**THE UNITED REPUBLIC OF TANZANIA NATIONAL EXAMINATIONS COUNCIL OF TANZANIA**

**FORM TWO NATIONAL ASSESSMENT**

**041 BASIC MATHEMATICS**

*Time: 2:30 Hours Tuesday, 13th November 2018 a.m.*

**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. Four figure mathematical tables, **geometric **instruments and graph papers may be used where necessary.

5. All communication devices, calculators and any **unauthorized **materials

are not allowed in the examination room.

6. Write your **Examination Number** at the top right hand corner of every page.

1.(a) A block is cut into equal units of l0g, 20g and 35g. Use prime factorization method to find the smallest possible mass of the block form which the pieces can be cut.

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(b) Evaluate 0.864 ÷ 0.0246 giving your answer correct to 2 significant figures.

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2.(a) Find out which of the two fractions, is greater.

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(b)If 0.125 of all students in a mixed class are girls, what percentage of students are boys?

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3.(a) Subtract:

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(b)Find the simple interest on sh. 10,000,000 invested for 5 years at the rate of 6% per annum.

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4.(a] calculate the size of angle x and y in the following figure:

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(b) Find the perimeter of a right angled triangle whose base is cm and height is cm

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5. (a) Solve the equation

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(b) Solve the following Eqn. 4(p + 1)(1 - p)=3

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6.(a) If the slope of the straight line through the points (7,4) and (-2, k) is 1, find the value of k.

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(b) By using a sketch, find the image of the point A (5, 2) under a reflection in the line y = 0, followed by another reflection in the line y = *x*

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7. (a) Use laws of exponents to simplify

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(b) If log 2 = 0.3010, log3 = 0.4771 and log 7 = 0.8451, find log 42.

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8. (a) Rectangle ABCD is similar to rectangle WXYZ. If

*BC = 9cm, AB = 4CM* and *WX* = *5cm;* calculate the length of XY.

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(b) The figure below shows that *AC = BD .* Prove that *ACB = ADB*

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9. (a) A ladder on the ground leans against a vertical wall whose height is 5 metres. The ground distance between the ladder and the wall is 12 metres.

(i) Draw a diagram to represent this information.

(ii) Using the diagram in part (i), find the length of the ladder.

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(b) Given that where A is an acute angle, find without using mathematical tables the values of :

(i)Cos A

(ii)Tan A

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10. (a) In a class of 32 students, 18 play golf, 16 play piano and 7 play both golf and piano. Use a formula to find the number of students who play neither golf nor piano.

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(b) A survey was done among students in a certain school in order to find the most popular subject. In this survey each student voted once and the results were as follows.

**Subject** | Maths | Englis | Biology | History | Geograph | Physics |

**NQ of Pupils** | 50 | 80h | 120 | 40 | 80y | 30 |

Show this information in a pie chart.

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