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