THE PRESIDENT'S OFFICE

MINISTRY OF REGIONAL GOVERNMENT AND LOCAL GOVERNMENT

PRE-NATIONAL  EXAMINATION SERIES-1

MATHEMATICS  FORM-4

2020

TIME: 3:00 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) Mangoes are to be exactly divided into groups of 20, 30 or 36 .What is the minimum number of mangoes required?

(b) Mary was given 60,000 shillings by her mother. She spent 35 percent of the money to buy shoes and 10 percent of the remaining money to buy books. How much money remained?

2. (a). Evaluate log₁₀ 40,500 given that log₁₀ 2 = 0.3010 , log₁₀ 3 = 0.4771 and log₁₀ 5 = 0.6990.

 (b). Find the values of x and y if 

3(a) Factorize the following expressions:

(i)     16y² +xy -15x²

(ii)  4 - (3x - 1)²

(b)  At Moiva’s graduation ceremony 45 people drank Pepsi-Cola, 80 drank Coca-Cola and 35 drank both Pepsi-Cola and Coca-Cola. By using a Venn diagram, found out how many people were at the ceremony if each person drank Pepsi-Cola or Coca-Cola.

4.  (a) Given vectors a = 6i + 12j, b = 17i + 18j :

(i) Find the vector c = 2a – b and its magnitude correctly to 3 significant figures. (ii) Represent vector c in part (a)(i) on the x - y plane.

(b)  Find the equation of the line passing passing through the midpoint of the points A(− 3 2, ) and B(1,− )4 and which is perpendicular to line AB .

5.  (a) In triangle ABC , X , Y and Z are the midpoints of sides AB , AC and BC respectively. If

ZX = ZY and ZXBˆ = ZY Cˆ = 90°;

(i) Represent this information diagrammatically, (ii) Show that ABZˆ = ACZˆ .

(b)  The areas of two similar polygons are 27 and 48 square metres. If the length of one side of the smaller polygon is 4.5 cm, find the length of the corresponding side of the larger polygon.

6. (a) The variable v varies directly as the square of x and inversely as y. Find v when x = 5 and y = 2 ? given that when v = 18 and x = 3 the value of y = 4 .

(b) The temperature (T_i) inside a house is directly proportional to the temperature (T_o) outside the house and is inversely proportional to the thickness (t) of the house wall. If T_i = 32°C when T_o = 24°C and t = 9cm , find the value of t when T_i = 36°C and T_o = 18°C

7.(a)Given that 49, x and 81 are consecutive terms of a geometric progression. Find:

(i)   The value of x.

(ii)The geometric mean.

(b) A wall is in the shape of a trapezium. The first level of wall is made-up of 50  bricks where as the top level has 14 bricks. If the levels differ from each other by 4 bricks, determine the number of 

(i) levels of the bricks.

(ii) bricks used to make the wall.

8.  (a)   Three relatives shared Tshs 140,000 so that the first one got twice as much as the second, and the second got twice as much as the third. How much money did the first relative get? 

(b) Kitwana paid Tshs 900,000 for a desktop computer and sold it the following year for Tshs  720,000. Find:

1.  The loss made, 
2. The percentage loss.

10.  (a) Solve the equation 4x² ? 32x + 12 = 0 by using the quadratic formula.

(b)  Anna is 6 years younger than her brother Jerry. If the product of their ages is 135, find how old is Anna and Jerry.

9.  (a) A river with parallel banks is 20 m wide. If P and Q are two points on either side of the river, as shown in the figure below, find the distance PQ.

(b)  In the triangle LMN , LM = 5m, LN = 6m and angle MLN = 66°. Find MN .

SECTION B (40 Marks)

Answer four (4) questions from this section.

11.  A shopkeeper sells refrigerators and washing machines. Each refrigerator takes up 1.8 m ² of space and costs 500,000 ² of space and costs 300,000 shillings; whereas each washing machine takes up 1.5 mshillings. The owner of the shop has 6,000,000 shillings to spend and has 27 m 2 of space.

(a)  Write down all the inequalities which represent the given information.

(b)  If he makes a profit of 30,000 shillings on each refrigerator and 40,000 shillings on each washing machine, find how many refrigerators and washing machines he should sell for maximum profit.

12.  (a) Given:

Opening stock 01-01-2012 34,430/=

Closing stock 31-12-2012 26,720/=

Net purchases during 2012 212,290/=

Expenses for the year 45,880/=

Gross Profit is 50% of cost of goods sold

Find: (i) Cost of goods sold (ii) The gross profit

(b)  On 1 ^st June, 2013 Mrs. Lemisha started business with capital of 100,000/= and mad ehte following transactions

June 2 bought furniture 40,000/=

7 bought goods 70,000/=

11 sold goods 65,000/=

16 paid Sundry expenses 30,000/=

19 cash sales 80,000/=

24 paid wages 50,000/=

26 withdraw cash 30,000/=

(i)  Prepare the cash account

(ii)  Prepare the balance sheet as at 30/06/2013

(iii)  Explain the importance of the balance sheet you have prepared in part (b)(ii) above.

 13.(a) Given matrices

And

Such that

Find elements of matrix P

(b) Determine the matix A from the equation

14.(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 and R_E=6370km to find speed of ship in km/h 

(b) Sketch a square pyramid whose base is PQRS, vertex is at W and centre is at N, then answer the questions that follow: 

(i)     State the projection of  

(ii)  Name the angles between  

(c)  The volume of a square pyramid is 28.2 cm³. If the sides of its base are 4 cm long, find the height of the pyramid correct to one decimal place.