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 = k² where k is the ratio of the sides

(b)If  is isosceles where AD=BD and E and C are the mid-points 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 10cm², 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 x-intercept and y-intercept)

(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.

PRESIDENT’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 

1. The greatest possible number
2. The smallest possible number

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 + 2P-3Q, find the value of 

1. 2*3
2. Q if 2*Q=20

4. Find

5. Factorize the expression 15x² + xy – 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 x° is 18° less than y°. Find the values of x° and y°.

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(A-B)

(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 36°30’ at a point 5 metres from the foot of the tree. Calculate.

24. (a)The pie – chart below shows the number of students in one examination Centre in Different subjects sat for the national examination.

MINISTRY OF EDUCATION AND VOCATION TRAINING

MID TERM EXAMINATIONS

041                                                 BASIC MATHEMATICS

TIME 2:30 HOURS                                                                               AUG: 2021

Instructions

1. This paper consists of ten (10) compulsory questions.
2. Show clearly all the working and answers in a space provided.
3. All writing must be in blue or black ink except drawing must be in pencil.
4. Mathematical tables, geometric instruments and graph papers may be used where necessary
5. All communication devices and calculators are not allowed in assessment room.
6. Write your assessment Number in top write corner of every page.

1. (a)  Find the sum of all prime numbers between 80 and 100

(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 36cm²

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

1.  The slope of the line.

2. The equation of line in form of Y = MX+C

   b)  The vertices of the triangle are A(2,2) , B (3,4) and C (4,3). If the triangle is reflected under x-axis ,Write down the coordinate of the image of points A, B and C

7.  (a)Find the value of p given that  ()^{2p +1} = ()^3p.

           (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 a²-b²

Hence find the exact valueof 672²-328²

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,

1.                                                                                                                                                                                                             Which mark were scored by many student  ………………………………….
2.                                                                                                                                                                                                          Which marks was the lowest mark ………………………………………………….
3.                                                                                                                                                                                                       If 50% was the pass mark of the test if above 50%, How many student passed examination

THE PRESIDENT’S OFFICE

MINISTRY OF EDUCATION, REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT

SECONDARY EXAMINATION SERIES

BASIC MATHEMATICS MID TERM EXAMINATION

FORM TWO-2021

Time: Hours       20^th March 2021

1. This paper consists of ten (10) compulsory questions.
2. Answer all questions showing clearly all the working and answers in the spaces provided.
3. All writing must be in blue or black ink except drawing which must be in pencil.
4. All communication devices and calculators are not allowed in the examination room.
5. Write your Examination Number at the top right corner of every page.

---------------------------------------------------------------------------------

1. (a)  Find the sum of the LCM and GCF of 13, 52 and 104.

(b) Juhudi village received 586 389 bags of fertilizers for distribution to farmers. Round off this number to the nearest thousands and ten thousands

2. (a) Find the unknown numbers in the following equivalent fractions.

(b) Change  into a recurring decimal

3. (a) Change 15 km into centimeters

(b) Find the time in which sh.200 000 will earn sh.48 000 at the rate of 4% simple interest per annum.

4. (a) In the following figure, find the size of the angles labeled and. (give reasons for your answers)

(b) A square has an area of, find its perimeter.

5. (a) Find the equation of the straight line passing through the points. (Express your answer in the form).

(b) Solve the absolute valued equation:  

6. The sum of interior angles of a regular polygon is.

1. Find the number of sides of the polygon

2. Find the size of each exterior angle

3. What is the name of the polygon? ____________________________

7. (a) Find the value of in the equation:

(b) Factorize the expression  by splitting the middle term.

8. (a) Rationalize the denominator and simplify

(b) Given the formula:   make  the subject of the formula.

9. (a) What number must be added to the expression  to make it a perfect square?

(b) Given that  find the value of 

10. (a) Use the factors of the difference of two squares to find the value of

(b) Solve the following pair of simultaneous equations by elimination method                                                                        

THE PRESIDENT’S OFFICE

MINISTRY OF EDUCATION, REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT

SECONDARY EXAMINATION SERIES

BASIC MATHEMATICS MID TERM EXAMINATION

FORM TWO-2021

Time: Hours       20^th March 2021

1. This paper consists of ten (10) compulsory questions.
2. Answer all questions showing clearly all the working and answers in the spaces provided.
3. All writing must be in blue or black ink except drawing which must be in pencil.
4. All communication devices and calculators are not allowed in the examination room.
5. Write your Examination Number at the top right corner of every page.

---------------------------------------------------------------------------------

1. (a)  Find the sum of the LCM and GCF of 13, 52 and 104.

(b) Juhudi village received 586 389 bags of fertilizers for distribution to farmers. Round off this number to the nearest thousands and ten thousands

2. (a) Find the unknown numbers in the following equivalent fractions.

(b) Change  into a recurring decimal

3. (a) Change 15 km into centimeters

(b) Find the time in which sh.200 000 will earn sh.48 000 at the rate of 4% simple interest per annum.

4. (a) In the following figure, find the size of the angles labeled and. (give reasons for your answers)

(b) A square has an area of, find its perimeter.

5. (a) Find the equation of the straight line passing through the points. (Express your answer in the form).

(b) Solve the absolute valued equation:  

6. The sum of interior angles of a regular polygon is.

1. Find the number of sides of the polygon

2. Find the size of each exterior angle

3. What is the name of the polygon? ____________________________

7. (a) Find the value of in the equation:

(b) Factorize the expression  by splitting the middle term.

8. (a) Rationalize the denominator and simplify

(b) Given the formula:   make  the subject of the formula.

9. (a) What number must be added to the expression  to make it a perfect square?

(b) Given that  find the value of 

10. (a) Use the factors of the difference of two squares to find the value of

(b) Solve the following pair of simultaneous equations by elimination method                                                                        

THE PRESIDENT’S OFFICE MINISTRY OF EDUCATION AND VOCATIONAL TRAINING

024      MATHS- TWO

Duration: 2:30 Hours

INSTRUCTIONS.

• This paper consists of two sections A and B. 
• Answer all questions in both sections 
• Show clearly all working for each question
• Geometrical instruments and graph paper may be used where necessary

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) 2-significant figure  ii) 2-decimal places

4. Change the following into 12-hours 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, x-intercept and y-intercept of line 5x-2y-7=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) 8x² + 2x -3   b) x2-15x +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 ax²+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) x² – 8x +P=0  

 ii) x² - 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)