags of planting fertilizers and 2 bags of growing fertilizers, he remains with 9000 Tanzanian shillings. If he buys 1 bag of planting fertilizers and 3 bags of growing fertilizers he spends all the money. Using the inverse matrix method, find the price of each bag of planting fertilizers and each bag of growing fertilizers. (c) Find the coordinates of a point 𝑃(3, 0) after a rotation through 1800 clockwise about the origin followed by a reflection in the line 𝑦 = 𝑥√3. Leave your answer in surd form. Page 5 of 6 14. (a) A step function 𝑓 is defined on the set of real numbers such that 𝑥 2 𝑖𝑓 𝑥 > 1 𝑓(𝑥) = {. Compute 𝑓(−3) and 𝑓(√5) 𝑥 − 4 𝑖𝑓 𝑥 ≤ 1 (b) The Upendo furniture company Limited has two workshops which produce timber used in manufacture of tables and chairs. In one day operation, workshop A can produce timber required to manufacture 20 tables and 60 chairs and workshop B can produce the timber required to manufacture 25 tables and 50 chairs. The company needs enough timber to manufacture at least 200 tables and 500 chairs. If it costs 100,000 shillings to operate workshop A for one day and 90,000 shillings to operate workshop B for one day, then; (i) How many days should each workshop be operated in order to produce a sufficient amount of timber at a minimum cost? (ii) Determine that minimum cost. 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