**THE UNITED REPUBLIC OF TANZANIA MINISTRY OF EDUCATION AND ****VOCATIONAL TRAINING FORM TWO SECONDARY EDUCATION EXAMINATION, **

**0041 BASIC MATHEMATICS ****2012**

__TIME: 2½ HOURS____ __**INSTRUCTIONS**

1.This paper consists of sections A and B.

2.Answer **ALL** questions showing clearly all the working and answers in the spaces provided.

3.**ALL** writing must be in blue or black ink **EXCEPT** drawings which must be in pencil.

4.Write your examination number on the top left corner of every page.

5.Mathematical tables, geometrical instruments and graph papers may be used where necessary.

6.Cell phones and calculators are not allowed in the examination room.

**SECTION A (60 MARKS)**

**SECTION A**

1. Given the fraction, , find the fraction which is greater than **½**

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2. If an object travels at 5 metres per second, how many metres does it travel in one hour?

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3. Find the average of all multiples of ten from 10 to 190

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4. Evaluate leaving your answer in radical form.

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5. Factorize the expression

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6. Express in decimal notation percent of

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7. Given the following diagram, find the value of x in degrees

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8. If determine the value of

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9. Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns Tshs 32,400 in those working days per week. How much does she earn per hour?

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10. If the production of 6 integers is negative, find the maximum number of integers in that product which are negative.

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11. Express R as the subject of

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12. Simplify the expression

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13. Calculate the number of degrees that the hour hand of a clock moves through between 12:00 noon and 2:30 in the afternoon of the same day.

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14. Given that 3x + y= 19 and x+3y=1, Find the value of 2x + 3y

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15. Evaluate 99^{2} - 1

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16. Find the slope of a straight line which passes through points A (0, a) and B(3a,0)

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17. Complete

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18. Solve for x given the equation leaving your answer in logarithmic form

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19.

Find the value of x.

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20. A real estate agent received a 6% discount on the selling price of a house. If the discount was Tshs. 888,000 what was the selling price of the house?

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**SECTION B**

21. The area of a right-angled triangle is 50cm^{2}. If one of its angles is 45°, calculate the lengths of the sides and the hypotenuse of the triangle.

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22. In a group of 40 people, 10 are healthy and every person of the remaining 30 has either high blood pressure, high level of sugar content in the body or both. If 15 people have high blood pressure and 25 people have high level of sugar content in their bodies, how many people have high blood pressure and high level of sugar content?

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23. From the top of a 200 metres high building, the angle of depression to the bottom of a second building is 20°. From the same point, the angle of elevation to the top of the second building is 10°. Calculate the heigh of the second building correct to 2 decimal places.

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24. The following table shows marks which were scored by Form One students in a mathematics test at Chilulumo Secondary school.

**Marks%** | 40 | 45 | 50 | 55 | 60 | 65 | 70 |

**Number of students** | 6 | 8 | M | 5 | 9 | 4 | 3 |

From the table, determine the value of M if the total number of students was 48, hence calculate the percentage of the students who scored at least 55 marks.

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25. Explain how each of the following types of transformation differs from the other. Translation from Reflection, Reflection from Rotation, and Rotation from Translation.

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