O-STUDY LIBRARY
FORM THREE ANNUAL EXAMINATION- NOV, 2023
BASIC MATHEMATICS
TIME:3.00 HRS
INSTRUCTION
1. This paper consist of two sections A and B
2. Answer all questions
3. Calculators and mathematical tables may be used
4. All diagramsdiagram must be drawn by using pencil
5. All writing must be in a blue or black ink
SECTION A (60 MARKS)
(a)Write 490.032578 correct to
(b)The anterior angle of a regular polygon is four times its exterior angle. Find
Size of each exertion angle
(a)Solve the following exponential equation
(b)Given log 52 = 0.4307 and log 53 = 0.6826
(a)A painter placed a 20m ladder against the wall of a house so that the base of the ladder is 4m away from the wall. How high does the ladder touch the wall from the ground?
(b)If 
Where
A is an active angle find
Sin A
Cos A
(a)If
simplify 
(b)Describe application of Logarithm in daily life
(a) In the following figure.
and 
if 
=13cm
and 
Find
area of BCDE
(b) What do the following terms mean as used in accounting
(a)A company bought two vans 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 transaction, there was no loss. What was the profit made by the company?
(b) If the square of the hypotenuse of an isosceles right angle Triangle is 128cm2. Find the length of each side.
(a)From the top of a tower of height 60m the angles of depression of the top and bottom of a building are observed to be 30° and 60° respectively. Find the height of the building.
(b)Three bells commence tolling together and toil at an interval of 8, 10 and 12 seconds respectively. How many times do they together is 50minutes?
(a) If the length of each side of a square is mixed eased to 16times the area of Small Square. Find the length of one side of Original square
(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 is 2800m2 how wide is the walkway?
(a)
.
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 
(a) Let
be
a universal set and A and B be sub-set of
,
if ฮผ = {a, b, c, d, e, f, g, h}
A = {c, g, f} and B = {b, d, h} find
The number of subsets of set A
n(A'∩B)
(b)The traffic lights at three different road crossings change 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
(a)The marks in Basic Mathematics terminal examination obtained by 40 students in one of secondary schools in the same district 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.
Prepare a frequency distribution table with class interval 10 – 19, 20 – 29, etc
Find class that contain medium
Find the mean
(b)Find the value of angle x in figure below, where O is in the center of the circle.
(a) Two towns P and Q on latitude 48° are 370 nautical milesMiles apart. Find the difference in their longitude.
(b)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.
(a)If
and
.
Find 
and 
(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:
(a)(i) With using table of values draw the graph of
(ii) State the domain and range of f(x)
(b) Solve for x and y if
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