MATHEMATICS FORM THREE NEW NECTA FORMAT

THE PRESIDENT'S OFFICE

MINISTRY OF REGIONAL GOVERNMENT AND LOCAL GOVERNMENT

AUGUST-SEPTEMBER   EXAMINATION SERIES

MATHS  FORM-3

2020

TIME: 2:30 HRS

Instructions

  1. This paper consists of sections A and B with a total of fourteen (14) questions.
  2. Answer all questions in sections A and B. Each question in section A carries six (6) marks while each question in section B carries ten (10) marks.
  3. All necessary working and answers for each question must be shown clearly.
  4. NECTA mathematical tables may be used.
  5. Cellular phones, calculators and any unauthorised materials are not allowed in the examination room.
  6. Write your Examination Number on every page of your answer booklet(s).

SECTION A (60 Marks)  

Answer all questions in this section.

 1.(a) If  image and image find the fraction of image in its simplest form

(b).Find the GCF of 210, 357 and 252.

2.(a)image

(ii)   log3 10 + log3 8.1

(b)  If nlog5125 =  log264 , find the value of n.

3.  (a) By substituting a = 1x and b = 1y in the system of equations: 

image, find the solution set (x,y).

(b)  Let U be a universal set and A and B be the subsets of U where:

U = {1,2,3,4,5,6,7,8,9,10}, A = {odd numbers} and B = {prime numbers} (i) Represent this information in a venn diagram.

(ii)  Find A ? B′ and (A ? B) ′

 

4.  (a) Given vectors (i) the vector a = 3i + 2 j , b = 8i +­ 3j and c = 2i + 4 j find:

(i) d=3a -b +1/2c 

(ii) a unit vector in the direction of d.

(b) Find the equation of the line passing at point (6, ­2) and it is perpendicular to the line that crosses the ­x-axis at 3 and the y­-axis at ­4.

 

 

5.  (a) Two triangles are similar. A side of one triangle is 10 cm long while the length of the corresponding side of the other triangle is 18 cm. If the given sides are the bases of the triangles and the area of the smaller triangle is 40 cm2 , find the area and the height of the larger triangle.

(b) In the figure below CB = BD = DA and angle ACD = x .

image

(i)  Show that angle ADE = 3x ,

(ii)  Calculate the measure of angle CDA if x = 39°.

6.  (a) A shopkeeper makes a 20% profit by selling a radio for sh. 480,000.

(i)  Find the ratio of the buying price to the selling price.

(ii)  If the radio would be sold at 360,000, what would be the percentage loss?

(b)  A farmer sold a quarter of his maize harvest and gave one third of the remaining to his relatives. If the farmer remained with 25 bags of maize find how many bags of maize did the farmer harvest.

 

7.  (a) Mariam, Selina and Moses contributed 800,000, 1,200,000 and 850,000 shillings respectively while starting their business.

(i)  Find the ratio of their contributions in simplest form.

(ii)  If the business made a profit of 1,900,000 shillings; find how much each got if the profit was shared in the same ratio as their contributions.

 

(b)  A dealer bought 10 books for 200,000. He sold 25 of them at 30,000 shillings each and the remaining at 25,000 shillings each. What was his percentage profit?

 

8.  (a) The number of tablets given to a patient was found to be directly proportional to the weight of the patient. If a patient with 36 kg was given 9 tablets, find how many tablets would be given to a patient whose weight is 48 kg.

(b)  Four people can eat 2 bags of rice each weighing 10 kg in 12 days. How many people can eat 6 bags of rice of the same weight in 18 days?

9.  (a) If the sum of n terms of a geometric progression with first term 1 and common ratio imageis image , find the number of terms.

 

(b)  How many integers are there between 14 and 1,000 which are divisible by 17?

10.(a)   Use factorization method to solve the quadratic equation x2 ? 9x + 14 = 0.

 

 (b) Find the values of x that satisfies the equation 

image

SECTION B( 40 Marks)

Answer All Questions

 

11.(a)  A ship sails from Pemba (4.5°S, 39.5°E) to Dar es salaam (7.5°S, 39.5°E). If it leaves Pemba at 11:30 am and arrived in Dar es salaam at 13:30 pm, use imageand RE=6370km to find speed of ship in km/h 

11.(b)  Calculate the values of  imageif f is defined as  

image 

12.Mwanne commenced business on 1st April, 2015 with capital in cash 200,000/=

April  2 bought goods for cash 100,000/=

3 bought goods for cash 300,000/=

4 purchased shelves for cash 230,000/=

5 sold goods for cash 400,000/=

9 paid wages for cash 50,000/=

12 purchased goods for cash 70,000/=

13 sold goods for cash 600,000/=

  16 paid rent for cash 100,000/=

20 bought goods for cash 60,000/=

   25 sold goods for cash 300,000/=

   27 paid salary for cash 70,000/=

Prepare the following:

(a) Cash account, (b) Trial balance.

 

13. The heights of 50 plants recorded by a certain researcher are given below:

56 82 70 69 72 37 28 96 52 88 41 42 50 40 51 56 48 79 29 30 66 90

99 49 77 66 61 64 97 84 72 43 73 76

76 22 46 49 48 53 98 45 87 88 27 48

54 79 80 73

(a)  Copy and complete this tally table for the data given above.

Height (cm)

Tally

Frequency

21-30

31-40

41-50

51-60

61-70

71-80

81-90

91-100

Use this table to:

(b)  Draw a histogram for the height of the plants.

(c)  Find the mean height of the plants (do not use the assumed mean method).

(d)  Find the median of the heights of the plants.

14.  (a) In the figure below, BD is a tangent to the circle having the centre O .

image

Given that angle OEC = 28°, find the values of angles marked X , Y and Z .

(b) Find the equation of the line passing at point (6, ­2) and it is perpendicular to the line that crosses the ­x-axis at 3 and the y­-axis at ­4.

 

 

 

 

 

 

 

 

 

 

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BASIC MATHEMATICS EXAMINATION FORM THREE

ANNUAL

NAME…………………………………………..CLASS……………………………TIME: 3HRS

INSTRUCTIONS:-

  1. This paper consists of three sections- A, B and C.
  2. Answer all questions in section A and B, but only ONE question in section C.
  3. Write in blue/black pen and drawing using pencil.
  4. All answers must be written in the spaces provided in each question.

 

SECTION A: (60 marks)

1. (a) Express 2.0 in form of whose a and b is an integers and b ≠ 0.

     (b) If a*b = a ÷ b – 2a, find P given 5*P = 20

 

2. (a) Find the value of x for which  27 =

    (b) Solve log b (x2 + 3) – log bx = 2log b2

 

3. (a) Given that  n (A) = 39, n (B) = 21, and n (AnB) = 10, find n (AUB).

    (b) Mary used tiles to build the floor of her sitting room measuring 15m by 20m. If she used only whole ones and they were a like, what is the

          greatest size of each tile?

 

4. (a) Solve for x if   2x – 3    = 5

    (b) Rationalize the denominator         

 

5. (a) Solve the equation , 6x + 14x – 12 = 0

    (b) Two bags of maize have masses of 45 kilograms and 0.005 tons respectively. Find the total mass in kilogram.

 

6. (a) An alley consists of three metals A, B and C in the proportions A: B = 3: 5 and B: C = 7: 6. Calculate A: C.

    (b) Without using mathematical table, evaluate: 

                                                                                    

 

7. (a) The sum of two numbers is 35 and their difference is 21. Find the two numbers.

    (b) Find

 

8. (a) From the set of number  write down:

              i) The prime numbers

             ii) The multiple of 3

            iii) The factors of 60

 

    (b) Mariam, Selina, and Moses contributesd 800,000, 1,200,000 and 850,000 shillings respectively while starting their business.

           i) Find the ratio of their contributions in simplest form.

          ii) If the business made a profit of 1,900,000 shillings; find how much each got if the profit was shared in the same ratio as their

               contribution.

 

9. (a) In a survey of 400 students in a school, 100 were listed as taking apple juice, 150 as taking orange juice and 75 were listed as taking both

            Apple as well as Orange juice. Find how many students were taking neither Apple nor orange juice.

       (b) The sum of the ages of a mother and a daughter is 52 years. Eight years ago, the Mother was eight times as old as her daughter. How old

             is the Mother now?

 

10. (a) Given that A =    (1,2), (3,4), (5,6), (7,8)     . Draw a pictorial diagram.

 

 

    (b) If R =     y: y = 2x + 1      for x = 1, 2, 3, 4 and 5. Find domain and range.

 

    (c) Given that f(x) = 3x + 6, Find i) f (2) ii) f (0)

 

 

 

 

 

11. The following is the distribution of marks obtained in a test given to 50 candidates.

 

 

Marks

10 – 20

20 – 30

30 – 40

40 – 50

50 – 60

60 – 70

70 – 80

Frequency

1

3

10

21

6

5

4

 

 (a) Calculate the mean mark by using assumed mean from the modal class.

 (b) Calculate the median mark.

 (c) Calculate mode.

 

 

 

 

12. MR. MFINANGA Commenced a business as follows;

 March 1:  Capital in Cash shs.   260,000/=

 March 2:  Purchases in goods for cash shs.    70,000/=

 March 3:  Sold goods for cash shs.    90,000/=

 March 7:   Purchases goods for cash shs.    30,000/=

 March 13:  Bought packing Material shs.       5,000/=

 March 19:  Paid transport charges shs.       3,000/=

 March 21:  Bought more goods for cash shs.      20,000/=

 March 24:  Paid insurance of cash shs.        6,000/=

 March 27:  Sold goods for cash shs.      60,000/=

Enter the above transactions in the cash account only and extract trial balance.

 

13. (a) Given that (Z + 1) is direct proportional to x and inversely proportional to the square root of y. If x = 2 when y = 4 and Z = 4,

             Find Z when x = 3 and y = 9.

      (b) The number of tablets given to a patient was found to be direct proportional to the weight of the patient. If a patient with 36 kg was given

            9 tablets, find how many tablets would be given to a patient whose weight is 48 kg.

      (c) Four people can eat 2 bags of rice each weighing 10kg in 12 days. How many people can eat 6 bags of rice of the same weight in 18 days?

 

14. (a) Mr. Komba deposited Tsh 400,000 in a bank at compound interest 5% annual for 2 years. Calculate the amount he received at the end of

            the period.

       (b) If the 5th term of an arithmetic progression is 23 and the 12th term is 37, find the first term and the common difference.

       (c) Find the sum of the first four terms of a geometric progression which has a first term of 1 and a common ratio

 

 

 

 

 

 

 

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