PRESIDENT’S OFFICE REGIONAL, ADMINISTRATION AND LOCAL GOVERNMENT
SECONDARY EXAM SERIES
FORM THREE ANNUAL EXAMINATION
041 BASIC MATHEMATICS
TIME:3 HOURS NOV, 2023
INSTRUCTION
SECTION A (60 MARKS)
(b)The anterior angle of a regular polygon is four times as its exterior angle. Find
(b)Given log 52 = 0.4307 and log 53 = 0.6826
(b)If Where A is an active angle find
(b)Describe application of Logarithm in daily life
(b) What do the following terms mean as used in accounting
(b) If the square of the hypotenuse of an isosdes right angle Triangle is 128cm2. Find the length of each side.
(b)Three bells commerce tolling together and toil at an interval of 8, 10 and 12 seconds respectively. How many times do they together is 50minutes?
(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 the garden by the same width. If the area of the walkway 2800m2 how wide is the walkway?
(b)Write “L” in terms of M, N and T from the formula
(c)Determine the value of x if
A = {c, g, f} and B = {b, d, h} find
(b)The traffic lights at three different road crossing changing after every 48 seconds, 72seconds, and 108 seconds respectively. If they change simultaneously at 7am at what time will they change simultaneously again?
SECTION B (40 Marks)
Answer all questions
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.
(b)Find the value of angle x in figure below, where O in the center of the circle.
(b)A regular hexagon is inscribed in a circle. If the perimeter of hexagon is 42cm. Find the radius of the circle and its area.
(b)From the following information given by Mbeya Co. Ltd for the year ended 31st Dec 2022.
Stock (01.01.2022) ................... Three quarter of closing
Stock (31.12.2022) .............. of Net purchases
Net purchases during 2022 ................ 432.000
Gross Margin ........................... 15%
Expense .................................... 20% of Net profit
Calculate:
(ii) State the domain and range of f(x)
(b) Solve for x and y if
FORM THREE MATHEMATICS EXAM SERIES 151
FORM THREE MATHEMATICS EXAM SERIES 151
THE PRESIDENT’S OFFICE
MINISTRY OF EDUCATION, REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT
COMPETENCE BASED SECONDARY EXAMINATION SERIES
MATHS ANNUAL EXAMINATIONS
FORM THREE-2022
INSTRUCTIONS
SECTION A (60 MARKS)
Answer all questions in this section.
(b)(i) Estimate the value of
(ii)Simplify the ratio of a tob, given that and b= to its lowest form.
(b) If 3x – y=4, What is the value of
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
(b)In a triangle ABC, angle ABC=50° and point X lies on such that with the aid of a diagram, calculate
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:
(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.
(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.
(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
Marks (in %) | 99 – 89 | 88 – 78 | 77 – 67 | 66 – 56 | 55 – 45 |
Number of students | 2 | 5 | 20 | 11 | 7 |
(b) are secants that intersect at A in the figure below. Given that chords Find the angles x and y.
(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)
(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
(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?
FORM THREE MATHEMATICS EXAM SERIES 113
FORM 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
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
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.
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;
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
Find :
(i)
(ii)
(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.
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;
(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
(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).
FORM THREE MATHEMATICS EXAM SERIES 103
FORM THREE MATHEMATICS EXAM SERIES 103
PRESIDENT'S OFFICE REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT
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 - 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) 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 -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
Find The value of
(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
(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)= is undefined?
FORM THREE MATHEMATICS EXAM SERIES 39
FORM THREE MATHEMATICS EXAM SERIES 39