PRESIDENT’S OFFICE
REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT
MID TERM EXAMINATION AUG- 2023
SECONDARY EXAMINATION SERIES
MATHEMATICS FORM FOUR
TIME: 3 HOURS AUG-2023
Instructions
SECTION A (60 MARKS)
(b) (i) Mr. Tumai Distributed Tshs 960,000/= awards to students who passed well in their examinations and their respective teachers as follow: 23% to all students who passed Arts Subjects. 15% to students who passed Mathematics and 27% to students who passed science subjects. The remained amount was distributed to teachers. Find the amount that were awarded to teachers.
(ii) Three bells commence tolling together and toll at intervals of 8, 10 and 12 seconds respectively. How many times do they toll together in 50 minutes?
(b) Describe the applications of Logarithm in real life situations
(ii) How many numbers were mentioned by either OKWI or FEITOTO?
(b) A perpendicular line from the point P(2,-4) to the line meets the line at point Z(-1,3). Find:
i. Distance
ii. If the point Z(-1,3) is a mid-point of the line , find the coordinates of point
(b) By considering the Alternating opposite angles theorem, draw the diagram hence identify the corresponding angles.
(b) Mayele bought 3 bottles of juice of capacity 350 ml and Dialo bought 1 bottle of juice of capacity 1 litre.
i. Who had more juice to drink?
ii. How much more?
(b) A company bought two cars for Tshs 25,000,000/= each. If one car was sold at a profit of 18% and another was sold at a loss of 6%. In the whole transactions there were no loss. What was the profit made by a company?
(b) The number 19683 is in which term in the following Geometric sequence; 3, 9, 27 …?
the length of each other sides
(b) From the top of a tower of height 60m the angles of depression of the top and the bottom of a building are observed to be 30^{0} and 60^{0} respectively. Find the height of the building.
(b) A large rectangular garden in a park is 120m wide and 150m long. A contractor is called in to add a brick walkway to surround this garden by the same width. If the area of the walkway is 2800m^{2}, how wide is the walkway?
SECTION B (40 MARKS)
Class Mark | 10 | 15 | 20 | 25 | 30 | 35 |
Frequency | 3 | 2 | 10 | 5 | 4 | 1 |
By using the data above reconstruct a frequency distribution table including class interval and frequency.
(b) Prove that equal chords of a circle subtend equal angles at a centre.
difference in their longitude.
(b) A pyramid with vertex V and edges VA, VB, VC, VD each 15cm long has a rectangular base ABCD where AB = CD = 10cm and AD = BC = 8cm.
i. Sketch the pyramid using the above information.
ii. Calculate the height “VO” of the pyramid where “O” is the centre of the rectangle.
(ii). By using matrix method, solve the equations
(b). A transformation is given and , find the image of the equation 2x – 3y = 6 under the transformation matrix which performs the above transformations.
Find (i) f(1.95) (ii) f(15) (iii) Domain of f (iv) identify the type of a function f
(b) A school is preparing a trip for 400 students. The company who is proving the
transportation has 10 buses of 50 seats each and 8 buses of 40 seats, but only 9 drivers available. The rental cost for a large bus is 800,000/= and 600,000/= for the small bus. How many buses of each type should be used for the trip for the least possible cost?
Page 1 of 6
FORM FOUR MATHEMATICS EXAM SERIES 172
FORM FOUR MATHEMATICS EXAM SERIES 172
PRESIDENT OFFICE REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT
SECONDARY EXAMINATION SERIES
BASIC MATHEMATICS
FORM FOUR
TERMINAL EXAMINATION - MAY, 2023
TIME 3:00 HOURS
Instructions
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 L_{2} is perpendicular to L_{1} and passes through point (-3, -2). What is the equation of L_{2}?
(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 cm^{2}, 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 cm^{2} and the area of the triangle ABC is 96 cm^{2}. 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.
9. (a) Find the value of
Sin (150^{0}) cos (315^{0}) Without using mathematical tables
Tan (300^{0})
(b) Calculate the angles of a triangle which has sides of lengths 4m, 5m and 7m
10. (a). Given that x^{2} –y^{2} = 27 and x + y = 9 find the value of xy
(b). Solve the equation 2x^{2} – 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
No.of absent | 0 – 4 | 5 – 9 | 10 – 14 | 15 – 19 | 20 – 24 | 25 - 29 |
Cumulative frequency | 5 | 13 | 30 | 45 | 48 | 52 |
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
13.
14. (a). A function F is defined by the formula f(x) = where x is a whole number
(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 1m^{2} of mild steel sheet per unit and type B requires 2m^{2}. He has only 12 m^{2} 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?
FORM FOUR MATHEMATICS EXAM SERIES 157
FORM FOUR MATHEMATICS EXAM SERIES 157
THE PRESIDENT’S OFFICE MINISTRY OF EDUCATION, REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT
COMPETENCY BASED SECONDARY EXAMINATION SERIES
BASIC MATHEMATICS
FORM FOUR- SEPT 2022
INSTRUCTION
SECTION A: (60 MARKS)
Answer all questions in this section
If k=0.5 and P=0.8, find the value of
(b)Find the solution set of the system
Determine
(b)(i) What do the mutually exclusive events mean as used in probability?
(ii))Find the probability of obtaining a 3 or 5 in one roll of a die
(b)Given vectors calculate,
(i) (ii) |w|w
(b)The interior angle of regular polygon is 120° greater than the exterior angle. Find the number of sides of the polygon and hence identify the name of the polygon.
1 us dollar = 118 Japanese Yen
1 us dollar = 76 Tanzanian shillings
Calculate the total cost of buying a car including the charged custom duty of 25% in Tanzania shillings.
(b) The number of eggs which a goose lays in a week varies as the cube root of the average number of hours of sleep she has. When she has 8 hours sleep, she lays 4 eggs. How long does she sleep when she lays 5 eggs?
(b)(i)The ratio of boy to girls at Mtakuja secondary school is 3:7. If the school has 500 students, find the number of boys at the school.
(ii)Define the term trial balance as used in Accounts and write one uses of it.
(b)A building has an angle of elevation of 35° from point P, and angle of the elevation of 45°from a point Q. if the distance between points P and Q is 30cm, what is the height of the building (Write your final answer to the nearest whole number)
(b)Find two consecutive numbers such that the sum of their squares is equal to 145.
SECTION B: (40 Marks)
Answer all questions in this section
Class interval | 40-49 | 50-59 | 60-69 | 70-79 | 80-89 | 90-99 |
Cumulative frequency | 2 | 4 | 9 | 17 | 29 | 33 |
(b)Show that the radius of a circle with an arc of a length m and central angle is 6m
(b)Calculate the distance from Ruvuma (15°S, 45°E) to Mtwara (15°S, 49E) in km. use and the diameter of the earth as 12800km and the answer should be correct to two decimal places.
(b)A liner transformation maps the point (x,y) onto (x' y') where x'=4x + 3y and y'=x – 2y. Find
Find (i) f^{-1} (x)
(ii) the domain and range of f(x)
(b)A shopkeeper buys two types of sugar, White sugar and brown Sugar. The white sugar is sold at shs 40,000/= per bag and the brown sugar is sold at shs 60,000/= per bag. He has shs 1,500,000/= available and decides to buy at least 30 bags altogether. He has also decides that at least one third of 30 bags should be brown sugar. He buy x bags of white sugar and y bags of brown sugar.
FORM FOUR MATHEMATICS EXAM SERIES 120
FORM FOUR MATHEMATICS EXAM SERIES 120
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.
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;
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 180cm^{2} has a mass of 200g
(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 20cm^{2}. 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
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;
12.From a linear programming problem the following graph is draw
From the graph
13.The number of workers in 52 working days is given in a cumulative frequency table below.
Number of absences | 0-4 | 5-9 | 10-14 | 15-19 | 20-24 | 25-29 |
Cumulative frequency | 5 | 13 | 30 | 45 | 48 | 52 |
Find;
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
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?
FORM FOUR MATHEMATICS EXAM SERIES 93
FORM FOUR MATHEMATICS EXAM SERIES 93
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.
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;
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 180cm^{2} has a mass of 200g
(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 20cm^{2}. 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
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;
12.From a linear programming problem the following graph is draw
From the graph
13.The number of workers in 52 working days is given in a cumulative frequency table below.
Number of absences | 0-4 | 5-9 | 10-14 | 15-19 | 20-24 | 25-29 |
Cumulative frequency | 5 | 13 | 30 | 45 | 48 | 52 |
Find;
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
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?
FORM FOUR MATHEMATICS EXAM SERIES 92
FORM FOUR MATHEMATICS EXAM SERIES 92
PRESIDENTâ€™S OFFICE
REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT
SECONDARY EXAM SERIES
FORM 4 BASIC MATHEMATICS
SECTION A (60 MARKS)
Answer ALL questions in this section
1(a)Express the number 0.000038583
(b)Change into fraction
2(a)Solve the following equation simultaneously:
(b)Rationalize the denominator of the expression
3(a)Solve the following equations simultaneously
(b)Given . Find:
4(a)Find the equation of the perpendicular bisector of the points A(4,8) and B (-4,-6)
giving your answer in the form
(b)Given that .
Find the relation between the three vectors a, b and c
5. In the figure below // and
If the area of DECB is 21cm^{2}; find the area of
6(a) Given that w is directly proportional to x^{2} and inversely proportional to t and that
w=12 when x=2 and t=2. Find the value of w when x=3 and t=3
(b)Sophia and Alex had each Tsh.10,000. If Sophia wanted to buy the South African Rand and Alex wanted to buy the Malawian Kwacha, how much would each one receive?
(1 Rand =210 Tanzania shillings; and 1 Malawian Kwacha=10.80 Tanzanian shillings)
7(a)Given that A:C=10:7 and B:C=5:14; Find A:B
(b)Anna paid Tsh. 20,000 for 10 books. She sold of them at Tsh. 3,000 each and the remaining at Tsh. 3,500each. What was her percentage Loss or percentage profit?
8.(a)The sum of three terms which are in G.P is 28 while the product of these terms is 512.
Find the largest term.
(b)The fourth and sixth terms of an arithmetic progression are 45 and 55 respectively. Find;
9.(a)Find value of x in the following triangle and hence find the area of the triangle.
(b)It is known that , find the relationship between
10(a)Factorize
(b)Find the only solution of the equation
SECTION B (40 MARKS)
Answer any four (4) questions from this section
11(a)The following graph shows the feasible region of a linear programming problem where the shaded region is the feasible region. Study the graph and answer the questions that follow.
12. The following frequency distribution table shows scores of marks of 50 students in a Mathematics Test:
CLASS INTERVAL | 1.0 â€“ 2.0 | 2.0 â€“ 3.0 | 3.0 â€“ 4.0 | 4.0 â€“ 5.0 | 5.0 â€“ 6.0 | 6.0 â€“ 7.0 |
FREQUENCY |
Calculate the measures of central Tendency
13(a) Town X and Y are located at (60Â°N, 30Â°E) and (60Â°N, 45Â°W) respectively on the earthâ€™s surface. Calculate the distance between the two towns in Kilometers.
(b)Find the value of the angles marked X and Y in the figure below, given that O is the center of the circle.
(c)Find the area of a prism (rectangular) with l=8cm, w=6cm and h=4cm
14.from the balances given below, prepare a balance sheet at 31^{st} December 2010. Capital shs 205,000; Furniture shs.54,000; cash in hand shs 16,000; Net profit sh.74,000; Motor van sh 30,000; stock sh. 110,000; Drawings shs. 24,000; shop fittings shs 20,000; loan from Bank sh. 80,000; Debtors shs. 180,000; Creditors shs.45,000 and Bank Overdraft shs. 30,000
15.(a)Use the inverse of matrix B to find matrix A given that;
(b)Write two conditions fr a transformation to be a linear.
(c)By using a sketch and not otherwise, find the image of P(3, 4) when rotated about 90Â° anticlockwise followed by another rotation of 180Â° clockwise.
16.(a)The ordered pairs of a Quadratic function f are Find the function f(x)
(b)A fair die is tossed once. Find the probability that an even number or a prime number occurs
(c) Given that
1
FORM FOUR MATHEMATICS EXAM SERIES 82
FORM FOUR MATHEMATICS EXAM SERIES 82
THE UNITED REPUBLIC OF TANZANIA
PRESIDENT’S OFFICE
REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT
FORM FOUR MID TERM EXAMINATION-2021
041 BASIC MATHEMATICS
Time: 3 Hours AUG, 2021
Instructions
SECTION A (60 MARKS)
Answer all questions in this section
(b) Jenk and Jemry are riding on a circular path. Jenk completes a round in 24 minutes where as Jemry completes a round in 36 minutes. If they started at the same place and time and go in the same direction, after how many minutes will they meet again at the starting point?
(b) Find the value of x and y if = 2025
(b) Find the probability that a king appears in drawing single card from an Ordinary deck of 52 cards
(b)The gradient of line is -2. Another line L_{2} is perpendicular to L_{1} and passes through (-3,-2). What is the equation of L_{2}
(b) (i) Given = = = 3 where , and are the sides of the triangle ABT and , and are the sides of the triangle KLC. What does this Information imply?
(ii) A regular Hexagon is inscribed in a circle if the perimeter of the hexagon Is 42cm, find the radius of the circle and its Area
(b) The headmaster has enough food to last for his 600 students for 20 days from tomorrow. If 120 students leave the school today for UMISSETA game, how long will the food last?
(b) The following trial balance was extracted from the books of Nzilandodo on 31^{st} December 2005.
TX MARKET LTD
TRIAL BALANCE AS AT 31.12.2005
Note: Stock at close 31^{st} December 7360. Required, prepare balance sheet as that date.
(b) Find the sum of the first four terms of a geometric progression which has a first term of 1 and a common ratio of
Find (i). Cos A + Sin A (ii). – Cos^{2} A – Sin^{2} A
(b) A and B are two points on the ground level and both lie west of flagstaff. The angle of elevation of the top of the flagstaff from A is 56^{0} and from B is 43^{0}. If B is 28m from the foot of the flagstaff. How far apart are the points A and B?
(b) A field is 10m longer than its wide. The area is 7,200m^{2}. What is the width?
SECTION B (40 marks)
Answer all questions in this section
Marks | 0-9 | 10-19 | 20-29 | 30-39 | 40-49 | 50-59 | 60-69 | 70-79 | 80-89 | 90-99 | 100-109 | 110-119 |
Freq | 1 | 2 | 5 | 11 | 21 | 20 | 17 | 10 | 6 | 4 | 2 | 1 |
Draw the histogram and use it to estimate the mode in one decimal place.
b) Find the value of angle X in the figure below.
Calculate (i) The length AC (ii) The angle between WC and AC
(b) Two places P and Q both on the parallel of latitude N differ in longitudes
by find the distance between them along their parallel of latitude.
(b) Solve the following simultaneous equation by matrix method
2x + y = 7
4x+3y = 17
(c) Find the image of (3, 5) after rotation of 270^{o} about the origin in anticlockwise direction.
f(x)=
(b) A transport company is hired to transport 420 people it has two types, P and Q of vehicle to be used. Type P carries 35 passengers and type Q carries 14 passengers. There are at least 10 vehicles of type Q and not more than 9 vehicles of type P. Write down inequalities to represent this information.
1 of 5
FORM FOUR MATHEMATICS EXAM SERIES 64
FORM FOUR MATHEMATICS EXAM SERIES 64
THE PRESIDENTâ€™S OFFICE MINISTRY OF EDUCATION, REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT
COMPETENCE BASED SECONDARY EXAMINATION SERIES
FORM FOUR BASIC MATHEMATICSÂ TERMINALÂ EXAMINATION
Time: 3 Hours Year: 2021
Instructions
1.This paper consists of sections A and B with a total of fourteen (14) questions.
2.Answer all questions in sections A and B.
3.Each question in section A carries six (06) marks while each question in section B carries ten (10) marks.
5.NECTA mathematical tables and non-programmable calculator may be used.
6.All communication devices and any unauthorized materials are not allowed in the examination room.
7.The following constants for your calculations
Radius of the Earth =6370km,Â Â Â
SECTION A (60 Marks) Â
Answer All Question In This Section
1.(a) Calculate without using Mathematical tables, correct to two decimal places
Â
(b) Each student of Leo academy belongs to one club. Â are members in drama club. Â are members in mathematics club and the number of science club is twice that of drama club .The rest are members of research club. What fraction of students are members of research club? 2. (a) Make x subject of the formula
Â
(b)Three variables p, q and r are such that p varies directly as q and inversely as square of r. When p=9, q=12 and r=2. Find p when q=15 and r=5.
3.(a) ) Given thatÂ Â Â andÂ ,Â where X is an integer. Represent this in a venn diagram, hence find elements of: Â
(i)AuB
(ii)AnBÂ
Â (b) In a school of 95 pupils, 42 of the pupils take Biology but not Chemistry, 32 take both subject and 10 of them take Chemistry but not Biology. How many pupils do not take either Biology or Chemistry?
4.(a) Let P and Q be two points at (2,5) and (4, -1) respectively. Find
(i)Find equation of the line that passes through the midpoint of PQ and is perpendicular to it in form of ax + by +c=0
(ii)The distance between P and Q
Â (b) A chord is 6cm from the center of a circle with radius 10cm. What is the length of a chord?
5.(a) In triangle PQR, PR=5cm, PQ=6cm andÂ
(i)The length of side QR
(ii)
(b) The size of the exterior angle of a regular polygon is 45^{0}. Find
(i)The number of sides
(ii)The sum of all interior angles.
6.(a) Given t=3^{x} , by using the substitution solve the equationÂ 3^{2(1+x)} - 3^{x} =3^{(x+3)} - 3
(b) A shopkeeper makes a profit of 40% by selling an article for T.Sh. 63,000/=. What would be his percentage loss if he sold the article for T,Sh. 40,000/=
7.(a) Prepare the balance sheet for the balances given below
Capital 4,500,000/=
Drawings 800,000/=
Creditors 430,000/=
Closing stock 500,000/=
Debtors 800,000/=
Buildings 1,600,000/=
Motor Van 800,000/=
Bank 400,000/=
Cash 900,000/=
Net profit 270,000/=
Loan 600,000/=
(b) What is the aim of preparing balance sheet
8.(a) The third, fifth and eighth terms ofÂ arithmetic progressionÂ A.P form the first three terms of Geometric Progression G.P . If the common difference of the A.P is 3, find
(i)The first term of the G.P
(ii)The sum of the first 9 terms of the G.P to one decimal place. (b)Â Find the sum of first eight terms of the following sequence 1, -2, 4, -8 . . . . . Â
9. (a) In the figure belowÂ BD=5cm, DC=5cm and DE=3cm. Find length of AC and AE
Â
(b) A plane is flying at a constant height. The pilot observed of an angle of depression of 27^{0} to one end of the lake and 15^{0}Â to the opposite end of the lake. IfÂ the lake is 12 km long. Determine the altitude of the plane.
10. (a) 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.
(b) Find the values of x that satisfy the equation
log(x+5) + log(x + 2) = log4
SECTION B ( 40 marks)
Answer all questions from this section.
11. The examination scores in Basic Mathematics of 40 Form IV students are given in the following cumulative frequency table
Class Interval | 10-19 | 20-29 | 30-39 | 40-49 | 50-59 | 60-69 |
Cumulative Frequency | 3 | 6 | 12 | 22 | 35 | 40 |
(a)Find the mean score using assumed mean A=44.5
(b)Draw Histogram and use it to estimate the mode
(c)Calculate the median
12.(a) The two towns P and Q lie on the earths surface such that P(65^{0}N, 96^{0}E) and Q(65^{0}N, 84^{0}W). Find the distance between the towns in kilometers and nautical miles.
(b) The figure below shows a tetrahedron. The length of each edge is 8cm. O is the centre of triangle ABC.
Â
Calculate
(i)The length of VO
(ii)The angle between line AV and the plane ABC
(c) Find the volume of a cone which has a base diameter of 10 cm and slant height of 13 cm.
13. (a) The matricesÂ
Â Â Â Â Â andÂ Â Â Â Â Â Â Â Â Â Â Â
are such that AB=A + B.
Find the values of a, b, c and d
(b)Triangle PQR vertices at P(2, 2), Q(5, 3) and R(4, 1) is mapped onto triangle PQR by transformation matrixÂ
Â
Find coordinate of triangle PQR
(c)Determine the values of x which the matrix below has no inverse
Â
14.(a)Given that h(x)= -1 - | x + 3|
i.Sketch the graph of h(x)
ii.Use the graph to deduce domain and range
(b) The manager of a car park allows 10m^{2} of parking space for each car and 30m^{2} for each lorry. The total space available is 300m^{2}. He decides that the maximum number of vehicles at any time must not exceed 20 and also insists that there must be at least as many cars as lorries. If the number of cars is X and the number of lorries is Y.
(i) Write down the inequities which must be satisfied
(ii)If the parking charge is sh.10 for each car and sh.50 for each lorry. How many vehicles of each kind he should admit to maximize his income and calculate his income
FORM FOUR MATHEMATICS EXAM SERIES 53
FORM FOUR MATHEMATICS EXAM SERIES 53
PRESIDENTâ€™S OFFICE REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT
041BASIC MATHEMATICS
(For Both School and Private Candidates)
Time:3 HoursWednesday, 5^{th} August 2020 a.m.
Instructions
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 L_{2} is perpendicular to L_{1} and passes through point (-3, -2). What is the equation of L_{2}?
(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 cm^{2}, 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 cm^{2} and the area of the triangle ABC is 96 cm^{2}. 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.
9. (a) Find the value of
Sin (150^{0}) cos (315^{0}) Without using mathematical tables
Tan (300^{0})
(b) Calculate the angles of a triangle which has sides of lengths 4m, 5m and 7m
10.(a). Given that x^{2} â€“y^{2} = 27 and x + y = 9 find the value of xy
(b). Solve the equation 2x^{2} â€“ 3x â€“ 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
No.of absent | 0 â€“ 4 | 5 â€“ 9 | 10 â€“ 14 | 15 â€“ 19 | 20 â€“ 24 | 25 - 29 |
Cumulative frequency | 5 | 13 | 30 | 45 | 48 | 52 |
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
(i) The angle between VA and the base ABCD
(ii) The volume of the pyramid
13.
14. (a). A function F is defined by the formula f(x) = where x is a whole number
(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 1m^{2} of mild steel sheet per unit and type B requires 2m^{2}. He has only 12 m^{2} 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?
FORM FOUR MATHEMATICS EXAM SERIES 45
FORM FOUR MATHEMATICS EXAM SERIES 45
Student’s Examination No.....................................
THE PRESIDENT’S OFFICE
MINISTRY OF EDUCATION, REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT
SECONDARY EXAMINATION SERIES
MATHEMATICS MID TERM EXAMINATION-MARCH
FORM FOUR-2021
Time: 3Hours
Instructions.
SECTION A (20 Marks)
Answer All questions in this section.
(b) Use mathematical tables to evaluate
(b) Evaluate without using mathematical tables
(b) A mother’s age is four times the age of her daughter. If the sum of their ages is 50 years, find the age of the mother.
Find the magnitude of
Leaving your answer in the form of
(b) Find the equation of the line passing at the point (6,-2) and it is
perpendicular to the line crosses the – axis at 3 and the – axis at -4
(b) Find the length of a side and the perimeter of a regular nonagon inscribed in a circle of radius 6cm
(b) A car is travelling steadily covers a distance of 480km in 25 minutes. What is its rate in
(b) A factory employs skilled, semi-skilled and office workers in the ration 6:5:4 respectively. If there are 120 semi-skilled workers, how many skilled workers are there?
(b) Find the amount accumulated at the end of 2 years after investing 500,000/= at a compound interest rate of 10% annually.
(b) a ladder reaches the top of a vertical wall 18m high when the other end on the ground is 8m from the wall. Find the length of the ladder correct to one decimal place
(b) Pulukuchu is 6 years younger than her brother Mpoki. If the product of their age is 135, find how old is Pulukuchu and Mpoki
SECTION B (40 MARKS)
Scores | 30-39 | 40-49 | 50-59 | 60-69 | 70-79 | 80-89 | 90-99 |
Frequency | 5 | 10 | 15 | 17 | 4 | 6 | 7 |
(b) If a bus leaves Chagwe at 8.00 am on Monday and travels at 40km/hour, at what time will it reach Minga?
(c) Find the values of in the figure below;
NB: Closing stock was Tshs 7,400;
Prepare:
A
(b) Use the result of part (a) to solve the simultaneous equation;
(c) Find the value of which the matrix has no inverse
(b) The probability that Anna and John will be selected for advanced level is 0.5 and 0.3 respectively. Determine the probability that;
1 | Page
FORM FOUR MATHEMATICS EXAM SERIES 44
FORM FOUR MATHEMATICS EXAM SERIES 44
THE PRESIDENT'S OFFICE
MINISTRY OF REGIONAL GOVERNMENT AND LOCAL GOVERNMENT
PRE-NATIONAL EXAMINATION SERIES-1
MATHEMATICS FORM-4
2020
TIME: 3:00 HRS
Instructions
SECTION A (60 Marks)
Answer all questions in this section.
1. (a) Mangoes are to be exactly divided into groups of 20, 30 or 36 .What is the minimum number of mangoes required?
(b) Mary was given 60,000 shillings by her mother. She spent 35 percent of the money to buy shoes and 10 percent of the remaining money to buy books. How much money remained?
2. (a). Evaluate log_{10} 40,500 given that log_{10} 2 = 0.3010 , log_{10} 3 = 0.4771 and log_{10} 5 = 0.6990.
(b). Find the values of x and y if
3(a) Factorize the following expressions:
(i) 16y^{2} +xy -15x^{2}
(ii) 4 - (3x - 1)^{2}
(b) At Moiva’s graduation ceremony 45 people drank Pepsi-Cola, 80 drank Coca-Cola and 35 drank both Pepsi-Cola and Coca-Cola. By using a Venn diagram, found out how many people were at the ceremony if each person drank Pepsi-Cola or Coca-Cola.
4. (a) Given vectors a = 6i + 12j, b = 17i + 18j :
(i) Find the vector c = 2a – b and its magnitude correctly to 3 significant figures. (ii) Represent vector c in part (a)(i) on the x - y plane.
(b) Find the equation of the line passing passing through the midpoint of the points A(− 3 2, ) and B(1,− )4 and which is perpendicular to line AB .
5. (a) In triangle ABC , X , Y and Z are the midpoints of sides AB , AC and BC respectively. If
ZX = ZY and ZXBˆ = ZY Cˆ = 90°;
(i) Represent this information diagrammatically, (ii) Show that ABZˆ = ACZˆ .
(b) The areas of two similar polygons are 27 and 48 square metres. If the length of one side of the smaller polygon is 4.5 cm, find the length of the corresponding side of the larger polygon.
6. (a) The variable v varies directly as the square of x and inversely as y. Find v when x = 5 and y = 2 ? given that when v = 18 and x = 3 the value of y = 4 .
(b) The temperature (T_{i}) inside a house is directly proportional to the temperature (T_{o}) outside the house and is inversely proportional to the thickness (t) of the house wall. If T_{i} = 32°C when T_{o} = 24°C and t = 9cm , find the value of t when T_{i} = 36°C and T_{o} = 18°C
7.(a)Given that 49, x and 81 are consecutive terms of a geometric progression. Find:
(i) The value of x.
(ii)The geometric mean.
(b) A wall is in the shape of a trapezium. The first level of wall is made-up of 50 bricks where as the top level has 14 bricks. If the levels differ from each other by 4 bricks, determine the number of
(i) levels of the bricks.
(ii) bricks used to make the wall.
8. (a) Three relatives shared Tshs 140,000 so that the first one got twice as much as the second, and the second got twice as much as the third. How much money did the first relative get?
(b) Kitwana paid Tshs 900,000 for a desktop computer and sold it the following year for Tshs 720,000. Find:
10. (a) Solve the equation 4x^{2} ? 32x + 12 = 0 by using the quadratic formula.
(b) Anna is 6 years younger than her brother Jerry. If the product of their ages is 135, find how old is Anna and Jerry.
9. (a) A river with parallel banks is 20 m wide. If P and Q are two points on either side of the river, as shown in the figure below, find the distance PQ.
(b) In the triangle LMN , LM = 5m, LN = 6m and angle MLN = 66°. Find MN .
SECTION B (40 Marks)
Answer four (4) questions from this section.
11. A shopkeeper sells refrigerators and washing machines. Each refrigerator takes up 1.8 m ^{2} of space and costs 500,000 ^{2} of space and costs 300,000 shillings; whereas each washing machine takes up 1.5 mshillings. The owner of the shop has 6,000,000 shillings to spend and has 27 m 2 of space.
(a) Write down all the inequalities which represent the given information.
(b) If he makes a profit of 30,000 shillings on each refrigerator and 40,000 shillings on each washing machine, find how many refrigerators and washing machines he should sell for maximum profit.
12. (a) Given:
Opening stock 01-01-2012 34,430/=
Closing stock 31-12-2012 26,720/=
Net purchases during 2012 212,290/=
Expenses for the year 45,880/=
Gross Profit is 50% of cost of goods sold
Find: (i) Cost of goods sold (ii) The gross profit
(b) On 1 ^{st} June, 2013 Mrs. Lemisha started business with capital of 100,000/= and mad ehte following transactions
June 2 bought furniture 40,000/=
7 bought goods 70,000/=
11 sold goods 65,000/=
16 paid Sundry expenses 30,000/=
19 cash sales 80,000/=
24 paid wages 50,000/=
26 withdraw cash 30,000/=
(i) Prepare the cash account
(ii) Prepare the balance sheet as at 30/06/2013
(iii) Explain the importance of the balance sheet you have prepared in part (b)(ii) above.
13.(a) Given matrices
And
Such that
Find elements of matrix P
(b) Determine the matix A from the equation
14.(a) A ship sails from Pemba (4.5^{°}S, 39.5^{°}E) to Dar es salaam (7.5^{°}S, 39.5^{°}E). If it leaves Pemba at 11:30 am and arrived in Dar es salaam at 13:30 pm, use and R_{E}=6370km to find speed of ship in km/h
(b) Sketch a square pyramid whose base is PQRS, vertex is at W and centre is at N, then answer the questions that follow:
(i) State the projection of
(ii) Name the angles between
(c) The volume of a square pyramid is 28.2 cm^{3}. If the sides of its base are 4 cm long, find the height of the pyramid correct to one decimal place.
FORM FOUR MATHEMATICS EXAM SERIES 28
FORM FOUR MATHEMATICS EXAM SERIES 28
THE PRESIDENT’S OFFICE MINISTRY OF EDUCATION AND VOCATIONAL TRAINING
MID TERM EXAMIATIONS
024 MATHS- FOUR
Duration: 3 Hours
INSTRUCTIONS.
SECTION A (60 MARKS)
1. a) Use mathematical table, evaluate
b)Express 45.456 in form of where a and b are both integers.
2. a) If ,
evaluate
b)Solve for x the following equation 32^{x-3 }X 8^{x+4} = 64 2^{x}
c)Rationalize the denominator
3. a) Find value of P which makes the following equations perfect square
i) x^{2} + 8x +P=0
ii) x^{2} - x + P=0
b) Solve for x the equation
4. a)Given the universal set U={p, q, r, s, t, x, y,z} A={p, q, r, t} B={r, s, t, y }. Find i)(AUB) ii)(A’nB’)
b)In a class of 60 students, 22 students study Physics only, 25 study Biology only and 5 students study neither Physics nor Biology. Find i) Number of students study Physics and Biology. ii) Number of students that study Biology.
5. a) A, B and C are to share T.sh 120,000/= in the ratio of. How much will each get?
b)A radio is sold at T. sh 40,500/= this price is 20% value added tax(V.A.T). Calculate the amount of V.A.T.
6.a) The sum of 1^{st} n-terms of certain series is 2^{n}-1, show that this series is Geometric Progression. Find an the n^{th} term of this series.
b) Point P is the mid-point of a line segment AB where A(-3,8) and B(5,-2), find an equation through P which is perpendicular to AB.
7.a) Without using mathematical table, evaluate
b) A man standing on top of cliff 100m high, is in line with two buoys whose angles of depression are 17^{0} and 21^{0}. Calculate the distance between the buoys.
8.a) The lengths of two sides of triangle are 14cm and 16cm. Find the area of the triangle if the included angle is 30^{0}.
b)The area of a regular 6-sided plot of land inscribed in a circular track of radius r is 720cm^{2}. Find the radius of the track.
9.a) Find values of angles marked x^{0} and y^{0} in the figure below
b) Prove that exterior angle of cyclic quadrilateral is equal to interior opposite angle.
10. a)Solve for x if
b) A two-digit of positive number is such that, the product of the digits is 8. When 18 is added to the number, then the digits are reversed. Find the number.
SECTION B (40 MARKS)
11. The daily wages of one hundred men are distributed as shown below
Wages in T.Sh. x 1,000 | 3.0-3.4 | 3.5-3.9 | 4.0-4.4 | 4.5-4.9 | 5.0-5.4 | 5.5-5.9 | 6.0-6.4 | 6.5-6.9 |
Number of men | 4 | 6 | 10 | 14 | x | 20 | 14 | 6 |
a) Find the value of x
b) Calculate the daily mean wage of the 100 men
c) Draw histogram to represent this data and use it to estimate Mode
d) Draw cumulative frequency curve and use it to represent Median
12. Shirima makes two types of shoes A and B. He takes 3hours to make one shoe of type A and 4hours to make one shoe of type B. He works for a maximum of 120hours. It costs him sh. 400 to make a pair of type A and sh. 150 to make of type B. His total cost does not exceed sh.9000. He must make at least 8 pairs of type A and more than 12 pairs of type B.
a) Write down the inequalities that representing the given information.
b) Represent these inequalities graphically
c)Shirima makes a profit of sh. 150 on each pair of type A and sh.250 on each pair of type B. Determine the maximum possible profit he makes.
13. The following trial balance was extracted from the books of Magoma Moto at 31^{stt} December 2015
Name Of Account | Dr | Cr |
Sales | 1,800,000/= | |
Purchases | 1,155,000/= | |
Opening Stock | 377,000/= | |
Carriage inwards | 32,000/= | |
Carriage outwards | 23,000/= | |
Return Inwards | 44,000/= | |
Return Outwards | 35,000/= | |
Salaries and wages | 244,000/= | |
Motor expenses | 66,000/= | |
Rent | 45,000/= | |
Discount allowed | 12,000/= | |
General office expenses | 120,000/= | |
Motor vehicles | 2,400,000/= | |
Furniture and Fittings | 600,000/= | |
Debtors | 457,000/= | |
Creditors | 304,000/= | |
Discount Received | 35,600/= | |
Cash at bank | 387,000/= | |
Cash in hand | 12,000/= | |
Drawings | 205,000/= | |
Capital | 4,005,000/= |
Stock at 31^{stt} December 2015 was Tsh.499,000/=
a) Prepare trading, profit and loss account for the year ended 31^{stt} December 2015
b)The balance sheet as at 31^{stt} December 2015
14.a) In the triangle ABC below, find values of angles marked x^{0} and
y^{0 } where AB=12cm, BC=7cm and AC=8cm
b) Solve the following equations given that
i)
ii)
c) Show that
15. a) In a figure below, represents a room 8m by 6m by 4m. Calculate
i)Length of diagonal AR
ii) Angle that AR makes with the floor
iii) Angle which plane TSAD makes with plane TSBC.
b)A water pipe made of material 2cm thick has an external diameter of 16cm. Find the volume of material used in making of the pipe 200m long.
16. a) The function f is defined as follows:
F(x) =
i) Sketch the graph of f(x)
ii) Determine domain and range
iii) Find i) f(1) ii) f(-4) iii) f(π)
b)For what values of x is function f(x)= is undefined?
FORM FOUR MATHEMATICS EXAM SERIES 6
FORM FOUR MATHEMATICS EXAM SERIES 6