PRESIDENT’S OFFICE, REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT

SECONDARY EXAMINATION SERIES,

MID TERM ONE – MARCH-2024

MATHEMATICS FORM FOUR

Time: 3Hours

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

3.   Each question in section A carries six (6) marks while each question in section B carries ten (10) marks.

4.   All necessary working and answers for each question must be shown clearly.

5.   NECTA Mathematical tables and non-programmable calculator may be used.

6.   All communication devices and any unauthorized materials are not allowed in the examination room.

7.   Write your examination number on every page of your answer sheet(s).

SECTION A. (60 MARKS)

Answer all questions in this section. 

1.                      (a)  Given the number 857636721. Write this number

1.                  To the nearest thousands
2.                To hundreds
3.             In expanded form

              (b) Three brothers visited their grandfather at interval of 5 days, 7 days and 12 days. If they started together on 15^th July. Find the date they will visit the grandfather together next time. (Each month has 30days)

2.                      (a) (i) Solve for X if  =16

    (ii) Simplify  

(b) given that log 3⁴ =1.262 and log 3⁵=1.1465. Find log 3 0.8

3.                      (a)In a class of 60 students, 40 students like history, 36 like geography, 24 students like both subjects. Find the number of students who like

1.                  History only
2.                Either history or geography
3.             Geography only
4.              Neither history nor geography

(b) When a fair die is tossed, find probability that the number obtained is 

1.                  More than five
2.                At least one
3.             At most six

4.                      If a=5i+4j, b= -3i+3j, and c = -2i+5j. find

1.                  V= 3a+b-3c
2.                The magnitude of V

(b) given the point A (3,3) B (-3,1) C (-1,-1) and D (1,-7)

1.                  Show the line through AB and CD are perpendicular to each other.
2.                Find the equation of the line through point (-4,5) which is parallel to BC

5.                      (a) A school cow produces18 litres of milk every day. How many cows of same type should the school keep to get 126 litres of milk every day.

(b) One family from England traveled for holiday to France and exchanged 450 pounds for Euros when exchange rate was 1.41 Euros to Pound. They spent 500 Euros and then exchanged the remaining amount into pounds by that time the exchange rate had become 1.46 Euros to Pound. How much money remained in terms of pounds? 

6.                      (a) A school hall has 32 rows of seats. If there are 26 seats in the first row, 30 seats in 2^nd row, 34 seats in 3^rd row and so on. How many seats are there in a theatre?

(b) Mr Cuthbert starts an employment with a monthly salary of 340,000 and receives an increment of Tsh 12,000/= per year.

1.                  What will be his salary in fourteen year of employment
2.                After how long will he earning Tsh 592,000 per month.

7.                      (a) The fifth and eleventh terms of AP are 8 and -34 respectively. Find the sum of first ten terms.

(b) A school wishes to invest Tsh 100,000,000 in a bank which pays an interest rate of 2% compounded annually.

1.                  Find total amount of money that will accumulate after  2years
2.                Calculate the interest after 2 years

8.                      (a) Asha is three years older than her brother Juma. Three years to come the product of their age will be 130 years.

1.                  Formulate the quadratic equation representing information above
2.                Use the quadratic equation formula to find present age of Asha and Juma
3.             Solve the equation by completing the square

2x²-3x-5=0

9.                      What do the following terms mean as used in Accounts

1.                  Cash book
2.                Asset
3.             Credit transactions

         (b) A company bought two cars for Tsh 25,000,000/= each. If one car was sold at a profit of 18% and another was sold at a loss of 6%. In the whole transaction there was no loss. What was the profit made by the company?

10.                 If the square of the hypotennce of an isosceles right angled Triangle is 128cm². Find the length of each other sides.

(b) From the top of the tower, of height 60m the angle of depression of the top and the bottom of a building are observed to be 30⁰ and 60⁰ respectively. Find height of the building.

SECTION B. 40 MARKS

11.                 (a) If matrix A is singular, what will be value of Y given that

(b) Solve the following simultaneous equation by matrix method 

2x+y=7

4x+3y=17

(c) Find the image of (3,5) after rotation of 270⁰ about the origin in the ant-clockwise direction.

12.                 (a) A rectangular box with top WXYZ and base ABCD has AB= 9 cm, BC =12 cm, WA=3cm. calculate

1.                  The length of AC
2.                The angle between WC and AC

13.                 Consider the following frequency distribution table below.

(a)Draw the histogram and use it to estimate the mode in one decimal place

(b) Find the value of angle x in the figure below

14.           (a) A function F is defined by the formula f(x) =  where x is a whole number.

1.            If f(x) =25. Find the value of x
2.         Fund the value of 

  (b)A craftsman wishes to decide how many of each type A and B charcoal stove has to fabricate in order to maximize profit for the month. Unit profit for type A stove is 1000/= and 1500/= for type B. type A stove requires 1m² of mild steel sheet per unit and type B 2m² . He has only 12m² of mild steel available. He can fabricate a total of 8 stoves of either type per month. How many stove of each type should be fabricated.

 PRESIDENT’S OFFICE

REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT

MID TERM EXAMINATION AUG- 2023

SECONDARY EXAMINATION SERIES

MATHEMATICS FORM FOUR

TIME: 3 HOURS                                                                                     AUG-2023

Instructions 

1.                  This paper consists of section A and B with fourteen (14) questions.
2.                  Answer all questions.
3.                  Each question in section A caries six (06) marks while each question in section B carries ten (10) marks.
4.                  All necessary working and answers for each question must be shown clearly.
5.                  Mathematical tables and non – programmable calculators may be used.
6.                  All communication devices and any unauthorized materials are not allowed in the examination room
7.                  Write your Examination number on every page of your answer booklet(s).

SECTION A (60 MARKS)

1.                 (a) Simplify the sum of 85% of 9861 and  of 12458. Write your answer correct to two significant figures.

(b)    (i)  Mr. Tumai Distributed Tshs 960,000/= awards to students who passed well in their examinations and their respective teachers as follow: 23% to all students who passed Arts Subjects. 15% to students who passed Mathematics and 27% to students who passed science subjects. The remained amount was distributed to teachers. Find the amount that were awarded to teachers.

(ii) Three bells commence tolling together and toll at intervals of 8, 10 and 12 seconds respectively.  How many times do they toll together in 50 minutes?

2.                (a) If . Simplify

(b) Describe the applications of Logarithm in real life situations

3.                In a certain class MSUVA displayed counting numbers less than 30. From the displayed numbers, OKWI mentioned all numbers divisible by 2 and FEITOTO mentioned all numbers that were the multiples of 3.

1.              (i)  Outline all numbers that were mentioned by OKWI and FEITOTO in common.

(ii)  How many numbers were mentioned by either OKWI or FEITOTO?

2.            If a number was selected at random from the numbers displayed by MSUVA, what is the probability that a selected number was a multiple of 3?

4.                (a) Given that = 4i + 3j and = 6i – 3j, find the value of “h” and “k” if h + k = 10i + j

(b) A perpendicular line from the point P(2,-4) to the line meets the line at point Z(-1,3). Find:

i. Distance 

ii. If the point Z(-1,3) is a mid-point of the line , find the coordinates of point  

5.                (a) In the following figure; // and ; If   and , find the Area of  BCDE

        (b)   By considering the Alternating opposite angles theorem, draw the diagram hence identify the corresponding angles.

6.                (a) The time “t” taken to buy fuel at LAKE OIL PETROL STATION in Morogoro varies directly as the number of vehicle “V” in the queue and inversely as the number of pumps “P” available in the station. In petrol station with 10 pumps it takes 20 minutes to fuel 40 vehicles.

1.                  Write vehicle “V” in terms of pumps “P” and time “t”
2.                Find the time it will take to fuel 60 vehicles in a station with 4 pumps.

(b) Mayele bought 3 bottles of juice of capacity 350 ml and Dialo bought 1 bottle of juice of capacity 1 litre. 

i. Who had more juice to drink? 

ii. How much more?

7.                (a)  What do the following terms mean as used in Accounts?

1.               Cash book
2.             Assets
3.           Credit transactions

(b) A company bought two cars for Tshs 25,000,000/= each. If one car was sold at a profit of 18% and another was sold at a loss of 6%. In the whole transactions there were no loss. What was the profit made by a company?

8.                (a) A BODA BODA driver rates after each kilometre. The fare is Tshs. 1000/= for the first kilometre and raise by Tshs. 500/= for each additional kilometre. If BALEKE want to travel 10 kilometres by BODA BODA. What will he be charged by BODA BODA driver?

(b) The number 19683 is in which term in the following Geometric sequence; 3, 9, 27 …?

9.                (a)  If the square of the hypotenuse of an isosceles right-angled triangle is 128 cm² find

the length of each other sides

(b) From the top of a tower of height 60m the angles of depression of the top and the bottom of a building are observed to be 30⁰ and 60⁰ respectively. Find the height of the building.

10.           (a)   If the length of each side of a square is increased by 6, the area become increased to 16 times the area of the small square. Find the length of one side of the original square.

(b) A large rectangular garden in a park is 120m wide and 150m long. A contractor is called in to add a brick walkway to surround this garden by the same width. If the area of the walkway is 2800m², how wide is the walkway?

SECTION B (40 MARKS)

11.           (a) In certain research the data were summarized as shown in a table below:

By using the data above reconstruct a frequency distribution table including class interval and frequency.

(b) Prove that equal chords of a circle subtend equal angles at a centre.

12.           (a) Two towns P and Q on the Latitude 48⁰ are 370 Nautical miles apart. Find the

difference in their longitude.

(b) A pyramid with vertex V and edges VA, VB, VC, VD each 15cm long has a rectangular base ABCD where AB = CD = 10cm and AD = BC = 8cm.

i. Sketch the pyramid using the above information.

ii. Calculate the height “VO” of the pyramid where “O” is the centre of the rectangle.

3.              Calculate the angle between the base and edge

13.           (a). (i). Find the possible values of x if the matrix  has no inverse.

       (ii). By using matrix method, solve the equations 

(b). A transformation is given  and , find the image of the equation     2x – 3y  = 6 under the transformation matrix which performs the above transformations.

14.           (a) A function f is defined as;

Find (i) f(1.95) (ii) f(15)   (iii) Domain of  f   (iv) identify the type of a function f

(b) A school is preparing a trip for 400 students. The company who is proving the 

     transportation has 10 buses of 50 seats each and 8 buses of 40 seats, but only 9 drivers available. The rental cost for a large bus is 800,000/= and 600,000/= for the small bus. How many buses of each type should be used for the trip for the least possible cost?

PRESIDENT’S OFFICE

REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT

SECONDARY EXAM SERIES

FORM 4 BASIC MATHEMATICS

SECTION A (60 MARKS)

Answer ALL questions in this section

1(a)Express the number 0.000038583

1. In standard form
2. Correct to 4 significant figures

(b)Change  into fraction

2(a)Solve the following equation simultaneously:

(b)Rationalize the denominator of the expression 

3(a)Solve the following equations simultaneously 

(b)Given . Find: 

4(a)Find the equation of the perpendicular bisector of the points A(4,8) and B (-4,-6) 

giving your answer in the form 

(b)Given that . 

Find the relation between the three vectors a, b and c

5. In the figure below  // and 

If the area of DECB is 21cm²; find the area of 

6(a) Given that w is directly proportional to x² and inversely proportional to t and that 

w=12 when x=2 and t=2. Find the value of w when x=3 and t=3

(b)Sophia and Alex had each Tsh.10,000. If Sophia wanted to buy the South African Rand and Alex wanted to buy the Malawian Kwacha, how much would each one receive?

(1 Rand =210 Tanzania shillings; and 1 Malawian Kwacha=10.80 Tanzanian shillings)

7(a)Given that A:C=10:7 and B:C=5:14; Find A:B

(b)Anna paid Tsh. 20,000 for 10 books. She sold  of them at Tsh. 3,000 each and the remaining at Tsh. 3,500each. What was her percentage Loss or percentage profit?

8.(a)The sum of three terms which are in G.P is 28 while the product of these terms is 512.

Find the largest term.

(b)The fourth and sixth terms of an arithmetic progression are 45 and 55 respectively. Find;

1. The first term
2. The tenth term

9.(a)Find value of x in the following triangle and hence find the area of the triangle.

(b)It is known that , find the relationship between 

10(a)Factorize

(b)Find the only solution of the equation 

SECTION B (40 MARKS)

Answer any four (4) questions from this section

11(a)The following graph shows the feasible region of a linear programming problem where the shaded region is the feasible region. Study the graph and answer the questions that follow.

1. Write the coordinates of Corner points A, B, C, D, E, and F
2. Write the equations represented by the letters and hence the corresponding inequalities of
3. Find the minimum value given that

12. The following frequency distribution table shows scores of marks of 50 students in a Mathematics Test:

Calculate the measures of central Tendency

13(a) Town X and Y are located at (60°N, 30°E) and (60°N, 45°W) respectively on the earth’s surface. Calculate the distance between the two towns in Kilometers.

(b)Find the value of the angles marked X and Y in the figure below, given that O is the center of the circle.

 (c)Find the area of a prism (rectangular) with l=8cm, w=6cm and h=4cm

14.from the balances given below, prepare a balance sheet at 31^st December 2010. Capital shs 205,000; Furniture shs.54,000; cash in hand shs 16,000; Net profit sh.74,000; Motor van sh 30,000; stock sh. 110,000; Drawings shs. 24,000; shop fittings shs 20,000; loan from Bank sh. 80,000; Debtors shs. 180,000; Creditors shs.45,000 and Bank Overdraft shs. 30,000

15.(a)Use the inverse of matrix B to find matrix A given that;

(b)Write two conditions fr a transformation to be a linear.

(c)By using a sketch and not otherwise, find the image of P(3, 4) when rotated about 90° anticlockwise followed by another rotation of 180° clockwise.

16.(a)The ordered pairs of a Quadratic function f are  Find the function f(x)

(b)A fair die is tossed once. Find the probability that an even number or a prime number occurs

(c) Given that 

THE UNITED REPUBLIC OF TANZANIA

PRESIDENT’S OFFICE

REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT

FORM FOUR MID TERM  EXAMINATION-2021

041                                                BASIC MATHEMATICS

Time: 3 Hours                                                                    AUG, 2021  

Instructions

1. This paper consists of section 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. NECTA Mathematical tables may be used
4. Cellular phones, calculators and any unauthorized materials are not allowed in the examination room
5. Write your examination number on every page of your answer sheet (s)

SECTION A (60 MARKS)

Answer all questions in this section 

1. (a) Simplify  without using mathematical table express your answer in four significant figures.

 (b) Jenk and Jemry are riding on a circular path. Jenk completes a round in 24 minutes where as Jemry completes a round in 36 minutes. If they started at the same place and time and go in the same direction, after how many minutes will they meet again at the starting point?

2.  (a)  Use mathematical table to evaluate     

(b) Find the value of x and y if     = 2025

3.  (a) Let U be a universal set and A and B be the subsets of U                where,  and.

1. Find the number of subsets of set A’
2. Find
3.  If an element is picked at random from the universal set (u), find the probability that it is an element of set B

(b) Find the probability that a king appears in drawing single card from an Ordinary deck of 52 cards

4. (a) The coordinate of P, Q and R are (2, m), (-3, 1) and (6, n) respectively. If the length of PQ is  units and midpoint of QR is  find the possible value of m and n

(b)The gradient of line  is -2. Another line L₂ is perpendicular to L₁ and passes through (-3,-2). What is the equation of L₂ 

5. (a) if   and angle ABD =  Calculate the length

(b) (i) Given   =  =  = 3  where  , and   are the sides of the triangle   ABT and , and  are the sides of the triangle KLC. What does this Information imply?

            (ii) A regular Hexagon is inscribed in a circle if the perimeter of the hexagon                                      Is 42cm, find the radius of the circle and its Area 

6.  (a) If y varies inversely as and x is multiplied by n. What is the ratio of the first y to the second y?

(b) The headmaster has enough food to last for his 600 students for 20 days from tomorrow. If 120 students leave the school today for UMISSETA game, how long will the food last?

7. (a) By selling an article at shs 22,500/= a shopkeeper makes loss of 10%. At what price must the shopkeeper sell the article in order to get a profit of 10%?

(b) The following trial balance was extracted from the books of Nzilandodo on 31^st December 2005.

TX MARKET LTD

      TRIAL BALANCE AS AT 31.12.2005

Note: Stock at close 31^st December 7360. Required, prepare balance sheet as that date.

8. (a) The sum of the first six terms of an A.P is 72 and the second term is seven times the fifth term.

1. Find the first term and the common difference
2. Find the sum of the first ten terms

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

9. (a) If   tan A =   , where A is an obtuse angle,

Find (i). Cos A + Sin A  (ii). – Cos² A – Sin² A

(b) A and B are two points on the ground level and both lie west of flagstaff. The angle of elevation of the top of the flagstaff from A is 56⁰ and from B is 43⁰. If B is 28m from the foot of the flagstaff. How far apart are the points A and B?

10. (a) Solve the quadratic equation x² – 8x +7 = 0

        (b) A field is 10m longer than its wide. The area is 7,200m². What is the width?

SECTION B (40 marks)

Answer all questions in this section

11. ( a) Consider the following frequency distribution tale below;

Draw the histogram and use it to estimate the mode in one decimal place.

b) Find the value of angle X in the figure below.

12. (a) A rectangular box with top WXYZ and base ABCD has AB=9cm, BC=12cm and WA = 3cm

               Calculate (i) The length AC        (ii) The angle between WC and AC

   (b) Two places P and Q both on the parallel of latitude N differ in longitudes 

                  by  find the distance between them along their parallel of latitude.

13.    (a) If matrix A is singular, what will be the value of y given that

(b) Solve the following simultaneous equation by matrix method

2x + y = 7

4x+3y = 17

  (c) Find the image of (3, 5) after rotation of 270^o about the origin in anticlockwise direction.

14.    (a) If f(x) is the function such that

f(x)=

1. Sketch the graph of f(x)
2. State the domain and range of f(x)

      (b) A transport company is hired to transport 420 people it has two types, P and Q of vehicle to be used.  Type P carries 35 passengers and type Q carries 14 passengers. There are at least 10 vehicles of type Q and not more than 9 vehicles of type P. Write down inequalities to represent this information.

THE PRESIDENT’S OFFICE MINISTRY OF EDUCATION, REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT

COMPETENCE BASED SECONDARY EXAMINATION SERIES

FORM FOUR BASIC MATHEMATICS  TERMINAL  EXAMINATION

Time: 3 Hours Year: 2021

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.

3.Each question in section A carries six (06) marks while each question in section B carries ten (10) marks.

5.NECTA mathematical tables and non-programmable calculator may be used.

6.All communication devices and any unauthorized materials are not allowed in the examination room.

7.The following constants for your calculations

Radius of the Earth =6370km,    

SECTION A (60 Marks)  

Answer All Question In This Section

1.(a) Calculate without using Mathematical tables, correct to two decimal places

(b) Each student of Leo academy belongs to one club.  are members in drama club.  are members in mathematics club and the number of science club is twice that of drama club .The rest are members of research club. What fraction of students are members of research club? 2. (a) Make x subject of the formula

(b)Three variables p, q and r are such that p varies directly as q and inversely as square of r. When p=9, q=12 and r=2. Find p when q=15 and r=5.

3.(a) ) Given that    and  ,  where X is an integer. Represent this in a venn diagram, hence find elements of:  

(i)AuB

(ii)AnB 

 (b) In a school of 95 pupils, 42 of the pupils take Biology but not Chemistry, 32 take both subject and 10 of them take Chemistry but not Biology. How many pupils do not take either Biology or Chemistry?

4.(a) Let P and Q be two points at (2,5) and (4, -1) respectively. Find

(i)Find equation of the line that passes through the midpoint of PQ and is perpendicular to it in form of ax + by +c=0

(ii)The distance between P and Q

 (b) A chord is 6cm from the center of a circle with radius 10cm. What is the length of a chord?

5.(a) In triangle PQR, PR=5cm, PQ=6cm and  0 . Find

(i)The length of side QR

(ii)

(b) The size of the exterior angle of a regular polygon is 45⁰. Find

(i)The number of sides

(ii)The sum of all interior angles.

6.(a) Given t=3^x , by using the substitution solve the equation  3^2(1+x) - 3^x =3^(x+3) - 3

(b) A shopkeeper makes a profit of 40% by selling an article for T.Sh. 63,000/=. What would be his percentage loss if he sold the article for T,Sh. 40,000/=

7.(a) Prepare the balance sheet for the balances given below

Capital 4,500,000/=

Drawings 800,000/=

Creditors 430,000/=

Closing stock 500,000/=

Debtors 800,000/=

Buildings 1,600,000/=

Motor Van 800,000/=

Bank 400,000/=

Cash 900,000/=

Net profit 270,000/=

Loan 600,000/=

(b) What is the aim of preparing balance sheet

8.(a) The third, fifth and eighth terms of  arithmetic progression  A.P form the first three terms of Geometric Progression G.P . If the common difference of the A.P is 3, find

(i)The first term of the G.P

(ii)The sum of the first 9 terms of the G.P to one decimal place. (b)  Find the sum of first eight terms of the following sequence 1, -2, 4, -8 . . . . .  

9. (a) In the figure below  BD=5cm, DC=5cm and DE=3cm. Find length of AC and AE

(b) A plane is flying at a constant height. The pilot observed of an angle of depression of 27⁰ to one end of the lake and 15⁰  to the opposite end of the lake. If  the lake is 12 km long. Determine the altitude of the plane.

10. (a) 10 years ago a man was 12 times as old as his son and 10 years from now a man will be twice as old as his son. Find their present age.

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

log(x+5) + log(x + 2) = log4

SECTION B ( 40 marks)

Answer all questions from this section.

11. The examination scores in Basic Mathematics of 40 Form IV students are given in the following cumulative frequency table

(a)Find the mean score using assumed mean A=44.5

(b)Draw Histogram and use it to estimate the mode

(c)Calculate the median

12.(a) The two towns P and Q lie on the earths surface such that P(65⁰N, 96⁰E) and Q(65⁰N, 84⁰W). Find the distance between the towns in kilometers and nautical miles.

(b) The figure below shows a tetrahedron. The length of each edge is 8cm. O is the centre of triangle ABC.

Calculate

(i)The length of VO

(ii)The angle between line AV and the plane ABC

(c) Find the volume of a cone which has a base diameter of 10 cm and slant height of 13 cm.

13. (a) The matrices 

      and             

are such that AB=A + B.

Find the values of a, b, c and d

(b)Triangle PQR vertices at P(2, 2), Q(5, 3) and R(4, 1) is mapped onto triangle PQR by transformation matrix 

Find coordinate of triangle PQR

(c)Determine the values of x which the matrix below has no inverse

14.(a)Given that h(x)= -1 - | x + 3|

i.Sketch the graph of h(x)

ii.Use the graph to deduce domain and range

(b) The manager of a car park allows 10m² of parking space for each car and 30m² for each lorry. The total space available is 300m². He decides that the maximum number of vehicles at any time must not exceed 20 and also insists that there must be at least as many cars as lorries. If the number of cars is X and the number of lorries is Y.

(i) Write down the inequities which must be satisfied

(ii)If the parking charge is sh.10 for each car and sh.50 for each lorry. How many vehicles of each kind he should admit to maximize his income and calculate his income

PRESIDENT’S OFFICE REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT

041BASIC MATHEMATICS

(For Both School and Private Candidates)

Time:3 HoursWednesday, 5^th August 2020 a.m.

Instructions

1. This paper consists of sections A and B with a total of fourteen (14) questions.
2. Answer all questions in section 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.

2.

3. (a) A box contains 4 white balls and 5 black balls. Two balls are selected at random without replacement. Find the probability that

(i) Both are white balls

(ii) The first is black and the second is the white ball

(b) In a class of 15 students who take either Mathematics or Biology, 12 students take Mathematics, 8 students take Biology. If each student takes either subjects find by using formula the number of students who take Biology but not Mathematics.

4. (a) The gradient of line is -2. Another line L₂ is perpendicular to L₁ and passes through point (-3, -2). What is the equation of L₂?

(b) The distance between (1,5) and (k+5, k+1) is 8. Find K, given that it is positive

5.(a) The area of the triangle ABC is 140 cm², AB = 20, AC = 14cm, find the angle BAC

(b) Triangle XYZ is similar to triangle ABC and XY = 8 cm. If the area of the triangle XYZ is 24 cm² and the area of the triangle ABC is 96 cm². Calculate the length of AB.

6.

7.

=

/=

19 bought Shelves for cash 110,000/=

20 sold goods for cash 900,000/=

21 purchases goods for cash 800,000/=

22 sold goods for cash 1, 400,000/=

26 paid rent 300,000/=

Record the above transactions in Cash account ledger and extract a Trial balance.

8. (a). The product of a three terms of a geometric progression (GP) is 8000. If the first term is 4. Find the second term and third term

(b). Mahona invested a certain amount of money in a Savings Bank whose interest rate was 10% compounded annually. After two years he got 5000 shillings.

1. How much did he invest at the start?
2. How much did he receives as Interest at the end of two years.

9. (a) Find the value of

Sin (150⁰) cos (315⁰) Without using mathematical tables

Tan (300⁰)

(b) Calculate the angles of a triangle which has sides of lengths 4m, 5m and 7m

10.(a). Given that x² –y² = 27 and x + y = 9 find the value of xy

(b). Solve the equation 2x² – 3x – 5 = 0 by completing the square.

SECTION B (40 Marks)

Answer all questions

11. (a) The number of workers absent in 52 working days is given in a cumulative frequency table below

Find (i) Percentage of workers who are absent at least for 20 days

(ii) Median

(b) Find the angle x in the figure below

12. (a) A ship sails from point A (40) due west along the same latitude to point B for 1000km. Find the latitude and longitude of point B. Use R=6370km and (give your answer in nearest degree)

(b) VABCD is a pyramid with VA=VB=VC=VD=5cm and ABCD is a square base of sides 4cm each. Assume that the centre of the base is at point N. Find

(i) The angle between VA and the base ABCD

(ii) The volume of the pyramid

13.

14. (a). A function F is defined by the formula f(x) = where x is a whole number

1. If f(x) = 25 find the value of x
2. Find the value of

(b). A craftsman wishes to decide how many of each type A and B charcoal stove he has to fabricate in order to maximize profit for this month. Unit profit for type A stove is shs. 1000 and Unit profit for type B is shs. 1500. Type A stove requires 1m² of mild steel sheet per unit and type B requires 2m². He has only 12 m² of mild steel available. He can fabricate a total of 8 stoves of either type per month. How many of each type should he fabricate?

THE PRESIDENT’S OFFICE

MINISTRY OF EDUCATION, REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT

SECONDARY EXAMINATION SERIES

MATHEMATICS MID TERM EXAMINATION-MARCH

FORM FOUR-2021

Time: 3Hours

Instructions.

1.              This paper consists of section A, and B with a total of 14 questions
2.              Answer all questions in section A and B.
3.              Each question in Section A carries 06 marks, while each question in section B carry 10 marks
4.              All necessary working and answers for each question must be shown clearly.
5.              NECTA mathematical tables and non programmable calculators may be used.
6.              Cellular phones and any unauthorized materials are not allowed in the examination room.
7.              Write your number on every page of your answer booklet.

 SECTION A (20 Marks)

 Answer All questions in this section.

1. (a) Write;

1. 4.20098 into two decimal places
2. 0.002758 into two significant figures
3. 0.0497 rounding off to hundredth

(b) Use mathematical tables to evaluate 

2. (a) Solve for

(b) Evaluate  without using mathematical tables

3. (a) Two sets A and B are subsets of a given universal set µ =  Find

(b) A mother’s age is four times the age of her daughter. If the sum of their ages is 50 years, find the age of the mother.

4. (a) Given that

Find the magnitude of 

 Leaving your answer in the form of 

(b) Find the equation of the line passing at the point (6,-2) and it is 

     perpendicular to the line crosses the  – axis at 3 and the  – axis at -4

5. (a)  The ratio of the areas of two similar polygons is 144:225.  If the length of a side of the small polygon is 60cm, find the length of the corresponding side of the other polygon.

(b) Find the length of a side and the perimeter of a regular nonagon inscribed in a circle of radius 6cm

6. (a) The variable is directly proportional to and inversely proportional to . If find

(b) A car is travelling steadily covers a distance of 480km in 25 minutes. What is its rate in 

7. (a) a car was bought for 4,000,000/= and sold for 4,500,000. Calculate

1. The profit made
2. The percentage profit

(b) A factory employs skilled, semi-skilled and office workers in the ration 6:5:4 respectively. If there are 120 semi-skilled workers, how many skilled workers are there?

8. (a) The sum of the first six terms of an A.P is 72 and the second term is seven times the fifth term. Find the sum of the first ten terms of this A.P

(b) Find the amount accumulated at the end of 2 years after investing 500,000/= at a compound interest rate of 10% annually.

9. (a) Without using tables, evaluate

(b) a ladder reaches the top of a vertical wall 18m high when the other end on the ground is 8m from the wall. Find the length of the ladder correct to one decimal place

10. (a) Solve the equation  by using quadratic formula.

(b) Pulukuchu is 6 years younger than her brother Mpoki. If the product of their age is 135, find how old is Pulukuchu and Mpoki

SECTION B (40 MARKS)

11. A small industry makes two types of clothes namely type A and type B. Each type A take 3 hours to produce and uses 6 meters of material and each type B take 6 hours to produce and uses 7 meters of material. The workers can work for a total of 60 hours and there is a 90 meters of materials available. If the profit on a type a cloth is 4,000  shillings and on type b Is 6,000 shillings, find how many each.

12.  The following distribution table shows the scores of 64 students in a chemistry weekly test;

1. Calculate the mean and mode (do not us assumed mean)
2. Draw the  give and use it to estimate the median

13.  (a) Calculate the distance from Chagwe (5ᴼS, 39ᴼE) to Minga (12ᴼS,39ᴼE) in kilometres. Use π  = 3.14, and th radius of the earth R = 6370 km and write the answer correct to 1 decimal place.

(b) If a bus leaves Chagwe at 8.00 am on Monday and travels at 40km/hour, at what time will it reach Minga?

(c) Find the values of  in the figure below;

14. Study the following trial balance and then answer the questions that follow:

 NB: Closing stock was Tshs 7,400;

 Prepare:

1. Trading profit and loss account
2. Balance sheet

15. (a) Find the inverse of matrix

A

(b) Use the result of part (a) to solve the simultaneous equation;

(c) Find the value of  which the matrix has no inverse

16. (a) The function  is defined by

1. Sketch the graph of
2. State the domain and range of

(b) The probability that Anna and John will be selected for advanced level is 0.5 and 0.3 respectively. Determine the probability that;

1. Both of them will not be selected
2. Anna will be selected and John will not be selected
3. One of them will be selected

THE PRESIDENT’S OFFICE MINISTRY OF EDUCATION AND VOCATIONAL TRAINING

024 MATHS- FOUR

Duration: 3 Hours

INSTRUCTIONS.

1. This paper consists of two sections A and B.
2. Answer all questions in Section A and only four questions in section B
3. Show clearly all working for each question
4. Mathematical tables, geometrical instruments and graph paper may be used where necessary

SECTION A (60 MARKS)

1. a) Use mathematical table, evaluate 

b)Express 45.456 in form of  where a and b are both integers.

2. a) If ,

evaluate

b)Solve for x the following equation 32^x-3 X 8^x+4 = 64 2^x

c)Rationalize the denominator

3. a) Find value of P which makes the following equations perfect square

i) x² + 8x +P=0 

ii) x² - x + P=0

b) Solve for x the equation

4. a)Given the universal set U={p, q, r, s, t, x, y,z} A={p, q, r, t} B={r, s, t, y }. Find i)(AUB) ii)(A’nB’)

b)In a class of 60 students, 22 students study Physics only, 25 study Biology only and 5 students study neither Physics nor Biology. Find i) Number of students study Physics and Biology. ii) Number of students that study Biology.

5. a) A, B and C are to share T.sh 120,000/= in the ratio of. How much will each get?

b)A radio is sold at T. sh 40,500/= this price is 20% value added tax(V.A.T). Calculate the amount of V.A.T.

6.a) The sum of 1^st n-terms of certain series is 2ⁿ-1, show that this series is Geometric Progression. Find an the n^th term of this series.

b) Point P is the mid-point of a line segment AB where A(-3,8) and B(5,-2), find an equation through P which is perpendicular to AB.

7.a) Without using mathematical table, evaluate

b) A man standing on top of cliff 100m high, is in line with two buoys whose angles of depression are 17⁰ and 21⁰. Calculate the distance between the buoys.

8.a) The lengths of two sides of triangle are 14cm and 16cm. Find the area of the triangle if the included angle is 30⁰.

b)The area of a regular 6-sided plot of land inscribed in a circular track of radius r is 720cm². Find the radius of the track.

9.a) Find values of angles marked x⁰ and y⁰ in the figure below

b) Prove that exterior angle of cyclic quadrilateral is equal to interior opposite angle.

10. a)Solve for x if

b) A two-digit of positive number is such that, the product of the digits is 8. When 18 is added to the number, then the digits are reversed. Find the number.

SECTION B (40 MARKS)

11. The daily wages of one hundred men are distributed as shown below

a) Find the value of x

b) Calculate the daily mean wage of the 100 men

c) Draw histogram to represent this data and use it to estimate Mode

d) Draw cumulative frequency curve and use it to represent Median

12. Shirima makes two types of shoes A and B. He takes 3hours to make one shoe of type A and 4hours to make one shoe of type B. He works for a maximum of 120hours. It costs him sh. 400 to make a pair of type A and sh. 150 to make of type B. His total cost does not exceed sh.9000. He must make at least 8 pairs of type A and more than 12 pairs of type B.

a) Write down the inequalities that representing the given information.

b) Represent these inequalities graphically

c)Shirima makes a profit of sh. 150 on each pair of type A and sh.250 on each pair of type B. Determine the maximum possible profit he makes.

13. The following trial balance was extracted from the books of Magoma Moto at 31^stt December 2015

Stock at 31^stt December 2015 was Tsh.499,000/=

a) Prepare trading, profit and loss account for the year ended 31^stt December 2015

b)The balance sheet as at 31^stt December 2015

14.a) In the triangle ABC below, find values of angles marked x⁰ and

y⁰  where AB=12cm, BC=7cm and AC=8cm

b) Solve the following equations given that

i)

ii)

c) Show that

15. a) In a figure below, represents a room 8m by 6m by 4m. Calculate

i)Length of diagonal AR

ii) Angle that AR makes with the floor

iii) Angle which plane TSAD makes with plane TSBC.

b)A water pipe made of material 2cm thick has an external diameter of 16cm. Find the volume of material used in making of the pipe 200m long.

16. a) The function f is defined as follows:

F(x) =

i) Sketch the graph of f(x)

ii) Determine domain and range

iii) Find i) f(1) ii) f(-4) iii) f(π)

b)For what values of x is function f(x)= is undefined?