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

**FORM TWO NATIONAL ASSESSMENT**

**041 BASIC MATHEMATICS**

*Time: 2:30 Hours Tuesday, 14 th November 2017 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) Find the LCM and GCF of 13, 52 and 104.

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(b) Round off the number 568,356 to the nearest thousands and ten thousands.

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2.(a) Determine the improper fraction of

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(b) Convert into a repeating decimal.

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3.(a) Change 15 km into centimeters.

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(b)Find the time in which sh. 200,000 will earn sh. 48,000 at the rate of 4% interest per annum.

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4.(a) In the following figure, AB is parallel to PQ - and RS is a transversal. Find the angles labeled a, *b, w, x,* y, and *z.*

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(b)Find the perimeter of a square, if its area is 25 *cm*^{2}

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5.(a) Find the value of x in the equation 9x3^{4x} =27^{(x-1)}

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(b)Factorize the expression 6x^{2} –11x +4 by splitting the middle term.

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6.(a) Find the equation of the straight line passing through the points (3, 5) and (7, 9). (Express your answer in the form y= mx + c).

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(b) The vertices's of a triangle are A (2, 2), B(3, 4) and C (4, 3). If the triangle is reflected in the y-axis, write down the coordinates of the image of points A, B and C.

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7. (a) Rationalize the denominator of

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(b) Without using mathematical tables, find the value of 3log 5+ 5log 2 – 2log 2.

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8.(a) PQR is an isosceles triangle whereby PQ =PR and QS = SR. If S is a point between Q and R prove that ?PQS

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(b) In the following figure, ?ABC ?APQR, AC =4.8 cm, AB = 4cm and PQ = 9cm. Find PR.

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9.(a) The sides of an equilateral triangle ABC are 10cm each. Find the length marked AD in surd form.

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(b) Without using mathematical tables, find the exact value of

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10.(a) In a primary school of 150 pupils 50 study Maths, 70 study Science and 40 study both subjects. By using the appropriate formula, calculate the number of pupils who study neither Maths nor Science.

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(b) The marks of 61 students are represented int he following table:

Mark in % | 30 | 35 | 45 | 50 | 60 | 75 | 80 | 85 | 90 |

Number of students | 3 | 5 | 7 | 10 | 18 | 9 | 4 | 3 | 2 |

**From the table answer the following questions:**

(i)Which mark was scored by few students?

(ii)What was the highest mark?

(iii)If 50% was the pass mark in the examination, how many students passed the examination?

(iv)Which mark was scored by many students?

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