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

**0041 BASIC MATHEMATICS 2010**

__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. Write 56 as a product of prime factors

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2. A square plot has a perimeter of 56m. Find the length of one edge of the plot.

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3. Write in logarithmic form

(a) 81=9^{2}

(b)125=5^{3}

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4. Three persons A, B and C divided Tshs 480,000 among themselves in the ratio of 3:4:5 respectively. How much money did each get?

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5. Given the following numbers 1,2,3,4,5,6,7,8,9,10. Identify all odd numbers and show them on a number line.

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6. A lorry can take a load of 15 tones at once. How many trips can be made by a pickup of capacity 3,000kg to carry the same amount of the load?

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7. Find 8.127 ÷3 correct to 2 significant figures.

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8. The image of A (4, 1) under an enlargement scale factor 3 is A (12, 3). Find the center of enlargement.

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9. Solve the equation m^{2}=16

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10. Without using mathematical Tables, find sin (10° + 20°) – tan (20° + 25°).

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11. A straight line which passes through A (-3, 6) has x-intercept -9. Find the equation of this line in the form of y = mx + c

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12. Write the sum of and

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13. Factorize the expression into three factors, hence find the value of the expression when

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14. If 2x + 70° and 3x + 20° are supplementary angles, determine the value of x.

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15. Given that . Evaluate

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16. Given that the unshaded part of the following figure is . What is the percentage of the shaded part?

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17. What must be added to to make the expression a perfect square? What the expression of the perfect square.

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18. Given that

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19. A boy spends of his pocket money on Monday and on Wednesday. What fraction of his money is left?

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20. A number is multiplied by 3 and 4 is added to the product. Write down an expression for the result.

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**SECTION B**

21. Given the universal set D {Natural numbers less than 11} P and Q are the subsets of set D where: P= {Prime numbers} and Q= {Even numbers}

Find

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22. The following table represents the number of pupils with their corresponding heights

**Height in cm** | 120 | 125 | 130 | 135 | 140 | 145 |

**Number of pupils ** | 4 | 2 | 3 | 2 | 3 | 6 |

- What is the percentage of pupils who are less than or equal to 135cm tall?
- Draw a histogram for the data.

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23. A girl walks 4m due East from point Q and then walks 3km due North to point T. Calculate the shortest distance from Q to T

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24. In the following figure, BC=16cm, DE=12cm, and AE=18cm. calculate the length EC.

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25. The side of an equilateral triangle is pp, its height is r. Express r in terms of p.

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