FORM THREE MATHEMATICS EXAMS SERIES

THE PRESIDENT’S OFFICE

MINISTRY OF EDUCATION, REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT

COMPETENCE BASED SECONDARY EXAMINATION SERIES

MATHS ANNUAL EXAMINATIONS

FORM THREE-2022

 

INSTRUCTIONS

  1. This paper consists of section A and B with a total of fourteen (14) questions.
  2. Answer all questions in both sections
  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 or non-programmable scientific calculator and graph papers may be used unless otherwise stated
  6. You are advised to spend no more than two (20 hours on section A
  7. All communication devices and any unauthorized materials are not allowed in the examination room.
  8. Write your Examination Number on every page of your booklet(s)

 

SECTION A (60 MARKS)

Answer all questions in this section.

  1. (a) At exactly 7:00a.m, two buses leave the bus terminal. Thereafter, every 40 and 70 minutes, a bus leaves the terminal. Find the time busses will leave the terminal together.

(b)(i) Estimate the value of 

(ii)Simplify the ratio of a tob, given that  and b= to its lowest form.

  1. (a) Solve for x in the equation

(b) If 3x – y=4, What is the value of 

  1. A bag contains 6 red balls and 8 blue balls. A random selection of balls from the bag is performed. If one ball is selected from the bag and then replaced before selecting the second ball:
  1. Draw a tree diagram showing all the possible outcomes and their corresponding probabilities
  2. Find the probability of selecting
  1. Balls of different colours
  2. Balls of the same colour
  1. (a)Three consecutive vertices of parallelogram are at A(-1, 2), B(5, 1), C(6, 5), and

D(x, y), Find the coordinate of vertex D.

(b) Two towns P and Q are 30km apart, Q being due East of P. Town R is situated at a bearing of 150° from P and 240° from Q. calculate the distance RQ

  1. (a)P and Q are markers on the banks of a canal which has parallel sides. R and S are telegraph poles which are directly opposite each other. PQ=30m and QR=100m. When Mr. Ates walked 20m from P directly away from the bank, he reached a point T such that T, Q and S lined up. How wide is the canal?

 

 

 

 

 

 

(b)In a triangle ABC, angle ABC=50° and point X lies on  such that  with the aid of a diagram, calculate 

  1. (a)An English family on holiday in France exchanged 450 for euros when the exchange rate was 1.41 euros to the pound. They spent 500 euros and then exchanged the rest back into pounds, by which time the exchange rate had become 1.46 euros to the pound. How much did the holiday cost? (Give your answer in pounds.
  2. The following balance sheet relates to Mr. Max Malipo, a trader, as at 31st December 2020

 

MR. MAX MALIPO

PARTICULARS 

AMOUNT

PARTICULARS

AMAUNT

CAPITAL

Add: Net Profit

 

Less: Drawings

 

LIABILITIES 

Creditors 

Salaries Accrued

Tel. Outstanding 

179,000

30,280

 

 

 

191,280

 

7,000

5,000

220

ASSETS

Furniture 

Machinery 

Debtors 

Cash at Bank

Rates Prepaid 

Closing Stock 

 

 

40,000

30,000

10,000

  3,000

     500

120,000

 

209,280

18,000

 

203,500

203,500

 

Use the information given in the balance sheet above to find:

  1. Total Fixed Assets
  2. Total Current Assets
  3. Total Current Liabilities
  4. Working Capital
  1. (a)Mr. Cathbert starts an employment with a monthly salary of 340,000/= Tshs and receives an increment of 12,000/= Tsh every year.
  1. What will be his salary in the fourteenth year of employment?
  2. After how long would he be earning 592,000 Tsh per month?

(b)The sum of the first two terms of a geometric progression is 27 whereas the sum of the 2nd and 3rd term of the same progression is 54. Find the first term and the common ratio.

  1. (a)At a point 200m from the foot of a tower on a level road, the angle of elevation of the top of the tower is 58°.
  1. Represent this information diagrammatically,
  2. Find the height of the tower.

(b)A rectangular frame ABCD, 48cm by 55cm, is made from wire. The diagonals of the frame are also made from wire.

 

 

 

 

 

 

Calculate the total length of wire needed to make the frame and the diagonals.

  1. (a)Find the values of m and n in system of linear equations

(b)Find the values of a andb if (ax + 5) (bx + 4) = 21x2 + 43x + 20.

SECTION B (40 Marks)

Answer all questions in this section

  1. (a)The table below shows the distribution of marks scored by 45 students in Physics examination

Marks (in %)

99 – 89 

88 – 78 

77 – 67 

66 – 56 

55 – 45 

Number of students 

2

5

20

11

7

 

  1. Determine the median class of marks
  2. Compute the mean mark
  3. Draw the histogram and hence use it to estimate the mark scored by many students

 

(b) are secants that intersect at A in the figure below. Given that chords  Find the angles x and y.

 

 

 

 

 

 

  1. (a)A circular tank has a base of 53-metre radius and height of 12 metres. If the tank is a half full of water, what is the volume of water in a tank? Give your answer in litres (1 cubic metre = 1000 litres)

(b)Mr. Paul went to buy a car. He wanted to buy a car that has not covered more than 2,500 kilometres (not much used). If he found only one car in the market which travelled from Nairobi (56°N, 40°E) to Dar-es-Salaam (26°N, 40°E). What can you advice Mr.Paul according to his need? (Use radius of the Earth, RE= 6370km)

 

  1. (a)Find value of K if the matrix

(b)Use inverse matrix method to solve for x and y in the following pair of equations of straight lines: 

(c) A linear transformation T maps .

Find 

  1. The transformation matrix T
  1. (a)Find the role of the following is solving linear programming problems:
  1. Non-negativity constraints
  2. Feasible region
  3. Objective function

(b) MzeeMalengo has 240 acres of land which he wants to plant maize and oats. For each acre of maize planted he will profit 400,000/= Tsh, and for each acre of oats planted he will profit 300,000/= Tsh. However, maize takes 2 hours to harvest, while oats require 1 hour harvesting, and he has only 320 hours available for harvesting. How many acres of each crop should he plant in order to maximize profits?

LEARNINGHUBTZ.CO.TZFORM THREE MATHEMATICS EXAM SERIES 113

THE UNITED REPUBLIC OF TANZANIA PRESIDENT'S OFFICE, REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT

FORM THREE ANNUAL EXAMINATION
041 BASIC MATHEMATICS

Time 3:00 Hours Year: 2022

INSTRUCTIONS

  1. 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. Mathematical tables and non-programmable calculators may be used.
  6. All communication devices and any unauthorized materials are not allowed in the examination room
  7. Where necessary, use the following constants
  • Pie, =3.142
  • Radius of the earth, R=6400km.

SECTION A: (60 MARKS)

Answer all questions from this section

1. (a)The traffic lights at three different road crossing changes after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m at what time they change simultaneously again?

(b) If x = 0.567567567… and y = 0.8 by converting these decimals to fractions, find the exact value of

2. (a) If  find the value of t

(b)Write “L” in terms of M, N and T from the formula

(c) Determine the value of x if

3. (a)Let  be a universal set and A and B be the subsets of

A= {c, g, f} and B= {b, d, h} find 

(b) Given that A= {x : 0 ≤ x ≤ 8}

B = {x : 3 ≤ x ≤ 8}

where x is an integer, in the same form, represent in a Venn diagram

  1. A u B
  2. A n B

and hence find the elements in each set.

4. (a) Find the slope of a straight line which passes through points A (0, a) and B(3a,0)

(b) The co-ordinates of the square PQRS are given by P(1, 4), Q(3, 4), R(3, 2), and S(1, 2). Write the co-ordinates of the image of the square P’Q’R’S’ under reflection in the x-axis.

 5. (a) Given  where are the sides of the triangle ABT and  Are sides of the triangle KLC. What does this information imply?

(b) Calculate the area of the following figure, if 0 is the centre of the circle and OABC is a square.

image

 6. (a)Twelve people can dig a trench in 15 days for 8 hours daily. How long can they take to finish the same work, working for 10 hours daily?

(b)A variable V varies jointly as the variable A and h. when A=63 and h=4, v=84.

Find;

  1. V when A=9 and h=7
  2. A when V=4.5 and h=0.5

7. (a)If a:b=2:3 and b:c=5:6. Find a:c and a:b:c

(b) PQR is an isosceles triangle whereby PQ =PR and QS = SR. If S is a point between Q and R prove that Δ PQS ≡ ΔPRS

8. (a)If the 5th term of an arithmetic progression is 23 and the 12th term is 37, find the first tem and the common difference.

(b) In how many years would one double one’s investment if Tshs 2500 is invested at 8% compounded semi –annually.

9. (a) Given that

image

Find :

(i)image 

(ii)image 

(b) A and B are two points on the ground level and both lie West of flagstaff. The angles of elevation of the top of the flagstaff from A is 56° and from B is 43°. If B is 28m from the foot of the flagstaff. How far apart are the point A and B?

10. (a)Solve for the quadratic equation x2 – 8x + 7=0

(b)Solve for x and y if

SECTION B (40 MARKS)

Answer all questions from this section

11.The marks in basic Mathematics terminal Examination obtained by 40 students in one of the secondary school in Katavi were as follows;

60, 54,  48,  43, 37 61, 43, 66, 65, 52, 37, 81, 70, 48, 63, 74, 67, 52, 48, 37, 48 42, 43, 52, 52, 22, 27, 37,44 38, 29, 19, 28 36, 42, 47, 36, 52, 50, 28.

  1. Prepare a frequency distribution table with class intervals 10 – 19, 20 – 29, etc.
  2. Find the class which contain the median
  3. Find the mean
  4. Calculate the median.

12. (a) From the following information given by Mbeya Co.ltd for the year ended 31st December 2021.

Stock (01.01.2021) ………………………….Three quarter of the closing stock

Stock (31.12.2021) …………………………  of net purchase

Net purchases during 2021 …………………. 432,000.

Gross margin …………………………. 15%

Expenses ……………………………… 20% of Net profit 

Calculate;

  1. Cost of goods sold
  2. Gross profit
  3. Net profit

(b) State Three uses of the trial balance

13. (a) Find the value of angle x in the figure below, where O is the centre of the circle

 (b)Two places P and Q both on the parallel of latitude 26°N differ in longitudes by 40°, find the distance between them along their parallel of latitude.

14. Given

image

(i) Sketch the graph of f(x).

(ii) State the domain and range of f(x) .

(iii) Is f(x) a one-­to-­one function? Give reason(s).

LEARNINGHUBTZ.CO.TZFORM THREE MATHEMATICS EXAM SERIES 103

THE PRESIDENT’S OFFICE MINISTRY OF EDUCATION, LOCAL ADMINISTRATION AND LOCAL GOVERNMENT

FORM THREE BASIC MATHEMATICS TERMINAL EXAMINATION

Time: 3:00 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 unauthorized materials are not allowed in the examination room.

SECTION A

ANSWER ALL QUESTIONS

1. (a) Write as a mixed fraction

(b)If and find x + y to 3-significant figure

2. (a)Find

(b) A farmer sold a quarter of his maize harvest and gave one third of the remaining to his relatives.

If the farmer remained with 25 bags. If maize, how many bags of maize did the farmer harvest?

3. (a)Factorize (i)

(ii)

(b)Simplify

(c)Solve for x:

4. (a)Solve for x: (i)

(ii)

(b)If log3 = 0.4771 and log2 = 0.3010

Find:

(i)

(ii) Without using tables.

5. Solve the following simultaneous equations

6. Given the universal

Set and

  1. Represent the above information in a Venn-diagram and use it to find elements of

  1. Show that

7. (a)Marium served Tshs 6 million in a serving account Bank where interest rate was 10% compounded annually. Find the amount in mariam’s account after 5years.

(b)In how many years would one’s investment double if 100,000/= is invested at 10% compounded semi-annually?

8. (a) Factorize:

(b) Given that

AB=EC

  1. Show that EA=ED
  2. Prove that

and state the postulate out of (SSS, AAS, SAS, RHS)

9. (a)The ratio of the areas of two similar polygons is 144:225. If the length of a side of the smaller polygon is 60cm, find the length of the larger polygon

(b)

Given that

  • DC//AB
  • AOB is diameter

Find an expression in terms of x

10. In a series between the integers 3 and 102. Find the sum of

  1. Even numbers (ii) Odd numbers

(b) A bacteria produces 10 bacteria after every minute and each of the 10 bacteria produces, 10 bacteria after every minute and so

  1. Form a sequence of number of bacteria produced after 1,2,3 and 4 minutes
  2. If the frequency is to form a series, what is the name of the series?
  3. Find the sum of bacteria produced after one hour.

SECTION B (Answer All Questions)

11. The table below represents the scores in general cleanliness of 30 students

SCORE x

FREQ f

fx

1

M

2

2m

3

10

4

8

5

3

Ɛf

Ɛfx

  1. Find the value of m
  2. Complete the table and find Ɛf, Ɛfx
  3. Find the mean (average) score
  4. Find the mode
  5. Construct an ogive and use it to estivate the median

12. Given the function f(x) = x2-8x + 12

  1. Find the x and y-intercepts
  2. Using (a) determine the axis of symmetry of f(x)
  3. Using (b) determine the coordinates of the minimum point
  4. Using (a) (b) and (c) sketch the graph of f(x)
  5. From the graph find
  1. Domain (ii)Range
  1. Construct a suitable line and sketch it on the same axes to find solution of the equation; x2 -10x + 16=0

13. (a)An aero plane fires from Tabora (5°S, 33°E) to Tanga (5°S, 39°E) at 332 km/her. Along parallel latitudes. If it leaves Tabora at 3 p.m., find the time of arrival at Tanga air-port

(b)Another plane flying at 595 km/hr leaves Dsm (7°S,39°E) at 8:00a.m it Addis Ababa (9°N, 39°E) (parallel longitude)

(Radius of the earth R 6370km)

14. (a) The volume V of a given mass of gas varies directly as the absolute temperature T and inversely as the pressure P

If V=450 and T= 288 when P=825, find V when T=320 and P = 720

(b) In the figure below, BD is a tangent to the circle having the centre O .

Given that angle OEC = 28°, find the values of angles marked X , Y and Z .

LEARNINGHUBTZ.CO.TZFORM THREE MATHEMATICS EXAM SERIES 92

OFFICE OF THE PRESIDENT, MINISTRY OF EDUCATION AND VOCATIONAL TRAINING

CERTIFICATE OF SECONDARY EDUCATION EXAMINATION

TERMINAL EXAMINATIONS- MAY 2022

FORM THREE 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)If a*b=b (a2 – 2b) Find (i) 3*2 (ii) n if 4*n=0

(b)Given 

2.A and B are two sets such that

  1.                 
  2.                In a class of 30 students 17 participate in English debate, 12 participate in English debate and sports. If every student is required to participate in at least one of the two subjects. Find the number of students who participate in

(i) English debate only    (ii) Sports only

3.(a)If 

(b)Express as single logarithm the expression 

4.Rewrite without absolute value  and sketch a graph of the resulting inequality 

5.(a)The second term of an A.P is 2 and the sixth term is 14. Find 

  1. The first term
  2. The common difference

(b)A function is defined by . Find 

(i) The inverse  of this function  (ii)

6.Given that  find value of 

  1. Cos A

7.Fine the remainder when  is divided by x + 1 and hence solve the equation 

8.If  evaluate

  1.                 Correct to 3 decimal places
  2.                Simplify
  3.                 Given  and  find

9.

  1.                 Given that = find value of
  2.                Make q the subject of the equation
  3.                 Solve the equation  by factorization

10. A line passes through point A (3,5) and B (8, K) has a slope of -2. Find the;

  1.                 Value of K
  2.                The equations of line

 

SECTION B

11.(a)Mpira club has the following number of goals scored against them, 0,1,0,2,9,0,1,2,1, what is the mean number of goals scored against them?

(b)The table below shows the masses of 100 students to the nearest kg

Mass kg

60-62

63-65

66-68

69-71

72-74

Frequency

5

18

42

27

8

  1. Determine the mean of the masses
  2. Calculate the mode
  3. Draw a cumulative frequency (give) curve and use it to determine the median of the masses

 

12.(a)(i) Find the distance between Mbeya (9°S.33°E) and Tabora (5°S,33°E) in km

(b)An airplane takes off from Tabora (5°S,33°E) to Tanga (5°S,39°E) at a speed of 332 kmh-1 if it leaves Tabora at 3:00pm, at what time will it arrive at Tanga airport?

13.Musa started business on 1st June, 1999 with Tshs 6000/= as capital

June 01 Bought goods cash    3000/=

June 02 Paid office cleaners    20/=

June 03 Sold all goods for cash   3400/=

June 05 Purchased goods for cash  2000/=

June 08 Paid carriage on goods sold  40/=

June 10 sold goods for cash    3000/=

June 15 paid wages     100/=

  1.                 Enter these transactions in cash book
  2.                Bring down the balance at the end of June

 

14. A house and flag post are on the ground. From an open window in a house 6m, above the ground, Abdulrazaq finds that the angle of elevation of the top of the flag post is 35° and the angle of depression of the bottom of the flag post is 20°.

 

15.(a) Draw the graph of  taking the value of x in the interval 

(b)State the running point of the graph and state whether it is a maximum or a minimum.

(c)Solve the equation 

(d)Use a suitable straight line, solve the equation 

 

16. (a). Box A contains 8 items of which 3 are defective and box B contains 5 items of which 2 are defective. An item is drawn at randomly from each box. What is the probability that? 

  1. Both items are non-defective?
  2. One item is defective and one item is not defective

(b)The radii of trastrom of a right cicular cone are 10cm and 7cm. If the height of this trastrom is 6cm. What will be the height of the original cone?

(c)If 

  1. Find an expression for
  2. Find the simplified algebraic expression for f(x-1)

LEARNINGHUBTZ.CO.TZFORM THREE MATHEMATICS EXAM SERIES 88

PRESIDENT’S OFFICE

REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT

SECONDARY EXAM SERIES

FORM 3 BASIC MATHEMATICS

SECTION A (60 MARKS)

Answer ALL questions from this section

1(a) Write 0.007357 correct to three significant figures

(b)Express  inform  where 

(c)Simplify  hence write your answer in percentage.

2.(a)Solve for x in the following equation 

(b)Rationalize the denominator 

3(a)In a school of 200 students 90like mangoes, 70 like oranges and 50 like Apples; 26 like oranges and mangoes, 20like oranges and apples, 16like Apples and mangoes while 10 like all three fruits.

Represent this information in a well labeled Venn diagram

How many students do not like mangoes?

(b)If , Find b in terms of A and C

4. Use the graph below, then find; 

Gradient

Equation of the line in the form of y=mx + c

5.(a)ABC is an isosceles triangle in which and are equal and if D is the mid-point of BC. 

Prove that 

(b)A regular polygon has an exterior angle of 72° find

  1. The size of the interior angle
  2. How many sides does this polygon have?

6.(a) If y varies directly as x2 and inversely as  when x=8, y=16 and z=25. 

Find y when x=5 and z=9

(b)Sixty people working 8 hours a day take 4 days to cultivate a village farm. How long will it take twenty people to cultivate the same farm if they work 15 hours a day?

7(a)Three people share a property in a ratio 2:x:y. It is known that y=x +2, if the largest shareholder had shs 780,000/= in monetary terms, find the value of this property.

(b)Mr.Mayube of Makole village shop made 60% loss by selling a bag of sugar for Shs. 80,000.00. What would be his percentage profit if he sold the bag of sugar for Shs 240,000.00?

8(a)Write down the next two terms in the sequence; 

(b)The first four terms of an A.P are 2,(m – n), (2m + n + 7 and (m – 3n) respectively where m and n are constants. Find the values of constant m and n

9(a)Given that Tan A=2.4 and A is an acute angle. Find in the simplified form the value of 

(b)From the top of a wall 8.8m above horizontal ground, the angle of depression of a stone lying on the ground 31°. Calculate the distance of the stone from the foot of the wall.

10(a)Find the factors  and hence use it to solve 

(b)The operation x*y denotes the number. Find the value of x if x*4=x*3

SECTION B –(40 MARKS)

Answer any four (4) questions from this section

11.(a)In the following figure  shorter than . Find the length of 

(b)In figure below O in the center of the circle. AB=6cm and ON=4cm show that  

12. The score of 50 candidates a mathematics examination were recorded as shown below.

26, 17, 42, 40, 40, 74, 26, 34, 34, 47, 52, 42, 69, 52, 43

67, 38, 52, 24, 34, 48, 73, 64, 55, 43, 67, 38, 56, 18, 53, 26

62, 32, 78, 17, 45, 34, 54, 24, 36, 34, 18, 48, 52, 73, 37, 64, 45, 54, 37

  1. Prepare a frequency distribution table with class mark 17, 22, 27 …………
  2. Draw histogram and use it to estimate mode
  3. Calculate mean, using assumed mean of 52

13.(a)Find the distance between A(20°N, 135°E) and B (35°N, 135°E) in

(i)Nautical miles  (ii) Kilometer 

(b)A ship sails from P(0°, 30°W) to Q(10°N, 30°W) at 15 knots. If it leaves P at 8:00am on Tuesday when will reach Q?

14.You are required to use the trial balance below to prepare trading, profit and loss Account and extract the balance sheet of Mwanahela as at 31-12-2012

S/NO

NAME OF ACCOUNT

DR

CR

Cash

1,907,000

Capital

2675000

Purchases 

2267000

Rent 

114000

Furniture 

305000

Shelves 

270000

Sales 

2309000

Salary

67000

Wages 

54000

4984000

4984000

15.(a)The sum of the first three terms of a geometric progression is 19 and their product is 216. Find the terms

(b)The third term of an arithmetic progression 9 and the common difference in 2. Find the sum of the first 20terms.

(c)If p, q and r are successive terms of a geometric progression. Find the value of q in terms of

p and r

16.Given that 

  1. Sketch the graph of f(x)
  2. State the domain and range of f(x)
  3. Find f(-5), f(10), f(3π) and f(0)
  4. Is f(x) one to one to one function?

1

LEARNINGHUBTZ.CO.TZFORM THREE MATHEMATICS EXAM SERIES 81

PRESIDENT’S OFFICE 
REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT AUTHORITY 

BASIC MATHEMATICS EXAMINATIONS- AUG 2021
FORM THREE

TIME: 3:00HRS

INSTRUCTIONS

  •         This paper consists of Sections A and II
  •         Answer ALL questions in both sections
  •         Mathematical table and graph paper may be used unless otherwise stated.
  •         Write your Examination Number on every page of your answer sheet(s) provided.

SECTION A (60MARKS)

  1.   (a) A school trip of 32 people went to a tour which costs a transport fee of 580/= each person. What was the approximate total transport cost?

b) Rajabu is making some small metal rods.He has three peaces of metals of length 432cm, 648cm,540cm.What is the largest length of a rod he can make if the rods have the same length and no metal is wasted.

  1.   (a) Without using mathematical table simplify √63+√72 

√32+√28

(b)Find the value of x in log( - 1) + 2 = log(3 + 2) + log 25

  1.   a)(i) List all the subsets of the following set A = {3, 6, 8} 
    ( ii) Work out the number of subsets in a set containing 6 elements.

b) In a class of 45 students, 19 study commerce but not physics, 16 study physics but not commerce and 3 studies neither commerce nor physics, find the number of students who study (i) Physics or commerce (ii) Both subjects

  1.   (a) The line joining (2,-3) and (k,5) has a gradient -2, find k

b) ∆PQR is such that PQPR and PQ:QR is equal to 3:4.If the perimeter of the triangle is 60cm. Calculate the value of QR.

  1.   (a) Calculate to 1 decimal place the area of an equilateral triangle of side 10cm.


(b) In the figure below find MK and MP


  1.        (a) A man is paid 6000/= for 8 hours work (i) What is his rate of pay? (ii) At this rate how long must he work to receive 30,000/=

b) In working for 10 hours a day, 12 men can do a certain piece of work in 6 days. For how many hours a day must 20 men work in order to do the same amount of work in 14 days?

  1.     a) By selling an article at Tsh 225,000 shopkeeper makes a loss of 10%.At what price must the shopkeeper sell the article in order to get a profit of 10%?

b) Find the total amount of money received if Tsh 800,000 is deposited in a bank at the rate of 9% compounded semi anually in one year.

  1.   (a) Given ̂

~

=,

L is a mid point of KM .Prove that L ≡ L

 

(b) Given the angles  C = 2x+30° and Ĉ D = (x+15)°. If two angles are complementary find the value of x and the size of each angle

  1.        (a) Given the right angled triangle below with sides marked x , y , z ,


Prove that cos2 + sin2=1

b) A pole 7.45m high casts a Shadow 4.05m long on horizontal ground. Find the angle of elevation of the sun.

10. (a) Expand the expression (ax + c) (bx  d)

(b) A boy bought some packets of biscuits for 120/=.If the biscuits had been 3/= a packet cheaper he would have received 2 more packets for his money. How many packets did he buy?

SECTION B (40MARKS)

11. In a mathematics Examination the following marks were obtained:

27 57 57 40 70 48 59 60 42 44 47 44 44 59 35 48 43 52 36 48 Group the marks in class interval of 20-29, 30 -39 , . . . Then

  1. Construct the frequency distribution table
  2. Calculate the mean marks by using assumed mean method (Take A =44.5)
  3. Calculate the mode
  4. Draw the cumulative frequency curve then estimate the median

12. (a)Four positive numbers are consecutive elements of geometric progression (G.P).The product of the first and the third number is 36 while the product of the second and fourth number is 324. Find the sum of nine terms of the G.P

(b) The second , fourth and eighth terms of an Arithmetic Progression form a Geometric progression and the sum of the third and fifth terms of AP is 20. Find the first four terms of the geometric progression.

13. (a) A function is defined as f(x ) = √4 - 2 find (i) Domain and Range of f(x) (b) Sketch the graph of function f(x)= { + 3 ℎ  < 1

2 ℎ > 1

Hence (i) state its domain and range (ii) Find f(6) , f(-2) (iii) State whether the graph is one to one function ?

14. The relation is defined as R={(, ): ≥ —4, 3 - 4 ≤ 12  5 + 4 ≤ 20}

  1. Draw the graph of R
  2.  State the domain and range of R

LEARNINGHUBTZ.CO.TZFORM THREE MATHEMATICS EXAM SERIES 64

THE PRESIDENT’S OFFICE MINISTRY OF EDUCATION, REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT

COMPETENCE BASED SECONDARY EXAMINATION SERIES

FORM III BASIC MATHEMATICS TERMINAL 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.

SECTION A (60 MARKS)

1.(a) Express the numbers 1470 and 7056 each as a product of its prime factors.

Hence evaluate and simplify

image

if m = 1470 and n = 7056.

(b)Express 0.00152 correct to: (i) two (2) significant figures

(ii)three (3) decimal places

(iii)in standard form

2.(a) Express x and y into fraction and hence find x + y, given that

image and image

(b)Solve for x in the following equation

image

3.(a) Solve for n

image

(b) Given that x2 + 8x +Q = (x + K)2

4 .In a certain school, 40 students were asked about whether they like tennis or football or both. It was found that the number of students who like both tennis and football was three times the number of students who like tennis only. Furthermore, the number of students who like football only was 6 more than twice the number of students who like tennis only. However, 4 students like neither tennis nor football.

(a)Represent this information in a Venn diagram, letting x be the number of students who like tennis only.

(b)Use the results obtained in part (a) to determine number of students who likes;

(i)Football only.

(ii)Both football and tennis.

5.(a) Find the equation of the line through the point (2,−2) crossing the image-axis at the same point as the line whose equation is y=2x- 4

(b) Express y in terms of x; 3x + 2y = 6 and Without drawing the graph, state the gradient, the y – intercept and x – intercept in the equation.

6.(a) The length of a rectangular field is 20m longer than the width. Find an expression for the perimeter of the field in terms of its length.

(b) In the figure below, Find angle x, y and z

image

7.(a) The parallel sides of a trapezium are 8cm and 12cm respectively. If the distance between the parallel sides is 9cm, calculate its area.

(b) A lady buys a printer for sh.26000 and when she sells it she realizes a loss of 40%. How much did she sell the printer for?

8. (a) If y2 varies directly as x-1 and inversely as x+d and if x=2, d=4 for y=1, then find x when y=2 and d=1.

(b)If 8 students in a typing pool can type 210 pages in 3 days, how many students will be needed to type 700 pages in 2 days?

9.(a) If image

Find

i) Cos A

(ii)

image

(b) Given the following figure, find the value of h, correct to one decimal place

image

10.(a)Compute the sum of the first ten terms of the series 1+5+9+....

(b)The 5th term of A.P is 23 and the 12th term is 37. Find

(i)The eleventh term

(ii)The sum of the first eleventh terms by using the values computed above without using the common difference for this progression.

SECTION B(40%)

Answer All Questions In This Section

11.Given the relation;

image

(i)Sketch the graph of R.

(ii)State its domain and range.

(iii)Find inverse of relation R

12. Given that

imageimage

(a) (i) Sketch the graph of f(x)

(ii) State its domain and range (iii) Is f(x) a one - to – one function?

(b) Find:

( i ) f(-4)

( ii ) f(2)

( iii ) imageimageimageimage

13. The masses of 40 parcels handled at transport office were recorded as shown in table below

Mass(kg)

1.0- 1.9

2.0-2.9

3.0-3.9

4.0 - 4.9

5.0 - 5.9

6.0 - 6.9

Number

Of

Parcels

6

2x

10

x

2

1

a)Find value of x

b)Determine modal class and its corresponding class mark

c)Find Median

14.( a) Given f(x) = x2 - 4x + 2. Find

i) Axis of symmetry ii) Maximum or minimum value

iii) Turning point

(b)Draw the graph of f(x) in 14(a) and use it to solve the equation x2 - 4x -2 =3

LEARNINGHUBTZ.CO.TZFORM THREE MATHEMATICS EXAM SERIES 56

PRESIDENT'S OFFICE REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT 

ANNUAL EXAMINATION MATHEMATICS FORM THREE 

Time: 3 Hours November 2020 a.m.

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. 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.mathematical tables may be used.

5.Cellular phones, calculators and any unauthorised materials are not allowed in the examination room.

SECTION A (60 Marks) 

Answer all questions in this section.

1.a) Use mathematical table, evaluate 

(b)Express 5.4545454545... in form of a/b where a and b are both integers.

2.(a)

b)Solve for x the following equation 32x-3 X 8x+4 = 64 ÷  2x

c)Rationalize the denominator 

3.a) Find value of P which makes the following equations perfect square

i) x2 + 8x +P=0 

ii) x2 - image 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 ofimage :image : image . 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) Triangles ABC and STBare similar. AB=3cm and ST=2cm. The area of triangle STU is 6cm2. Find the area of triangle ABC

(b) The translation T maps the origin onto a point P(4,8). Where will T map the points: (i) Q(0,4)?

(ii) N(−10,8)

7. (a) Find the equation of the line through the point (2,−2) crossing the image-axis at the same point as the line whose equation is y= x−4

(b) A farmer sold a quarter of his maize harvest and give one third of the remaining to his relatives.If the farmer remained with 36 bags of maize, find:- (i) How many bags of maize did the farmer harvest. (ii) How many bags of maize did the farmer sold.

8.(a) The sum of 1st n-terms of certain series is 2n-1, show that this series is Geometric Progression. Find an the nth term of this series.

(b) )The 5th term of A.P is 23 and the 12th term is 37. Find

(i)The tenth term

(ii)The sum of the first tenth terms by using the values computed above without using the common difference for this progression

9.(a) Given that 

image

Find The value of

image

(b) A man standing on top of cliff 100m high, is in line with two buoys whose angles of depression are 170 and 210. Calculate the distance between the buoys.

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)

Answer All Questions In This Section

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.(a ) Find values of angles marked x0 and y0 in the figure below

image

(b)Prove that exterior angle of cyclic quadrilateral is equal to interior opposite angle.

(c)Two places P and Q both on the parallel of latitude 260N differ in longitude by 400. Find the distance between them along their parallel of latitude

13. .(a)Prepare Balance sheet of Mr. Hamis from the following Assets and Liabilities on 31 st December 2009:

•Creditors 100,000/=

•Debtors 150,000/=

•Bank Overdraft 50,000/=

•Cash in hand 15,000/=

•Stock 85,000/=

•Furniture 42,000/=

•Premises 250,000/=

•Capital 392,000/=

(b) Use the transactions above to find

i.Total current asset

ii.Total Current liability

iii.Working Capital iv. Total fixed Asset

14. a) The function f is defined as follows:

i) Sketch the graph of f(x) 

(ii) Determine domain and range (

(iii) Find  f(1) ,  f(-4)  and f(π)

(b)For what values of x is function f(x)=image is undefined?

LEARNINGHUBTZ.CO.TZFORM THREE MATHEMATICS EXAM SERIES 39

THE PRESIDENT'S OFFICE

MINISTRY OF REGIONAL GOVERNMENT AND LOCAL GOVERNMENT

AUGUST-SEPTEMBER   EXAMINATION SERIES

MATHS  FORM-3

2020

TIME: 2:30 HRS

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. 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.(a) If  image and image find the fraction of image in its simplest form

(b).Find the GCF of 210, 357 and 252.

2.(a)image

(ii)   log3 10 + log3 8.1

(b)  If nlog5125 =  log264 , find the value of n.

3.  (a) By substituting a = 1x and b = 1y in the system of equations: 

image, find the solution set (x,y).

(b)  Let U be a universal set and A and B be the subsets of U where:

U = {1,2,3,4,5,6,7,8,9,10}, A = {odd numbers} and B = {prime numbers} (i) Represent this information in a venn diagram.

(ii)  Find A ? B′ and (A ? B) ′

 

4.  (a) Given vectors (i) the vector a = 3i + 2 j , b = 8i +­ 3j and c = 2i + 4 j find:

(i) d=3a -b +1/2c 

(ii) a unit vector in the direction of d.

(b) Find the equation of the line passing at point (6, ­2) and it is perpendicular to the line that crosses the ­x-axis at 3 and the y­-axis at ­4.

 

 

5.  (a) Two triangles are similar. A side of one triangle is 10 cm long while the length of the corresponding side of the other triangle is 18 cm. If the given sides are the bases of the triangles and the area of the smaller triangle is 40 cm2 , find the area and the height of the larger triangle.

(b) In the figure below CB = BD = DA and angle ACD = x .

image

(i)  Show that angle ADE = 3x ,

(ii)  Calculate the measure of angle CDA if x = 39°.

6.  (a) A shopkeeper makes a 20% profit by selling a radio for sh. 480,000.

(i)  Find the ratio of the buying price to the selling price.

(ii)  If the radio would be sold at 360,000, what would be the percentage loss?

(b)  A farmer sold a quarter of his maize harvest and gave one third of the remaining to his relatives. If the farmer remained with 25 bags of maize find how many bags of maize did the farmer harvest.

 

7.  (a) Mariam, Selina and Moses contributed 800,000, 1,200,000 and 850,000 shillings respectively while starting their business.

(i)  Find the ratio of their contributions in simplest form.

(ii)  If the business made a profit of 1,900,000 shillings; find how much each got if the profit was shared in the same ratio as their contributions.

 

(b)  A dealer bought 10 books for 200,000. He sold 25 of them at 30,000 shillings each and the remaining at 25,000 shillings each. What was his percentage profit?

 

8.  (a) The number of tablets given to a patient was found to be directly proportional to the weight of the patient. If a patient with 36 kg was given 9 tablets, find how many tablets would be given to a patient whose weight is 48 kg.

(b)  Four people can eat 2 bags of rice each weighing 10 kg in 12 days. How many people can eat 6 bags of rice of the same weight in 18 days?

9.  (a) If the sum of n terms of a geometric progression with first term 1 and common ratio imageis image , find the number of terms.

 

(b)  How many integers are there between 14 and 1,000 which are divisible by 17?

10.(a)   Use factorization method to solve the quadratic equation x2 ? 9x + 14 = 0.

 

 (b) Find the values of x that satisfies the equation 

image

SECTION B( 40 Marks)

Answer All Questions

 

11.(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 imageand RE=6370km to find speed of ship in km/h 

11.(b)  Calculate the values of  imageif f is defined as  

image 

12.Mwanne commenced business on 1st April, 2015 with capital in cash 200,000/=

April  2 bought goods for cash 100,000/=

3 bought goods for cash 300,000/=

4 purchased shelves for cash 230,000/=

5 sold goods for cash 400,000/=

9 paid wages for cash 50,000/=

12 purchased goods for cash 70,000/=

13 sold goods for cash 600,000/=

  16 paid rent for cash 100,000/=

20 bought goods for cash 60,000/=

   25 sold goods for cash 300,000/=

   27 paid salary for cash 70,000/=

Prepare the following:

(a) Cash account, (b) Trial balance.

 

13. The heights of 50 plants recorded by a certain researcher are given below:

56 82 70 69 72 37 28 96 52 88 41 42 50 40 51 56 48 79 29 30 66 90

99 49 77 66 61 64 97 84 72 43 73 76

76 22 46 49 48 53 98 45 87 88 27 48

54 79 80 73

(a)  Copy and complete this tally table for the data given above.

Height (cm)

Tally

Frequency

21-30



31-40



41-50



51-60



61-70



71-80



81-90



91-100



Use this table to:

(b)  Draw a histogram for the height of the plants.

(c)  Find the mean height of the plants (do not use the assumed mean method).

(d)  Find the median of the heights of the plants.

14.  (a) In the figure below, BD is a tangent to the circle having the centre O .

image

Given that angle OEC = 28°, find the values of angles marked X , Y and Z .

(b) Find the equation of the line passing at point (6, ­2) and it is perpendicular to the line that crosses the ­x-axis at 3 and the y­-axis at ­4.

 

 

 

 

 

 

 

 

 

 

LEARNINGHUBTZ.CO.TZFORM THREE MATHEMATICS EXAM SERIES 29

THE PRESIDENT’S OFFICE MINISTRY OF EDUCATION, LOCAL ADMINISTRATION AND LOCAL GOVERNMENT

BASIC MATHEMATICS TERMINAL EXAMINATION-MAY

FORM THREE

Time 3:00 Hours                                                                              MAY 2020 

Instructions 

  • This paper consists of two sections A and B. 
  • Answer all questions in Section A and only four questions in section B
  • Show clearly all working for each question
  • Mathematical tables, geometrical instruments and graph paper may be used where necessary 

                       SECTION A (60 MARKS) 

1. (a) Arrange the number in ascending order.

(b) Express 0.06896 correct to: 

     (i) three (3) significant figures

     (ii) three (3) decimal places

     (iii) in standard form

2. (a) Solve for x in the equation:  32x-3 x 8x+4 = 64 ÷ 2x

(b) Solve for x in the equation log(x2+8) – logx = log6

3.  (a) Find the solution set of the inequality  and indicate it on a number line.

(b) If find n if

(c) Simplify the following expression and state the coefficient of

4. (a) In a school of 75 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?

 ( b) The Venn diagram below shows the universal set U and its two subsets A and B

                                                                        Write down the elements of

 i) A’     ii)B’   iii)AUB    iv) A’UB’   

5. The figure ABCD below is rectangle with sides as shown where C1 and C2 are two quarter circles inside it.

Find:

a) Value x and y shown in the  figure above

b) Perimeter of the rectangle

c)Area of the rectangle ABCD

 d) Area of the shaded region

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 (Ti) inside a house is directly proportional to the temperature (to) outside the house and is inversely proportional to the thickness (t) of the house wall. If

 Ti = 320C when To =240C and t = 9 cm, find the value of t when Ti = 360C and To = 180C

7. (a) A shirt whose marked price is Tshs 80,000/= is sold at a 13% discount, if the trader makes a profit of 20%, find the selling price of the shirt.

(b) A regular polygon has an exterior angle of 360

  1. Find the size of the interior angle
  2. How many sides does this polygon have
  3. Find the sum of interior angles of this polygon

8. (a) Find the 10th  term of the G.P if the 4th term is 8 and the 7th term of this G.P is 16.

(b) Find the sum of the first 10 terms of the series: 4 + 6 + 8 + - - - - - - - - 

9. (a)Find the value of  without using mathematical tables.

(b) A ladder leans against vertical wall. If the ladder reaches 12m up the wall and its foot is 9 cm from the base of the wall. Find the length of the ladder.

10. (a) Factorize completely by splitting the middle term

(b) Factorize and hence find exact value of (10003)2 –(997)2

(c) Solve the equation

          SECTION B ( 40 MARKS )

  (a) The function f is defined as follows:

                   

 (i) Sketch the graph of .

(ii) Determine the domain and range of 

(b) If R-1 =. Find the domain and range of R

   12. The 4th, 6th and 9th terms of arithmetic progression forms first three terms of geometric progression. If the first term of the A.P is 3, determine the:

(a) Common difference of the arithmetic progression

(b)Common ratio of the geometric progression

(c) Kicheche deposited Tshs100000/= in a bank at a compound interest of 8% per annum for 4 years. Find how much interest he received 

13.  The weight in kg of 40 students were recorded as follows:

Weight in(kg)

10 - 19

20 - 29

30 - 39

40 - 49

50 - 59

60 - 69

70 - 79

Number of students

8

3

   x

8

7

2

2

Calculate:

(a) The value of x

(b) The mode by using the formula. 

(c) By using an assumed mean, find the average weight of the students

(d) Draw a cumulative frequency curve and hence use it to estimate median.

14. a) A farmer sold a quarter of his maize harvest and give one third of the remaining to his    relatives. If the farmer remained with 36 bags of maize, find:-

i) How many bags of maize did the farmer harvest. 

ii) How many bags of maize did the farmer sold.

b)A shopkeeper makes a profit of 20% by selling a TV for 480,000/=

 i) Find ratio of buying to selling price

 ii) If the radio would be sold for 360,000/=, what would be the percentage loss?     

15. 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(0)   ii) f(-6)   iii) f(π)

b)For what values of x is fuction f(x)= is undefined?

16. Mr. Chakubanga started business on 15th February, 2005 with capital in cash 1,055,000/=

February 16 Bought goods for cash 500,000/=

18 Bought shelves for cash 55,000/=

19 Sold goods for cash 450,000/=

20 Purchases for cash 400,000/=

21 Sold goods for cash 700,000/=

25 Paid rent for cash 150,000/=

Required:  Record the above transactions in the respective ledgers and extract a trial balance.

LEARNINGHUBTZ.CO.TZFORM THREE MATHEMATICS EXAM SERIES 21

THE PRESIDENT’S OFFICE MINISTRY OF EDUCATION AND VOCATIONAL TRAINING

MID TERM EXAMIATIONS

024      MATHS- THREE

Duration: 2:30 Hours

INSTRUCTIONS.

  1. This paper consists of two sections A and B.
  2. Answer all questions in section A and only Four Questions in Section B
  3. All writing must be in blue or black ink except drawing which must be in pencil.
  4. Calculators, cellular phones and any unauthorized materials are not allowed in the examination room.
  5. Write your Examination Number at the top right corner of every page.
  6. Show clearly all working for each question 

SECTION A( 60 %)

  1. a) 468 – 468 ÷39 + 39 correct to two significant figures

b) Calculate without using mathematical tables

 

2. Make x subject of the formula

P=

3. By using the substitution t=3x, solve the equation 32(1+x) – 3x=3(x+3)-3

4. The size of exterior angle of a regular polygon is 450. Find :

i)  The number of sides

ii) The sum of all interior angles

5. Find the values of x that satisfy the following equation log(x+5) + log(x + 2)=log4

6. A translation T carries the point (1,2) to (-2,8). Find where it map :

a) Pont A(-2,2)

b)  The origin

7. The lines with equations 2x=3 – y and 2y + 3x=4 meet at point Q. Find the coordinate of point Q.

8. Find two consecutive odd numbers whose product is 195.

9. In a class of 31 students, 17 participate in English debate, 12 participate in English and Sports. If every student is required to participate at lest one of the two events. Find the number of students who participate in i) Sport  ii) English only.

10. A dealer bought 10 books for 400,000/=. He sold 2/5 of them at 40,000/= shillings each and the remaining at 60,000/= shillings each. What was the percentage profit?

SECTION B(40%)

11. The examination scores in Basic Mathematics of 40 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 using Assumed mean A=44.5

b) Calculate median

c)  Draw histogram and use it to estimate Mode

12. a) Consider the figure below where PQ//BC.

                                                     

i)Prove that triangle ABC is similar with triangle APQ

ii) If the length of BC=15, PQ=9cm and PB= 6cm. Find the length of AP. 

b)Prove that, the sum of two angles of a triangle is equal to exterior angle of the third angle.

13. a) Find the expressions which describe the relation of the graph below

 

b)  Determine Domain and range of this relation.

c) Find inverse of this relation.

14 a) Given f(x) = -x2 + 4x – 5. Find 

i) Axis of symmetry

ii) Maximum or minimum value

iii) Turning point

b) Draw the graph of f(x) and use it to solve the equation  -x2 + 4x -15 =0

15.The function f is defined as follows:  

F(x) =                

   i) Sketch the graph of f(x)   

   ii) Determine domain and range 

   iii) Find

(a) f(1)   b) f(-4)   c) f(π)

16. 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 45% of cost of sold goods.

Find a) Average Stock  b) Cost of Sold Goods   c) The gross profit     d) Net Profit

LEARNINGHUBTZ.CO.TZFORM THREE MATHEMATICS EXAM SERIES 7

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