THE PRIME MINISTER’S OFFICE REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT

FORM ONE ANNUAL JOINT EXAMINATION

MATHEMATICS

TIME: 3:00 Hours November 2026

Instructions

1. This paper consists of 10 questions. Answer all questions.
2. All necessary working and answers for each question must be shown clearly.
3. Non-programmable calculators may be used. (Calculators are allowed in the examination room.)
4. All communication devices and any unauthorized materials are not allowed in the examination room.
5. Write your full name on every page of your answer sheets.

1. (a) Explain how mathematics is applied in our daily life activities by considering the following fields. (Give 5 points in each case.)

1. In Schools
2. In Industries

(b) Write an essay arguing whether or not learning mathematics is important in our lives. (Give three points.)

2. (a) If  and  evaluate:

1. x + yz
2. xy / z

(b) The mean income of a certain company is 77 million TZS per year. If the income varies by 1.2 million TZS, what are the minimum and maximum incomes of the company?

3. (a) Write 47628.03514 correct to:

1. 2 decimal places
2. 7 significant figures
3. The nearest hundredths
4. The nearest thousands

(b) Amina and her 17 friends bought 212 bottles of soft drink at a price of TZS 635 per bottle. If the total cost was shared equally among themselves, estimate how much each person paid.

4. (a) Jason has 500, 200, and 100 Tanzanian shillings coins. The ratio of the total amounts of these coins is 2:3:5 and the total amount is 780,000 TZS. Find the number of coins of each kind.

(b) Two consecutive numbers are in the ratio 2:7. If 6 is added to their sum, the result is 32. Find the sum of the numbers.

5. (a) Simplify −3(2y² − 7) + 8(3y² − 12) and state:

1. The coefficient of y²
2. The number of terms
3. The constant term

(b) Evaluate the following expression when a = −2, b = 4, c = −1 and d = 3:

−(3/4)b + (1/2)(ac + bd²).

6. (a) The age of the mother is ten times as old as Janeth. After 4 years, the sum of their ages will be 41 years. Find:

1. The difference of their ages now.
2. The sum of their ages 5 years ago. (Comment on your result.)

(b) The sum of two consecutive integers is at least negative fifteen. What are the smallest values of the consecutive integers that will make it true?

7. (a) Express each of the following statements in symbolic form:

1. “x is greater than 7”
2. “y is not equal to 10”

(b) Represent the solution of the following inequalities:

1. √(5x − 1) ≤ 3
2. |2 − 5x| > 12

8. If one side of a triangle is one-fourth of the perimeter, the second side is 7 cm and the third side is two-fifths of the perimeter:

1. Construct a triangle using the information given.
2. Find the perimeter of the triangle.
3. Write down the length of the unknown sides.

9. The average of two numbers x and y is 7 and three times y subtracted from x is 18.

1.      Determine the equations from the given information.
2.      Find graphically the point of intersection.

10. Amani applies 2 bags of fertilizers to his 4-acre farm while Jenifer applies 6 bags to her 12-acre farm. Taking x to be the number of bags of fertilizers and y to be the size of the farm in acres:

1.      Draw a line graph and calculate its gradient (slope)
2.   Find the equation of the line segment.
3. Using the equation of the line obtained in (b) above, determine:
   1. The number of bags of fertilizers Amani will need for his 24-acre farm.
   2. The size of Jenifer's farm if she bought 75 bags of fertilizers.

PRESIDENT OFFICE REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT

SECONDARY EXAMINATION SERIES

COMPETENCE BASED ASSESSMENT

BASIC MATHEMATICS FORM ONE

ANNUAL EXAMINATION 2023

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 drawing which must be in pencil.

1.(a) (i) Add the first three multiples of 2, 3 and 5.

(ii) The numbers K, 2, 3 and 5 have an average of 5. What is the number represented by the letter K?

(b) Re-write the number  as a mixed fraction.

2. (a) The number of pupils in three primary schools is as follows. Iganzo primary school is 1600 pupils, Ruanda primary school is 1500 pupils and Ilea primary school is 1800 pupils. Approximate the number of pupils of the three schools to the nearest thousands.

(b) Calculate  (80kg 49g) – (39kg 850g)

3.(a) (i)Arrange 2/5, 5/8 ,48% and 0.6 in ascending order

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

│2x+1│>3

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

4.(a) Solve 3 -  of (6x+9) = 5-2x

(b) Solve the following simultaneous equations 

2x+3y=5

4x+23=5y

5(a) One - third of the sum of ages of Ana and Asha is 50 years, and one - fifth of the difference of their ages is 2 years, find the age of Ana and Asha respectively.

(b) The width of the football ground is 40m. If the area of the same football ground is  1700m²

(i) find the length of the football ground

(ii) if the person has to walk around the football ground, what length of the football ground is expected to be covered by the person?

6.(a) Differentiate between rational number and irrational number

(b) Sketch the graph of the equation x-2y=4

7. (a) A car was sold at a profit of 90000 shillings. If the rate of profit is  % , find the purchasing price of the car and its selling price?

(b) Mr. Juma deposited a certain amount of money in a bank for a period of 3 years at the rate of 3.5% which gives an interest of 8400 shillings. Determine the amount of money that Mr. Juma deposited initially.

8.(a) (i) John, Ramadhani , Marry and Sam have 600 ,100, 500 and 300 shares in a cooperative shop respectively. Divide 150,000 shs among them in the ratio of their shares.

(ii) A real estate agent received a 6% discount on the selling price of a house . If the discount was Tsh.888,000. What was the selling price of the house ?

9. (a) Study carefully the figure below

1. Find the values of the angles marked p, q and r respectively.

2. Find the value of  p+q+r

(b) If 2x +70⁰ and 3x+20⁰ are supplementary angles, determine the value of x

10.(a) If the straight line CD which is passing through the points C (2 , 6) and D ( K , 3 ) has a gradient of -1, find the value of K.

(b) Find equation of a line passing through point ( 0 , 3 ) and ( 1 , 2 ) 

PRESIDENT OFFICE REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT

SECONDARY EXAMINATION SERIES

COMPETENCE BASED ASSESSMENT

BASIC MATHEMATICS FORM ONE

ANNUAL EXAMINATION 2023

Instructions

Answer all questions from this paper

1. (a) Nine best friends share 52 sweets equally. How many sweets does each friend get and how many remain

(b)A farmer uses  of his farm for giving bananas  pineapple  for mangoes and remaining portion of his land in used for growing oranges. What fraction of his land used to grow orange?

2. (a)A lorry is filed with 7.1 tones of land. During the Journey 210kg of sand either falls or blows away. What mass of sand in tones in delivered at end of Journey?

(b)Juma measured the height of his friend Moses by using a tape measure. He found that his friend was 167.5cm high. Approximate his height

1. To 1 significant figure
2. To nearest ten

3. (a)The perimeter of a square plot is 240m. What length is its side?

(b)A goat is tied on a post by a rope of length 7m

1. Draw the shape of a figure the goat can describe on the land when it is grazing
2. What is the area of land the goat can reach?

4. (a)The length and width of a rectangular field shown below are respectively (x + 6) metres and (x – 1) metres. Let P be the Perimeter of the field. Write the algebraic expression of P in terms of x

(b)A wooden table is bought for Tsh 80,000 and then sold for Tsh 96,000/=. Find

1. The profit made
2. Percentage profit

5. (a)If x= 0.2 and Y = 5 express X and Y in form of  where  and ‘a’ and ‘b’ are integers find value of find value of

(b)Mr. John has three classes. Each class has 28, 42 and 56 students respectively. Mr. John wants to divide each class into groups so that every group in every class has same number of students and there are no students left. What is the maximum number of students Mr. John can put in each group?

6. (a) Rectangular table top is 2m long. If the area of the rectangular table top is 3.96°m². Find its width

(b)Solve simultaneous equation below

7. (a) If Fatuma is 4years less than Bakari and 3times Fatuma’s age is equal to 2 times Bakaris age what are their ages?

(b) Solve

8. (a) John, Ramadhani, Mary and Sam have 60°, 100, 500, and 300 shares in a cooperative shop respectively. Divide 150,000 shs among them in ratio of their shares.

(b)A real estate agent received a 6% discount on selling price of a house. If the discount was Tsh 888,000. What was selling price of the house?

9 (a) Find the sum of 85% of 9861 and  of 12458. Write your answer in two significant figures.

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

10. (a)If the lines whose equation is y=3x – p passes through points (6,10) and (q, 22) Find the values of P and q, where P and q are integers

(b)Asha and Juma received 630,000 shillings from their father. The father wanted to give Asha twice as much as the amount that could be given to Juma. How much did Asha receive?

PRESIDENT'S OFFICE  REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT  

ANNUAL EXAMINATION  MATHEMATICS- FORM ONE

Time: 2:30 Hours   November 2020 a.m.

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.Four figure 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 examination room.

1. (a) Write the place value of digits in the brackets

i. 785061        (5) ii.  52401         (2)

(b) Write the following into expanded form 

i.720902              

ii.53901

2.(a) Write 0.003685 correct to 

i) 3-significant figure   ii) 3-decimal places

(b) Convert   into decimal, correct to 2-decimal places.

3. (a) Change 

i) 1608 hrs into 12 – hours clock system   ii) 7:08 pm into 24 – hours clock system

(b) The length of 200 dam is what percent of the length of 1.6 km?

4.(a) Find the H.C.F of 112, 168 and 420 by prime factorization. 

(b) Three traffic lights at three different road crossings change after 48 seconds, 72 seconds and 100 seconds respectively. If they all change simultaneously at 8:00 am. At what time will they change again simultaneously?  

5. (a) Express   in form of   where b ≠ 0

(b) Solve for x given that 

6.(a) Two complementary angles differ by 12⁰. Find the angles

(b) Two angles of polygon are right angles and each of the remaining is 125⁰. Find number of sides of the polygon and sum of the interior angle.

7.(a) Solve following system of simultaneous equations

4x - 3y = 22

(b) 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.

8. (a) What is the absolute value of : 

i)  5/6 - 6/7  ii)  -3 x 7

(b) Solve the following

9.(a) A loss of 15% on the price of an item is equal to T.sh 9,000/=. Find the selling price of an item for the profit of 25%.

(b) Find slope, y-intercept and x-intercept of a line 3x + 2y +6=0.

10. (a) In the figure below, find the value of: (i) x (ii) y 

(b) Twice the width of a rectangle is greater than its length by 3cm. If the perimeter of the rectangle is 36cm, find its dimensions