PRESIDENT OFFICE REGIONAL ADMNISTRATION

AND LOCAL GOVERNMENT

SECONDARY EXAMINATION SERIES 

COMPETENCE BASED ASSEMENT

MATHEMATICS FORM THREE

TERMINAL EXAMS MAY – 2023 

041

TIME: 3HOURS

INSTRUCTION

1. This paper consists of two sections A and B with total of fourteen (14) questions
2. Answer all questions
3. Programmable calculators, phones and any other unauthorized materials are not allowed in examination room
4. Write your examination on every page of your answer sheet provided
5. All diagrams must be drawn in pencils
6. All writings must be in black/blue ink

SECTION A. 60 MARKS

1. (a) Equal squares as large as possible are drawn on a rectangular board measuring 54cm by 78cm. Find the largest size of the squares.

(b) (i) Express 2.7̇9̇ as a fraction in the form a/b where a and b are integers and b≠0

(ii)Arrange 2/5, 5/8 ,48% and 0.6 in ascending order

(iii) Show on the number line the solution set of the inequality

│2x+1│>3

2. (a) i. If x² +ax +4=0 is a perfect square . Find the value of a

ii. If x² +bx +c =(x-3)(x+2) determine the values of b and c

iii. Solve the following quadratic equation by complete the square method x² + 6x +7=0

(b) i. Solve 3 -  of (6x+9) = 5-2x

ii. If U*V =UV+V, Find x given that (x*2)*5=60

3. (a) Rectangular table top is 2m long. If the area of the rectangular table top is

3.96m². find its width

(b) i. Solve the following simultaneous equations 

2x+3y=5

4x+23=5y

ii. If Fatuma is 4 years less than Bakari and 3 times Fatuma's age is equal to 2 times Bakari's age. What are their ages ?

4. (a) If  find the value of t

(b)Write “L” in terms of M, N and T from the formula 

(c) Determine the value of x if 

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

(b) In how many years would one double one’s investment if Tshs 2500 is invested at 8% compounded semi –annually.

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) 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 

8. (a) The gradient of line L₁is -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

9. (a) Find the value of

Without using mathematical tables. 

(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 

1. Percentage of workers who are absent at least for 20 days
2. 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. (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?

14. (a)The marks in basic Mathematics terminal Examination obtained by 40 students in one of the secondary school in Katavi were as follows;

60, 54,  48,  43, 37 61, 43, 66, 65, 52, 37, 81, 70, 48, 63, 74, 67, 52, 48, 37, 48 42, 43, 52, 52, 22, 27, 37,44 38, 29, 19, 28 36, 42, 47, 36, 52, 50, 28.

1. Prepare a frequency distribution table with class intervals 10 – 19, 20 – 29, etc.
2. Find the class which contain the median
3. Find the mean
4. Calculate the median.

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

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

FORM THREE BASIC MATHEMATICS TERMINAL EXAMINATION

Time: 3:00 Hours Year: 2022

Instructions

l . This paper consists of sections A and B with a total of fourteen (14) questions.

2. Answer all questions.

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 calculators may be used.

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

SECTION A

ANSWER ALL QUESTIONS

1. (a) Write as a mixed fraction

(b)If and find x + y to 3-significant figure

2. (a)Find

(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. If maize, how many bags of maize did the farmer harvest?

3. (a)Factorize (i)

(ii)

(b)Simplify

(c)Solve for x:

4. (a)Solve for x: (i)

(ii)

(b)If log3 = 0.4771 and log2 = 0.3010

Find:

(i)

(ii) Without using tables.

5. Solve the following simultaneous equations

6. Given the universal

Set and

1. Represent the above information in a Venn-diagram and use it to find elements of

2. Show that

7. (a)Marium served Tshs 6 million in a serving account Bank where interest rate was 10% compounded annually. Find the amount in mariam’s account after 5years.

(b)In how many years would one’s investment double if 100,000/= is invested at 10% compounded semi-annually?

8. (a) Factorize:

(b) Given that

AB=EC

1. Show that EA=ED
2. Prove that

and state the postulate out of (SSS, AAS, SAS, RHS)

9. (a)The ratio of the areas of two similar polygons is 144:225. If the length of a side of the smaller polygon is 60cm, find the length of the larger polygon

(b)

Given that

• DC//AB
• AOB is diameter

Find an expression in terms of x

10. In a series between the integers 3 and 102. Find the sum of

1. Even numbers (ii) Odd numbers

(b) A bacteria produces 10 bacteria after every minute and each of the 10 bacteria produces, 10 bacteria after every minute and so

1. Form a sequence of number of bacteria produced after 1,2,3 and 4 minutes
2. If the frequency is to form a series, what is the name of the series?
3. Find the sum of bacteria produced after one hour.

SECTION B (Answer All Questions)

11. The table below represents the scores in general cleanliness of 30 students

1. Find the value of m
2. Complete the table and find Ɛf, Ɛfx
3. Find the mean (average) score
4. Find the mode
5. Construct an ogive and use it to estivate the median

12. Given the function f(x) = x²-8x + 12

1. Find the x and y-intercepts
2. Using (a) determine the axis of symmetry of f(x)
3. Using (b) determine the coordinates of the minimum point
4. Using (a) (b) and (c) sketch the graph of f(x)
5. From the graph find

1. Domain (ii)Range

6. Construct a suitable line and sketch it on the same axes to find solution of the equation; x² -10x + 16=0

13. (a)An aero plane fires from Tabora (5°S, 33°E) to Tanga (5°S, 39°E) at 332 km/her. Along parallel latitudes. If it leaves Tabora at 3 p.m., find the time of arrival at Tanga air-port

(b)Another plane flying at 595 km/hr leaves Dsm (7°S,39°E) at 8:00a.m it Addis Ababa (9°N, 39°E) (parallel longitude)

(Radius of the earth R 6370km)

14. (a) The volume V of a given mass of gas varies directly as the absolute temperature T and inversely as the pressure P

If V=450 and T= 288 when P=825, find V when T=320 and P = 720

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

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

OFFICE OF THE PRESIDENT, MINISTRY OF EDUCATION AND VOCATIONAL TRAINING

CERTIFICATE OF SECONDARY EDUCATION EXAMINATION

TERMINAL EXAMINATIONS- MAY 2022

FORM THREE BASIC MATHEMATICS

(For Both School and Private Candidates)

Time: 3 Hours Year: 2022

Instructions

l . This paper consists of sections A and B with a total of fourteen (14) questions.

2. Answer all questions.

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 calculators may be used.

6. All communication devices and any unauthorised 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)

Answer all questions in this section.

1.(a)If a*b=b (a² – 2b) Find (i) 3*2 (ii) n if 4*n=0

(b)Given 

2.A and B are two sets such that

1.                 
2.                In a class of 30 students 17 participate in English debate, 12 participate in English debate and sports. If every student is required to participate in at least one of the two subjects. Find the number of students who participate in

(i) English debate only    (ii) Sports only

3.(a)If 

(b)Express as single logarithm the expression 

4.Rewrite without absolute value  and sketch a graph of the resulting inequality 

5.(a)The second term of an A.P is 2 and the sixth term is 14. Find 

1. The first term
2. The common difference

(b)A function is defined by . Find 

(i) The inverse  of this function  (ii)

6.Given that  find value of 

1. Cos A
2. 

7.Fine the remainder when  is divided by x + 1 and hence solve the equation 

8.If  evaluate

1.                 Correct to 3 decimal places
2.                Simplify
3.                 Given  and  find

9.

1.                 Given that = find value of
2.                Make q the subject of the equation
3.                 Solve the equation  by factorization

10. A line passes through point A (3,5) and B (8, K) has a slope of -2. Find the;

1.                 Value of K
2.                The equations of line

SECTION B

11.(a)Mpira club has the following number of goals scored against them, 0,1,0,2,9,0,1,2,1, what is the mean number of goals scored against them?

(b)The table below shows the masses of 100 students to the nearest kg

1. Determine the mean of the masses
2. Calculate the mode
3. Draw a cumulative frequency (give) curve and use it to determine the median of the masses

12.(a)(i) Find the distance between Mbeya (9°S.33°E) and Tabora (5°S,33°E) in km

(b)An airplane takes off from Tabora (5°S,33°E) to Tanga (5°S,39°E) at a speed of 332 kmh^-1 if it leaves Tabora at 3:00pm, at what time will it arrive at Tanga airport?

13.Musa started business on 1^st June, 1999 with Tshs 6000/= as capital

June 01 Bought goods cash    3000/=

June 02 Paid office cleaners    20/=

June 03 Sold all goods for cash   3400/=

June 05 Purchased goods for cash  2000/=

June 08 Paid carriage on goods sold  40/=

June 10 sold goods for cash    3000/=

June 15 paid wages     100/=

1.                 Enter these transactions in cash book
2.                Bring down the balance at the end of June

14. A house and flag post are on the ground. From an open window in a house 6m, above the ground, Abdulrazaq finds that the angle of elevation of the top of the flag post is 35° and the angle of depression of the bottom of the flag post is 20°.

15.(a) Draw the graph of  taking the value of x in the interval 

(b)State the running point of the graph and state whether it is a maximum or a minimum.

(c)Solve the equation 

(d)Use a suitable straight line, solve the equation 

16. (a). Box A contains 8 items of which 3 are defective and box B contains 5 items of which 2 are defective. An item is drawn at randomly from each box. What is the probability that? 

1. Both items are non-defective?
2. One item is defective and one item is not defective

(b)The radii of trastrom of a right cicular cone are 10cm and 7cm. If the height of this trastrom is 6cm. What will be the height of the original cone?

(c)If 

1. Find an expression for
2. Find the simplified algebraic expression for f(x-1)

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

COMPETENCE BASED SECONDARY EXAMINATION SERIES

FORM III 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.

SECTION A (60 MARKS)

1.(a) Express the numbers 1470 and 7056 each as a product of its prime factors.

Hence evaluate and simplify

if m = 1470 and n = 7056.

(b)Express 0.00152 correct to: (i) two (2) significant figures

(ii)three (3) decimal places

(iii)in standard form

2.(a) Express x and y into fraction and hence find x + y, given that

and

(b)Solve for x in the following equation

3.(a) Solve for n

(b) Given that x² + 8x +Q = (x + K)²

4 .In a certain school, 40 students were asked about whether they like tennis or football or both. It was found that the number of students who like both tennis and football was three times the number of students who like tennis only. Furthermore, the number of students who like football only was 6 more than twice the number of students who like tennis only. However, 4 students like neither tennis nor football.

(a)Represent this information in a Venn diagram, letting x be the number of students who like tennis only.

(b)Use the results obtained in part (a) to determine number of students who likes;

(i)Football only.

(ii)Both football and tennis.

5.(a) Find the equation of the line through the point (2,−2) crossing the -axis at the same point as the line whose equation is y=2x- 4

(b) Express y in terms of x; 3x + 2y = 6 and Without drawing the graph, state the gradient, the y – intercept and x – intercept in the equation.

6.(a) The length of a rectangular field is 20m longer than the width. Find an expression for the perimeter of the field in terms of its length.

(b) In the figure below, Find angle x, y and z

7.(a) The parallel sides of a trapezium are 8cm and 12cm respectively. If the distance between the parallel sides is 9cm, calculate its area.

(b) A lady buys a printer for sh.26000 and when she sells it she realizes a loss of 40%. How much did she sell the printer for?

8. (a) If y² varies directly as x-1 and inversely as x+d and if x=2, d=4 for y=1, then find x when y=2 and d=1.

(b)If 8 students in a typing pool can type 210 pages in 3 days, how many students will be needed to type 700 pages in 2 days?

9.(a) If

Find

i) Cos A

(ii)

(b) Given the following figure, find the value of h, correct to one decimal place

10.(a)Compute the sum of the first ten terms of the series 1+5+9+....

(b)The 5th term of A.P is 23 and the 12^th term is 37. Find

(i)The eleventh term

(ii)The sum of the first eleventh terms by using the values computed above without using the common difference for this progression.

SECTION B(40%)

Answer All Questions In This Section

11.Given the relation;

(i)Sketch the graph of R.

(ii)State its domain and range.

(iii)Find inverse of relation R

12. Given that

(a) (i) Sketch the graph of f(x)

(ii) State its domain and range (iii) Is f(x) a one - to – one function?

(b) Find:

( i ) f(-4)

( ii ) f(2)

( iii )

13. The masses of 40 parcels handled at transport office were recorded as shown in table below

a)Find value of x

b)Determine modal class and its corresponding class mark

c)Find Median

14.( a) Given f(x) = x² - 4x + 2. Find

i) Axis of symmetry ii) Maximum or minimum value

iii) Turning point

(b)Draw the graph of f(x) in 14(a) and use it to solve the equation x² - 4x -2 =3

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

BASIC MATHEMATICS TERMINAL EXAMINATION-MAY

FORM THREE

Time 3:00 Hours                                                                              MAY 2020 

Instructions 

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

                       SECTION A (60 MARKS) 

1. (a) Arrange the number in ascending order.

(b) Express 0.06896 correct to: 

     (i) three (3) significant figures

     (ii) three (3) decimal places

     (iii) in standard form

2. (a) Solve for x in the equation:  32^x-3 x 8^x+4 = 64 ÷ 2^x

(b) Solve for x in the equation log(x²+8) – logx = log6

3.  (a) Find the solution set of the inequality  and indicate it on a number line.

(b) If find n if

(c) Simplify the following expression and state the coefficient of

4. (a) In a school of 75 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?

 ( b) The Venn diagram below shows the universal set U and its two subsets A and B

                                                                        Write down the elements of

 i) A’     ii)B’   iii)AUB    iv) A’UB’   

5. The figure ABCD below is rectangle with sides as shown where C1 and C2 are two quarter circles inside it.

Find:

a) Value x and y shown in the  figure above

b) Perimeter of the rectangle

c)Area of the rectangle ABCD

 d) Area of the shaded region

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 = 32⁰C when T_o =24⁰C and t = 9 cm, find the value of t when T_i = 36⁰C and T_o = 18⁰C

7. (a) A shirt whose marked price is Tshs 80,000/= is sold at a 13% discount, if the trader makes a profit of 20%, find the selling price of the shirt.

(b) A regular polygon has an exterior angle of 36⁰

1. Find the size of the interior angle
2. How many sides does this polygon have
3. Find the sum of interior angles of this polygon

8. (a) Find the 10^th  term of the G.P if the 4^th term is 8 and the 7^th term of this G.P is 16.

(b) Find the sum of the first 10 terms of the series: 4 + 6 + 8 + - - - - - - - - 

9. (a)Find the value of  without using mathematical tables.

(b) A ladder leans against vertical wall. If the ladder reaches 12m up the wall and its foot is 9 cm from the base of the wall. Find the length of the ladder.

10. (a) Factorize completely by splitting the middle term

(b) Factorize and hence find exact value of (10003)² –(997)²

(c) Solve the equation

          SECTION B ( 40 MARKS )

  (a) The function f is defined as follows:

 (i) Sketch the graph of .

(ii) Determine the domain and range of 

(b) If R^-1 =. Find the domain and range of R

   12. The 4^th, 6^th and 9^th terms of arithmetic progression forms first three terms of geometric progression. If the first term of the A.P is 3, determine the:

(a) Common difference of the arithmetic progression

(b)Common ratio of the geometric progression

(c) Kicheche deposited Tshs100000/= in a bank at a compound interest of 8% per annum for 4 years. Find how much interest he received 

13.  The weight in kg of 40 students were recorded as follows:

Calculate:

(a) The value of x

(b) The mode by using the formula. 

(c) By using an assumed mean, find the average weight of the students

(d) Draw a cumulative frequency curve and hence use it to estimate median.

14. a) A farmer sold a quarter of his maize harvest and give one third of the remaining to his    relatives. If the farmer remained with 36 bags of maize, find:-

i) How many bags of maize did the farmer harvest. 

ii) How many bags of maize did the farmer sold.

b)A shopkeeper makes a profit of 20% by selling a TV for 480,000/=

 i) Find ratio of buying to selling price

 ii) If the radio would be sold for 360,000/=, what would be the percentage loss?     

15. 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(0)   ii) f(-6)   iii) f(π)

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

16. Mr. Chakubanga started business on 15^th February, 2005 with capital in cash 1,055,000/=

February 16 Bought goods for cash 500,000/=

18 Bought shelves for cash 55,000/=

19 Sold goods for cash 450,000/=

20 Purchases for cash 400,000/=

21 Sold goods for cash 700,000/=

25 Paid rent for cash 150,000/=

Required:  Record the above transactions in the respective ledgers and extract a trial balance.