**THE UNITED REPUBLIC OF TANZANIA NATIONAL EXAMINATIONS**

**COUNCIL OF TANZANIA **

**FORM TWO NATIONAL ASSESSMENT**

**041 BASIC MATHEMATICS**

__Time: 2:30 Hours Year: 2020__

**Instructions**

1.This paper consists of ten (10) compulsory questions.

2.Show clearly all the working and answers in the space provided.

3.All writing must be in blue or black ink except drawings which must be in pencil.

4.NECTA mathematical tables, geometric instruments and graph papers may be used where necessary.

5.All communication devices and calculators are not allowed in the assessment room.

6.Write your Assessment Number at the top right corner of every page

1. (a) Write each of the numbers 18, 24 and 36 as a product of prime factors and hence find their greatest common factor.

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(b) Write the number 0.009765:

(i)correct to three decimal places

(ii)correct to three significant figures

(iii)State the place value of 9 in the given number.

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2(a) Find the value of the expression

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(b) (i) In a sales promotion, the price of a shirt costing shs. 15,000/= is reduced by 15%. What is the new price of the shirt?

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(ii) Change into a fraction in its simplest form

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3.(a) A lorry carries 7.2 tonnes of sand from the mining area to the industrial site. On the way 230 kg of sand either fall off or blow away. What mass of sand will remain by the end of the journey? Give the answer in tonnes.

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(b) An article was sold for shs 160,000 at a profit of 25%. Find the buying price of the article.

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4.(a) Find the values of x and y in the following figure.

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(b) Suppose a metal wire is bent to form a semi-circle with a radius of 14 cm. Find; (i) The total length of the metal wire.

(ii) The area bounded by the metal wire.

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5(a) The sum of two timbers is 127. If the difference between the numbers is 7, find the numbers.

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(b) Solve the equation x^{2}-10x +13=0 by completing the square. Leave the answer in surd form

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6. (a) (i) Find the equation of a line passing through the point P(-1, 4) and has a gradient of 10.

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(b) Find the image of the point P (4,1) when it is;

(i)reflected in the x-axis

(ii)reflected in the line y = x. (iii) translated by the point T (3, 5)

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7.(a) If

Find values of x and y

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(b)(i) Find the value of 0.0000234x 120 in standard notation, correct to three significant figures

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(ii) Rationalize the denominator of the expression

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8.(a) the following figure, *AB = AC,* prove that the angles *ABD* and *ACD* are also equal

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(b) If the rectangular metal sheets *ABCD* and *WXYZ* are similar, calculate the length of XY when *AB =* 2 *cm* , *BC =*4 *cm* and *WX* = 2.5 *cm* .

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9.(a) Figure *PQR* represents a triangular floor such that *PQ =QR=* 2 cm and angle *PQR* is 90 . Find *PR ,* correct to two decimal places.

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(b) Given that

Find :

(i)

(ii)

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10. (a) In a certain village, 300 people were interviewed about their food preference. It was found that, 200 people like banana, 120 people like rice and 60 people like both banana and rice. By using formula, find the number of people who like neither banana nor rice.

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(b) The masses of a group of students from Kilimani secondary school were recorded as shown in the following table:

Mass in kilograms | 31 - 40 | 41 - 50 | 51 - 60 | 61 - 70 | 71 - 80 |

Frequency | 2 | 5 | 3 | 9 | 1 |

(i)How many students are there in the group?

(ii)State the class interval that has the largest number of students.

(iii)Prepare a table showing the class boundaries and the corresponding cumulative frequencies.

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