PRESIDENT OFFICE REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT

SECONDARY EXAMINATION SERIES 

BASIC MATHEMATICS

FORM FOUR

TERMINAL EXAMINATION - MAY, 2023

TIME 3:00 HOURS 

Instructions

1. This paper consists of sections A and B with a total of fourteen (14) questions.
2. Answer all questions in section A and B. Each question in section A carries six (6) marks while each question in section B carries ten (10) marks.
3. All necessary working and answers for each question must be shown clearly.
4. NECTA mathematical tables may be used.
5. Cellular phones, calculators and any unauthorised materials are not allowed in the examination room.
6. Write your examination number on every page of your answer booklet(s)

SECTION A (60 Marks)

Answer all questions in this section.

1.

2.

3. (a) A box contains 4 white balls and 5 black balls. Two balls are selected at random without replacement. Find the probability that

(i) Both are white balls

(ii) The first is black and the second is the white ball

(b) In a class of 15 students who take either Mathematics or Biology, 12 students take Mathematics, 8 students take Biology. If each student takes either subjects find by using formula the number of students who take Biology but not Mathematics.

4. (a) The gradient of line is -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

5. (a) The area of the triangle ABC is 140 cm², AB = 20, AC = 14cm, find the angle BAC

(b) Triangle XYZ is similar to triangle ABC and XY = 8 cm. If the area of the triangle XYZ is 24 cm² and the area of the triangle ABC is 96 cm². Calculate the length of AB.

6.

7.

=

/=

19 bought Shelves for cash 110,000/=

20 sold goods for cash 900,000/=

21 purchases goods for cash 800,000/=

22 sold goods for cash 1, 400,000/=

26 paid rent 300,000/=

Record the above transactions in Cash account ledger and extract a Trial balance.

8. (a). The product of a three terms of a geometric progression (GP) is 8000. If the first term is 4. Find the second term and third term

(b). Mahona invested a certain amount of money in a Savings Bank whose interest rate was 10% compounded annually. After two years he got 5000 shillings.

1. How much did he invest at the start?
2. How much did he receives as Interest at the end of two years.

9. (a) Find the value of

Sin (150⁰) cos (315⁰) Without using mathematical tables

Tan (300⁰)

(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 (i) Percentage of workers who are absent at least for 20 days

(ii) 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

1. The angle between VA and the base ABCD
2. The volume of the pyramid

13.  

14. (a). A function F is defined by the formula f(x) = where x is a whole number

1. If f(x) = 25 find the value of x
2. Find the value of

(b). A craftsman wishes to decide how many of each type A and B charcoal stove he has to fabricate in order to maximize profit for this month. Unit profit for type A stove is shs. 1000 and Unit profit for type B is shs. 1500. Type A stove requires 1m² of mild steel sheet per unit and type B requires 2m². He has only 12 m² of mild steel available. He can fabricate a total of 8 stoves of either type per month. How many of each type should he fabricate?

OFFICE OF THE PRESIDENT, MINISTRY OF EDUCATION AND VOCATIONAL TRAINING

CERTIFICATE OF SECONDARY EDUCATION EXAMINATION

TERMINAL EXAMINATIONS- MAY 2022

041 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) By using mathematical table evaluate  to three significant figures taking  

(b)If  Find Z = x + y hence express Z as fraction in its lowest form.

2(a) Simplify  

(b)Solve the equation 

3.(a)Given  then find 

(b)In class of 25 students, 12 students have taken mathematics, 8 have taken Biology. Represent this information on the Venn diagram hence or otherwise find number of students who.

1. Have taken mathematics and biology
2. Biology but not mathematics

4(a)If Alice deserves twice as many marks as Brenda and Brenda deserve half as much as many marks as Catherine, how many marks does each deserve when their total marks are 125.

(b)Given the vector  determine;

1. The value of k such that
2. A unit vector parallel to

5(a)The radius of the circle which inscribe an equilateral triangle is 2cm, find the perimeter of the triangle correct to two decimal places.

(b)In the diagram below O is the centre and  is the diameter of the circle  If  and Find the size of the angles of Quadrilateral ABCD

6(a)The mass of a plastic disc is inversely proportional to its area. If a disc of area 180cm² has a mass of 200g

1. Write down the equation relating mass (M) and area(A) of a disc.
2. If a similar disc has mass of 250g what is its area?

(b)Given  make t the subject of the formula

7.(a) If  determine 

(b)The sides of the rectangle are in the ratio 4:5. Given that the area of this rectangle is 20cm². Find the dimension of the rectangle.

8(a)The seventh term of a geometric progression is eighth times the fourth term and the fifth term is 48, find the term and the common ratio.

(b)A display of beef masala in supermarket is to have the form of a pyramid with 20 cans in the bottom row, 19 on the next row, 18 cans on the next row, and so on, with a single can at the top. How many cans of beef masala will be required for the display?

9.(a)If A and B are two complementary angles and  find  hence use the results to verify that 

(b)A man 12m directly away from a tree and from this position the angle of elevation of the top of the tree is 24°. If the measurement is taken from a point 1.5m above the ground level, find the height of the tree.

10(a)By completing the square solve the quadratic equation 

(b)Given Find

1. The value of a and b
2. 

SECTION B (40 MARKS)

Answer Any Four Questions from this section

11.One end of the rectangular tank of length 6m is a square  of side 2m. If AP is a diagonal of the tank, calculate;

1. AP correct one decimal places
2. The angle between AP and the plane ABCD
3. The surface area of the tank.

12.From a linear programming problem the following graph is draw

From the graph

1. Find the equation of lines L₁ and L₂
2. Write down the four inequalities representing the shaded region
3. Determine the corner points of the feasible region
4. Maximize the objective function  subjected to constraints in (ii)above

13.The number of workers in 52 working days is given in a cumulative frequency table below.

Find;

1. The percentage of workers who are absent at least 20days
2. Mean, use assumed mean A=17
3. Median

14.The following information relates to Mr. Mtipanga a trade as 31^st December, 2011

Net profit   2,000,000/=

Cost of sales   60% of sales

Purchases   8,000,000/=

Closing stock   20% of purchase

Sales to Net profit ratio  10:1

Determine 

1. Sales
2. Cost of sales
3. Closing stock
4. Opening stock
5. Expenses

15.(a)Find the image of the point (1, -5) after reflection on the line x=0, and then translated by a vector a= (0, -6)

(b) find two values of k such that 

(c) Find the inverse of matrix  hence use the results to solve the system of equations 

16(a)A bag contains 24 tennis balls, some white and some green. If a ball is chosen at random the probability of getting a green ball is . How many white balls are there?

(b)The probability that it’s raining at 8:30am on any one day is  The probability that a boy wears a rain coat as he leaves for school at 8:30am is  if it rain at any time. If it is not raining the probability that he wear a coat is . What is the probability that he wear a coat on any one day?

OFFICE OF THE PRESIDENT, MINISTRY OF EDUCATION AND VOCATIONAL TRAINING

CERTIFICATE OF SECONDARY EDUCATION EXAMINATION

TERMINAL EXAMINATIONS- MAY 2022

041 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) By using mathematical table evaluate  to three significant figures taking  

(b)If  Find Z = x + y hence express Z as fraction in its lowest form.

2(a) Simplify  

(b)Solve the equation 

3.(a)Given  then find 

(b)In class of 25 students, 12 students have taken mathematics, 8 have taken Biology. Represent this information on the Venn diagram hence or otherwise find number of students who.

1. Have taken mathematics and biology
2. Biology but not mathematics

4(a)If Alice deserves twice as many marks as Brenda and Brenda deserve half as much as many marks as Catherine, how many marks does each deserve when their total marks are 125.

(b)Given the vector  determine;

1. The value of k such that
2. A unit vector parallel to

5(a)The radius of the circle which inscribe an equilateral triangle is 2cm, find the perimeter of the triangle correct to two decimal places.

(b)In the diagram below O is the centre and  is the diameter of the circle  If  and Find the size of the angles of Quadrilateral ABCD

6(a)The mass of a plastic disc is inversely proportional to its area. If a disc of area 180cm² has a mass of 200g

1. Write down the equation relating mass (M) and area(A) of a disc.
2. If a similar disc has mass of 250g what is its area?

(b)Given  make t the subject of the formula

7.(a) If  determine 

(b)The sides of the rectangle are in the ratio 4:5. Given that the area of this rectangle is 20cm². Find the dimension of the rectangle.

8(a)The seventh term of a geometric progression is eighth times the fourth term and the fifth term is 48, find the term and the common ratio.

(b)A display of beef masala in supermarket is to have the form of a pyramid with 20 cans in the bottom row, 19 on the next row, 18 cans on the next row, and so on, with a single can at the top. How many cans of beef masala will be required for the display?

9.(a)If A and B are two complementary angles and  find  hence use the results to verify that 

(b)A man 12m directly away from a tree and from this position the angle of elevation of the top of the tree is 24°. If the measurement is taken from a point 1.5m above the ground level, find the height of the tree.

10(a)By completing the square solve the quadratic equation 

(b)Given Find

1. The value of a and b
2. 

SECTION B (40 MARKS)

Answer Any Four Questions from this section

11.One end of the rectangular tank of length 6m is a square  of side 2m. If AP is a diagonal of the tank, calculate;

1. AP correct one decimal places
2. The angle between AP and the plane ABCD
3. The surface area of the tank.

12.From a linear programming problem the following graph is draw

From the graph

1. Find the equation of lines L₁ and L₂
2. Write down the four inequalities representing the shaded region
3. Determine the corner points of the feasible region
4. Maximize the objective function  subjected to constraints in (ii)above

13.The number of workers in 52 working days is given in a cumulative frequency table below.

Find;

1. The percentage of workers who are absent at least 20days
2. Mean, use assumed mean A=17
3. Median

14.The following information relates to Mr. Mtipanga a trade as 31^st December, 2011

Net profit   2,000,000/=

Cost of sales   60% of sales

Purchases   8,000,000/=

Closing stock   20% of purchase

Sales to Net profit ratio  10:1

Determine 

1. Sales
2. Cost of sales
3. Closing stock
4. Opening stock
5. Expenses

15.(a)Find the image of the point (1, -5) after reflection on the line x=0, and then translated by a vector a= (0, -6)

(b) find two values of k such that 

(c) Find the inverse of matrix  hence use the results to solve the system of equations 

16(a)A bag contains 24 tennis balls, some white and some green. If a ball is chosen at random the probability of getting a green ball is . How many white balls are there?

(b)The probability that it’s raining at 8:30am on any one day is  The probability that a boy wears a rain coat as he leaves for school at 8:30am is  if it rain at any time. If it is not raining the probability that he wear a coat is . What is the probability that he wear a coat on any one day?