THE UNITED REPUBLIC OF TANZANIA NATIONAL EXAMINATIONS COUNCIL OF TANZANIA
CERTIFICATE OF SECONDARY EDUCATION EXAMINATION
041 BASIC MATHEMATICS
(For Both School and Private Candidates)
Time: 3 Hours Wednesday, 06^{th} November 2019 a.m.
Instructions
SECTION A (60 Marks)
Answer all questions in this section.
1. (a) Mangoes are to be exactly divided into groups of 20, 30 or 36 .What is the minimum number of mangoes required?
View Ans(b) Mary was given 60,000 shillings by her mother. She spent 35 percent of the money to buy shoes and 10 percent of the remaining money to buy books. How much money remained?
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2(b) Find the value of expression
By using mathematical table
View Ans3.(a)Use the following diagram to answer the question that follows
(i) Find the number of subsets of set B (ii) Find the elements of set AnB.
(iii) If an element is picked at random from the universal set (U), find the probability that it is not the element of set B.
View Ans3(b) The Ministry of Business and Industries has planned to employ 54 people who will work in the business sector, 36 people who will work in industries sector only, 12 people who will work in both sectors and 21 people who will neither work in business sector nor in industries sector. How many people will be employed by the Ministry? (Use a Venn diagram).
View Ans4(a) Find the equation of a line which passes through the point A(3, 4) and which is parallel to the line 3x + 4y  15=0.
View Ans4(b) The points P, Q and R are (5, —3), (6, I) and (1, 8) respectively. Show that these points form an isosceles triangle.
View Ans5.(a) If AB is parallel to CD and PQ is a transversal. sketch the line segments and label on the same diagram the following pairs angles:
(i) corresponding angles a and g.
(ii) alternate interior angles f and g, (iii) vertically opposite angles c and d.
View Ans5. (b) Given that triangle ABC is similar to triangle PQR, AB = 4 cm, BC =5 cm, PQ = 18 cm and angle PQR is 30, find the area of triangle PQR.
View Ans6.(a) Mr. Ogango from Kenya visited Tanzania. He had 5,000 Kenya shillings (Kshs) and wanted to change the money into US dollar. If 1 US dollar was equivalent to 2500 Tanzania shillings (Tshs) and Ksh 1 was equivalent to Tshs 20, how much US dollars did he get?
View Ans6. (b) A gardener has found that the time t to cut the grass on a square field varies directly as the square of its length (L) and inversely as the number of men (m) doing that job. If 5 men cut grass on a field of side 50 m in 3 hours, how many more men are required to cut grass on a field of side 100 m in 5 hours? Assume that the men are working on the same pace.
View Ans7(a) Misumbwi, Shuma and Kiyando contributed 770,000, 560,000 and 1,050,000
shillings respectively to start a business. Find the ratio of their contribution in its simplest form.
View Ans(b) Use the following trial balance to prepare trading, profit and loss account of Mr.
Rwaichi as at 31^{st} December 2015
Account Name  Dr  Cr 
Cash  1,750,000 

Capital 
 2,500,000 
Purchases  2,300,000 

Rent  200,000 

Furniture  550,000 

Shelves  350,000 

Sales 
 3,000,000 
Salary  250,000 

Wages  100,000 

 5,500,000  5,500,000 
8.(a)Given that 49, x and 81 are consecutive terms of a geometric progression. Find:
(i) The value of x.
(ii)The geometric mean.
View Ans(b) A wall is in the shape of a trapezium. The first level of wall is madeup of 50 bricks where as the top level has 14 bricks. If the levels differ from each other by 4 bricks, determine the number of
(i) levels of the bricks.
(ii) bricks used to make the wall.
View Ans9.(a) The following diagram shows the location of the houses A, B and C. How far is house A from B? Give your answer to the nearest meter.
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9. (b) A rectangular frame is made of wooden bars. The diagonal of the frame is 25 cm long and its width is 15 cm. Find the length of the frame.
View Ans10.(a) Factorize the quadratic expression 3x^{2}  11x  20 by splitting the middle term
View Ans10.(b) Solve the equation 2x^{2} + 3x  5=0 by completing the square
View AnsSECTION B( 40 Marks)
Answer All Questions
11.The number of patients who attended maternity clinic daily in June 2 in a certain village was recorded as follows:
52  61  42  27  38  44  56  36  73  22 
41  48  77  30  46  43  72  63  43  76 
47  53  38  55  60  51  47  58  33  37 
(a) Make a frequency distribution by grouping the number of patients in the class intervals: 20  29, 30  39, 40  49, ....
(b)By using the frequency distribution table obtained in part (a), calculate the mean number of patients per day.
(c) Construct a pie chart for the frequency distribution obtained in part (a).
View Ans12.(a) A ship sails from Pemba (4.5^{°}S, 39.5^{°}E) to Dar es salaam (7.5^{°}S, 39.5^{°}E). If it leaves Pemba at 11:30 am and arrived in Dar es salaam at 13:30 pm, use and R_{E}=6370km to find speed of ship in km/h
View Ans(b) Sketch a square pyramid whose base is PQRS, vertex is at W and centre is at N, then answer the questions that follow:
(i) State the projection of
(ii) Name the angles between
View Ans(c) The volume of a square pyramid is 28.2 cm^{3}. If the sides of its base are 4 cm long, find the height of the pyramid correct to one decimal place.
View Ans13.(a)(i) Given the matrices .
Find
View Ans(ii) If the matrix is singular, find the possible value of k
View Ans(b)Solve the following system of linear equations by using inverse matrix method
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(c) By using transformation matrix find image of point . Hence state the axis in which point is reflected.
View Ans14.(a) Calculate the values of if f is defined as
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(b) Using information given in part (a), find
View Ans(c) A trader has a space for 5 refrigerators. The trader plans to spend 2,400,000 shillings to buy refrigerators of two brands, Hitachi and Sony. Each Hitachi refrigerator costs 600,000 shillings whereas each Sony refrigerator costs 400,000 shillings. The unit profits for Hitachi and Sony refrigerators are 200,000 shillings and 150,000 shillings respectively. Denoting x and y as the number of Hitachi and Sony refrigerators respectively, determine the number of refrigerators for each brand that maximizes the profit.
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