THE UNITED REPUBLIC OF TANZANIA
PRESIDENT’S OFFICE REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT
COMPETENCY BASED EXAMS
FORM TWO PREFTNA ASSESSMENT
041 BASIC MATHEMATICS
TIME: 2:30 hours October, 2022
Instructions
FOR EXAMINER’S USE ONLY  
QUESTION NUMBER  SCORE  EXAMINER’S INITIAL 
01 


02 


03 


04 


05 


06 


07 


08 


09 


10 


TOTAL 


CHECKER’S INITIAL 


(ii) When two different signs are multiplied, a product is obtained. Multiply the product obtain with a negative sign. Give the last sign you Will obtain.
(i) Four significant figures
(ii) Four decimal places
(b) write 20.025 into hundredth.
(c) Aisha’s mom took 30 minutes to cut the vegetables, and she took 1 hour in cooking. Find how many Seconds she took to complete the whole cooking?
3. (a) In the figure below M<RTS = 80^{}
LEARNINGHUBTZ.CO.TZFORM TWO MATHEMATICS EXAM SERIES 131
THE UNITED REPUBLIC OF TANZANIA
PRESIDENT’SOFFICEREGIONALADMINISTRATIONANDLOCALGOVERNMENT
COMPETENCY BASED EXAMS
FORM TWO PREFTNA ASSESSMENT
041 BASIC MATHEMATICS
TIME:2:30hours October,2022
Instructions
FOR EXAMINER’S USE ONLY  
QUESTIONNUMBER  SCORE  EXAMINER’S INITIAL 
01  
02  
03  
04  
05  
06  
07  
08  
09  
10  
TOTAL  
CHECKER’S INITIAL 
(ii) When two different signs are multiplied, a product is obtained. Multiply the product obtain with a negative sign. Give the last sign you Will obtain.
(i) Four significant figures
(ii) Four decimal places
(b) write 20.025 into hundredth.
(c) Aisha’s mom took 30 minutes to cut the vegetables, and she took 1hour in cooking. Find how many Seconds she took to complete the whole cooking?
3. (a) In the figure below M<RTS = 80^{}
LEARNINGHUBTZ.CO.TZFORM TWO MATHEMATICS EXAM SERIES 129
THE PRESIDENT’S OFFICE MINISTRY OF EDUCATION, REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT
COMPETENCY BASED SECONDARY EXAMINATION SERIES
BASIC MATHEMATICS FORM TWO
INSTRUCTIONS
(b) Find the value of n if
(b)What is the product of LCM and GCF of 16,24 and 36
(b)Rationalize the denominator to the simplest form
(b)By using elimination method solve for x and y in
4y – 41=14x
6x – 30 – 10y
(b)By using mathematical table evaluate
(b)What is the centre of an enlargement, given that the image of A(3,2) under the enlargement scale factor 2 is A(6,4)?
Marks in %  25  35  45  50  65  75  80  85 
Numbers of students  14  18  11  10  5  14  2  6 
LEARNINGHUBTZ.CO.TZFORM TWO MATHEMATICS EXAM SERIES 119
FORM TWO TERMINAL EXAMINATION
BASIC MATHEMATICS
Time: 2:30 Hours Year : 2022
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. NECTA 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 assessment room.
6. Write your Assessment Number at the top right corner of every page.
1. (a) Calculate the sum of the GCF and LCM of 42, 45, 50.
(b)
2.(a) Convert (i)256800cm into km
(ii)0.125 into percentage
(b) Round off (i) 260743 to the nearest thousand
(ii) 0.04261 to three decimal places
3.(a) Factorize the expression
(b)
4. (a) Make A the subject of the formula
(b) If 4tanB=3 and B is an acute angle, find the value of;
(c) A straight line passes through two points A(3, 6) and B (6, 3). Find the gradient of the line AB
5. (a) Find (i) the largest possible number; and
(ii) The smallest possible number by changing order of the digits in 47986.
(b).Write 0.0.346 in standard form.
6. (a) In a certain office, every man owns either a car or a lorry or both 23 own lorries, 14 own cars and 5 own both lorries and cars. How many men are there in that office?
(b) .Joyce used 1/3 of her money to buy sugar, 1/4 of it to buy soap and she remained with Shs 35/=
7. (a) Simplify
(b)Use a number line to find the sum of
(c)Arrange 2/5, 5/8, 48% and 0.6 in ascending order of magnitude.
(d)Decrease 160,000 by 16%
8. (a) Rationalize the denominator of
(b) Show on the number line the solution set of the inequality
9. (a)Without using Tables evaluate
(b)Given A=^{1}/_{2} where A is an acute angle, find the value of 1 – cos^{2} A.
10. (a) Simplify
(b)If N=2x10^{8} find the value of ^{1}/_{N} in scientific form
(c) Find the equation of a line through the point (2, 2) crossing the yaxis at the same point as the whose equation is
LEARNINGHUBTZ.CO.TZFORM TWO MATHEMATICS EXAM SERIES 106
THE PRESIDENT’S OFFICE MINISTRY OF EDUCATION, LOCAL ADMINISTRATION AND LOCAL GOVERNMENT
FORM TWO BASIC MATHEMATICS TERMINAL EXAMINATION
Time: 2:30 Hours Year: 2022
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.NECTA mathematical tables, geometric instruments and graph papers may be used where necessary.
5.All communication devices, calculators and any unauthorised materials are not allowed in the assessment room.
ATTEMPT ALL QUESTIONS
1. (a)(i)List down all the prime numbers between 1 and 12 and represent the numbers on the number line
(ii) Find the H.C.F and L.C.M of the numbers 8, 12 and 20 by prime factorization
(b)(i) Evaluate
(ii) Evaluate
(iii)Evaluate
(c)Evaluate
.
Write your answer in repeating decimal notation
2. (a) The distance between two points is 30.567km. Write the distance in metres in one significant figure
(b) The velocity of a car between two stations AB and BC is 40m/sec and 60km/hr. respectively. Find the average velocity in m/minute assuming that AB and BC are straight roads
(c)If 6,000/= amount to 9,600/= in five years simple interact what is the percentage rate?
3. (a) Given that the rectangle ABCD is similar to rectangle MBCN below
AB=10 BC=6 and
NC=x
(i )Find the value of x
(ii) Verify that the ratio of the areas = k^{2} where k is the ratio of the sides
(b)If is isosceles where AD=BD and E and C are the midpoints of AD and BD
Prove that (congruent)
4. (a)Evaluate
i.
ii.
(b)Solve for x and y
i.
ii. If x=5 and y=3, Find the value of ,
(c) If , make p the subject
5. (a)Find the value of
i.
ii.
(b)Find x
i.
ii.
(c)With the use of common logarithm find x
i.
ii.
6. (a) A and B are two intersecting circles of radius 4cm and 6cm respectively. Find the area enclosed by AB, is 10cm^{2}, find the area enclosed by the circles (shaded)
(b) In figure below, Triangles ABD and ABC are two isoscetes triangles CD=36cm, AB=12cm and Find the area of the figure ACBD
(c)Find the area of squire whose length of the diagonal = 6cm
7. (a)Find the equation of the line perpendicular to the 2y – x – 6=0 and passing through the point (4,6)
(b) Represent the equation in (a) in forms
i. y=mx+c
ii. (A and B are xintercept and yintercept)
(c) The point A (4, 3) is reflected in the line y=x. What are the coordinates of the image?
8. (a)(i)Express; as a perfect squire
(ii) If (6+x)(8+x) = find the value of a and b
(b) Factorize.
i.
ii.
iii.
(c) Evaluate
9. (a) An item is sold at 480,000/= with profit of 20%
i. Find the ratio of the buying price to the selling price
ii. If the same item would be sold at 360,000/= what would be the percentage lose ?
(b)Find the interest for a principal of 100,000/= at 4% compound interest after 10years
(c)Tarimo wants to borrow 10 million Tanzania shillings from a Bank to promote his business. The Bank agree to charge his compound interact at 10% per year. How much interest Mr. Tarimo will owe the bank at the end of 5 years?
10. (a)Solve the equation: by
i. Factorization
ii. Completing the square (using the formula)
(b) Solve the following simultaneous equation
i.
ii.
(c)Solve the following inequalities
i. 3x + 6 < 10 – 5x
ii.
LEARNINGHUBTZ.CO.TZFORM TWO MATHEMATICS EXAM SERIES 105
PRESIDENTâ€™S OFFICE
REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT
SECONDARY EXAM SERIES
FORM 2 BASIC MATHEMATICS
SECTION A (60 MARKS)
1. Rearrange the digits 39175 to form
2. Mary used tiles to build the floor of her sitting room measuring 15m by 20m. If she used only whole ones and they were alike, what was the greatest size of each tile?
3. The operation on the integers P and Q is defined as P*Q=PQ + 2P3Q, find the value of
4. Find
5. Factorize the expression 15x^{2} + xy â€“ 6y2
6. In 2011 the population of a village was 800. It increased by 20% the following year. What was the population in the year 2012?
7. In triangle ABC below xÂ° is 18Â° less than yÂ°. Find the values of xÂ° and yÂ°.
8. If find the value of
9. Find the length of time between 0425 hours and 1812 hours
10. If the product of 5 integers is negative, What is the maximum number of integers in that product which are positive?
11. Make L the subject of the formula.
12. Simplify the expression
13. Find the rational number in the form where a and b are integers and from the Number
14. Given that Find the value of x +y.
15. Factorize the expression hence use the result to evaluate:
16. Find the equation of a line which passes through the points A(4,2) and B(5,3) giving your answer in the form y=mx + c
17. Express the following numbers in scientific notation (A)72500 (B)0.001325
18. Solve for x in the equation
19. If=1. Find the value of x
20. If shs.600/= amounts to 960=for 5years, what is the percentage rate of simple interest per annum?
SECTION B (40 MARKS)
21. (a)Given that
(b)Use Mathematical tables to find the value of
22(a) Let A and B be two sets such that n(A)=52, n(B)=60 and (AUB)=96. Find tn(AB)
(b)In a certain area 50 householders were asked if they had a radio set, a T.V. set or both 40 householders said they had a T.V. set, 30 had both a radio set and a T.V. set and 2 householders had neither. With the help of a Venn diagram, how many householders had a radio set but no T.V set?
23. The upper part of a tree broken by the wind falls to the ground without being detached. The top of the broken part touches the ground at an angle of 36Â°30â€™ at a point 5 metres from the foot of the tree. Calculate.
24. (a)The pie â€“ chart below shows the number of students in one examination Centre in Different subjects sat for the national examination.
1
LEARNINGHUBTZ.CO.TZFORM TWO MATHEMATICS EXAM SERIES 95
THE PRESIDENT’S OFFICE
MINISTRY OF EDUCATION, REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT
COMPETENCE BASED SECONDARY EXAMINATION SERIES
ANNUAL EXAMINATION
FORM TWO
BASIC MATHEMATICS
TIME: 2:30 HOURS November, 2021
Instructions
1. This paper consists of ten (10) compulsory questions.
2. Answer ALL questions
3. Each question carries ten (10) marks.
4. Show clearly all the workings and answers in the spaces provided.
5. All writings must be in blue or black ink except for drawings which must be in pencil.
6. Four figures/mathematical tables, geometric instruments and graph papers may be used where necessary.
7. Calculators, cellular phones and any unauthorized materials are not allowed in the examination room.
8. Write Your Examination Number at the top right corner of every page.
FOR EXAMINER’S USE ONLY  
QUESTION NUMBER  SCORE  EXAMINER’S INITIALS 
1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


TOTAL 


CHECKER’S INITIALS 

1. (a) Three bells ring at intervals of 20 minutes, 30 minutes and 40 minutes. If they start ringing together at 7.30 am
(i) After how long will they ring together again?
(ii) At what time will this be?
(b) Round off 349.678 to the nearest.
(i) Tens
(ii) Hundredth
(iii) One significant figure
2. (a) Write in form of , where b ï‚¹ 0.
(b) In a class of 40 students are boys. Two fifth of the girls wear spectacles.
How many girls do not wear spectacles?
3. (a) Perform:
(b) Find the time in which sh 200,000/= will earn sh 48,000/= at the rate of 4% interest per annum.
4. (a) Calculate the angles marked with letters X, Y and Z.
(b) Find the area of rectangle whose perimeter is 30cm and its length and width are (3W7) cm and (W+2) cm respectively.
5. (a) Factorize the expression
6x^{2} – 11x + 4 by splitting the middle term.
(b) The sum and difference of the two numbers are 9 and 3 respectively. Find the possible numbers.
6. (a) (i) Find the equation of the straight line passing through (3,5) and (7,9).
(ii) Calculate the gradient and coordinates of the yintercept of 2x+3y=12.
(b) Find the image of a point (4, 3) after a reflection on yaxis followed by another reflection on y=0.
7. (a) If ^{4x+2} = ^{9}. Find the value of X.
(b) Rationalize writing the answer in the form a where a, b, c and d are real.
(c) Given log2 = 0.3010, log3 = 0.4770 and log7 = 0.8451. Find the value of log294.
8. (a) Calculate the length of EC and CD in figure below:
B D
E
8. (b) Use the figure below to prove that triangle ADBï‚º Triangle ADC
A
C D B
9. (a) A rectangle has sides of 12mm and 16mm. Calculate the length of one of its diagonals.
(b) Calculate the exact value of .
10. (a) In the Venn diagram below:
U = { Boys in form II at a certain secondary school}
F = { Members in the football team}
(i) How many boys are in the football team?
(ii) How many boys are in both teams?
(iii) How many are in the football team but not in the basketball team?
(iv) How many are neither basketball nor football team?
(v) How many boys in form II at the school?
10. (b) The table below shows the distribution of the score of 60 students in Mathematics table at MJI MWEMA secondary school.
Marks %  45 – 55  56 – 66  67 – 77  78 – 88  89  99 
No. of students  11  15  X  17  10 
(i) Find the value of X.
(ii) Find the percentages of the student score ate most 77 marks.
LEARNINGHUBTZ.CO.TZFORM TWO MATHEMATICS EXAM SERIES 73
Student’s Assessment Number……………..……
MINISTRY OF EDUCATION AND VOCATION TRAINING
MID TERM EXAMINATIONS
041 BASIC MATHEMATICS
TIME 2:30 HOURS AUG: 2021
Instructions
FOR ASSESSOR’S USE ONLY  

(b) Round off:
(i) 9.67 to ones,
(ii) 0.205 to one decimal place,
(iii) 0.197 to two decimal places,
Hence, estimate the value of
2. (a) Evaluate 0.4 + 25% (0.220.2) + 0.45)
(b) If the new price of selling shoe is 40000Tsh. Findthe percentage increase of price if the old price was 30000Tsh.
3. (a) If the bus starts the journey from Babati at 0600 and takes eight hours and a half to reach at Chemba bus terminal. Write the time taken to reach in 24 hours clock.
(b) If 50000Tsh of money was invested at a bank which provide the rate of 5%. Find the amount at a bank after 4 years.
4 (a) Find the value of an angle marked in letter f,g and k in the figure below.
b) Find the perimeter of square ,if its area is 36cm^{2}
5 (a) The sum of two numbers is 127. If thedifference between the number is 7, Find the numbers
(b) Solve the equation by using quadratic formula.
6 a) If the line passes through the point (3,4) and (2,6). Find
b) The vertices of the triangle are A(2,2) , B (3,4) and C (4,3). If the triangle is reflected under xaxis ,Write down the coordinate of the image of points A, B and C
(b) (i) Find the value of 0.0000125 in standard notation.
(ii) Simplify the expression (3 + ) (4 )
8 (a) solve for the x in the inequality
3X – 4>, X+16
(b) Factorize the expression a^{2}b^{2}
Hence find the exact valueof 672^{2}328^{2}
9 the right angled triangle in the figure below has sides of length 7, 24 cm and 150cm
S
(a)Calculate the value of.
(b)Calculate the area of the triangle
10 (a) There are 48 men at the meeting of whom 24 are teachers, 36 are parents and 16 are both teachers and parents . By using venndiagram , find the number of men who are neither teacher nor parents.
b) The marks of 100 student were recorded as follow,
Marks  41  50  51 60  61  70  71  80  81 90  91  100 
Number of students  10  22  34  25  7  2 
LEARNINGHUBTZ.CO.TZFORM TWO MATHEMATICS EXAM SERIES 70
Candidate’s Examination Number………………………………
THE PRESIDENT’S OFFICE
MINISTRY OF EDUCATION, REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT
SECONDARY EXAMINATION SERIES
BASIC MATHEMATICS MID TERM EXAMINATION
FORM TWO2021
Time: Hours 20^{th} March 2021
Instructions

(b) Juhudi village received 586 389 bags of fertilizers for distribution to farmers. Round off this number to the nearest thousands and ten thousands
(b) Change into a recurring decimal
(b) Find the time in which sh.200 000 will earn sh.48 000 at the rate of 4% simple interest per annum.
(b) A square has an area of, find its perimeter.
(b) Solve the absolute valued equation:
(b) Factorize the expression by splitting the middle term.
(b) Given the formula: make the subject of the formula.
(b) Given that find the value of
(b) Solve the following pair of simultaneous equations by elimination method
Page 1 of 8
LEARNINGHUBTZ.CO.TZFORM TWO MATHEMATICS EXAM SERIES 54
Candidate’s Examination Number………………………………
THE PRESIDENT’S OFFICE
MINISTRY OF EDUCATION, REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT
SECONDARY EXAMINATION SERIES
BASIC MATHEMATICS MID TERM EXAMINATION
FORM TWO2021
Time: Hours 20^{th} March 2021
Instructions

(b) Juhudi village received 586 389 bags of fertilizers for distribution to farmers. Round off this number to the nearest thousands and ten thousands
(b) Change into a recurring decimal
(b) Find the time in which sh.200 000 will earn sh.48 000 at the rate of 4% simple interest per annum.
(b) A square has an area of, find its perimeter.
(b) Solve the absolute valued equation:
(b) Factorize the expression by splitting the middle term.
(b) Given the formula: make the subject of the formula.
(b) Given that find the value of
(b) Solve the following pair of simultaneous equations by elimination method
Page 1 of 8
LEARNINGHUBTZ.CO.TZFORM TWO MATHEMATICS EXAM SERIES 53
THE PRESIDENT’S OFFICE MINISTRY OF EDUCATION, LOCAL ADMINISTRATION AND LOCAL GOVERNMENT
MATHS TERMINAL EXAMINATIONMAY
FORM TWO
Time 2:30 Hours MAY 2020
Instructions
SECTION A (60 MARKS)
1. a) Rearrange the following in ascending order
b) Write 56 as the product of prime factors
2. Express in form of where p and q are both integers and
3. A room of length 270cm and 150cm is to be covered with square tiles. What is the largest size of the tiles to be used if no space of the room is left to be uncovered and how many tiles will be used?
4. Round off 34.9545 correct to i) Two significant figure ii) One decimal places
5. Write the following into 24hours system i) 03: 15 Pm ii) 01: 01Pm
6. Given , find i) 64*3 ii) a if
7. Two angles of pentagon are 58^{0} and 38^{0} and the other remaining three are in the ratio of 5:6:7. Find the largest angle.
8. Given a straight line 2y+5x+1=0, f
Fnd a) Slope b) yintercept c) xintercept
9. Two supplementary angles differ by 12^{0}. Find the angles.
10. Add the following
11. Anna is two years older than betty. Last year, Anna was two times as old as Betty. What is their age?
12. Make rsubject of formula in the following
13. Express in the form of
14. Use method of difference of two squares to evaluate the following
i) ii) 0.985^{2} – 0.015^{2}
15. Given log2=0.3010 and log7=0.8451, without using logarithm table evaluate:
a) log1.25 b) log 3.5
16. Factorize the following expression
a)15t^{2}14t8=0 b) (2c+3)^{2} – c^{2}
18.Simplifythe following
a)
b)
19. Expand the following
a) [y 3] [ + y ] b) (6n  )^{2}
20. For value of P which makes the following equations perfect square
(i) x^{2} – Px +16=0
(ii) x^{2}  x + P=0
SECTION B (40 MARKS)
21. a) From the quadratic equation show that
b) By using general formula of quadratic equation solve the following equation
22. 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
b) Perimeter of the rectangle
c)Area of the rectangle ABCD
d) Area of the shaded region
23.a) A rope is tired at the top of the flagpole and the other end of the rope is fixed on a point 36m from the base of the flagpole. If the flag pole is 15m high, what is the length of the rope?
b) In the figure below find the length of PQ and PS if QR=8cm, RQ=12cm and PR=17cm.
24. 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:
a) How many bags of maize did the farmer harvest.
b) How many bags of maize did the farmer sold.
25. a) By using logarithm tables, evaluate
b) Evaluate the following without using logarithm tables:
(i)
(ii)
(iii)
LEARNINGHUBTZ.CO.TZFORM TWO MATHEMATICS EXAM SERIES 14
THE PRESIDENT’S OFFICE MINISTRY OF EDUCATION AND VOCATIONAL TRAINING
MID TERM EXAMIATIONS
024 MATHS TWO
Duration: 2:30 Hours
INSTRUCTIONS.
SECTION A (60 MARKS)
1. Write the place value of digits in the brackets
a) 1485361 (8)
b) 7524693 (2)
2. Write the following into expanded form
a) 470059 b) 1290400
3. Round off 309.437 correct to
i) 2significant figure ii) 2decimal places
4. Change the following into 12hours system
i) 0404 hours ii) 0028 hours
5. Convert the following into fraction
i) 0.34 ii) 2.13
6. Find the greatest number that is exactly divides 360 and 456
7. Find solution of and show it no the number line.
8. Divide Sh. 1690 among Peter, Juma and Ali in the ratio of
9. There are 180 members of a committee. In a meeting, were present. How many members were absent?
10. Find
11. Simplify the following
a)
b)
12. Solve the following equation
13. Find slope, xintercept and yintercept of line 5x2y7=0
14. The ratio of exterior to interior angle of regular polygon is 5:7.
Find number of sides of the polygon and total degree measure of the polygon.
15. In a figure beside, AB//CD and line PQ and RS are transversal line. Find values of the angles marked x, y and z
16. In how many years would sum of the money double itself at 8% rate per annum?
17. Factorize the following expression a) 8x^{2} + 2x 3 b) x215x +58
18. By selling a computer for Sh. 800,000/=, a profit of Sh. 200,000/= is earned. Find the percentage profit.
19. Simplify the following
i)
ii)
20. Make v subject of the formula the following equation
SECTION B (40 MARKS)
21. a) From the quadratic equation ax^{2}+bx+c=0, show that
b) By using general formula of quadratic equation solve the following equation
22.John's father is 5 times older than John and John is twice as his sister Alice. In two years time the sum of their age will be 58. What is their present age?
23. a) Simplify the following by rationalizing the denominator
i)
ii)
b) Find value of P which makes the following equations perfect square
i) x^{2} – 8x +P=0
ii) x^{2}  x + P=0
24 a) If , evaluate:
i)
ii) Find r if
b) Solve for x the following
i)
ii)
25. a) Expand the following
i)
ii)
b) Factorize the following
i)
ii)
LEARNINGHUBTZ.CO.TZFORM TWO MATHEMATICS EXAM SERIES 7