PRESIDENT’S OFFICE, REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT

SECONDARY EXAMINATION SERIES,

MID TERM ONE – MARCH-2024

MATHEMATICS FORM THREE

Time: 3Hours

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 (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 calculator may be used.

6.   All communication devices and any unauthorized materials are not allowed in the examination room.

7.   Write your examination number on every page of your answer sheet(s).

SECTION A. (40 MARKS)

Answer all questions in this section. 

1.         (a) solve the value of x if ^x+3 -1  =1

(b) If log ₂ =0.0310, without mathematical time table find value of Log ⁵

2.         If a = 0.25 and b= 0.5. find the fraction  in its simplest form

(b) Round off (1) 0.002098 to two significant figures 

1.      7.67 to the nearest whole number
2.   2.77 to one decimal place

3.         (a) how many grams are there in 0.00912 tones

(b) the compression of 1 spring is directly proportional to the thrust T. Exerted on it . if the thrust of 4N produces a compression of 0.8, find 

1.      The compression when the thrust is 5N
2.   The thrust when the compression is 0.5 cm

4.         The product of three terms of 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 serving bank whose interest was 10% compounded annually. After 32 years he got 5000 shillings.

1.      How much did he invest at the start
2.   How much did he receive as interest at the end of two years

5.         (a) Given that log ₃4 = 1.262 and log ₃5 =1.1465. find log ₃0.8

(b) the dimension of first rectangular are length 23cm and width 16 cm. a second rectangle has length 12cm  and width 9cm with reasons state wether the two rectangles are similar.

6.         (a) solve for x in 1≤3x-2<8

(b)  By using completing square method, solve equation.

=4

7.         (a) find the value of Y given that 125^y+1+5^3y=630

(b) find the value of x given that 2log x= log 4+log (2x-3)

8.         (a) Given three points A (3,3) B (-3,1) C (-1,-1) and D (1,-7)

1.      Show that the line through A,B, And CD are perpendicular to each other
2.   Find equation of the line through point (-4,5) which is parrralel to BC

9.         (a) The fifth and the eleventh term of an arithmetic progression are 8 and -34 respectively. Find the sum of the first ten terms

(b)  Prove that the interior angle of a cyclic quadrilateral is equal to the opposite interior angle 

10.     (a) Mayele bought 3 bottles of juice of capacity 350ml and Dialo bought 1 bottle of juice of capacity 1 Litre

1.      Who had more juice to drink
2.   Bu how much more?

(b) Simplify the sum of 85% of 9861 and 3/5 of 12458. Write your answer to two significant figures.

SECTION B. 40 MARKS

11.     (a) in a certain research the data were summarized as shown on the table below

 By using the data above reconstruct a frequency distribution table including class interval and frequency 

(b) Prove that equal chords of a circle subtends equal angles at the centre

12.     (a) solve  for the quadratic equation x²-8x+7=0

(b) Solve for x and y if  

13.     (a) (i) without using table . Draw the graph of

F(x)=x²+2y-4

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

(b) A field is 10M longer than its width. The area is 7200m² . Find its width

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

(b) Amina invested a certain amount of money in a serving bank whose interest rate was 10% compounded annually. After two years she got 5000. 

1.      How much did she invest at the start
2.   How much did she receive as interest at the end of two years?

PRESIDENT OFFICE REGIONAL ADMNISTRATION

AND LOCAL GOVERNMENT

SECONDARY EXAMINATION SERIES 

COMPETENCE BASED ASSEMENT

MATHEMATICS FORM THREE 

MID-TERM EXAMS MARCH – 2023 

041

Time: 3Hours 

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.
4. All necessary working and answer for each question must be shown clearly
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. Write your Examination Number on every page of your answer booklet(s) 

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 7am at what time do they change simultaneously again? 

(b) If x = 0.567567567 and Y = 0.83 by Converting these decimal to fractions, find the exact value of

2. (a) If  Find the value of t

(b)Write ‘L’ in terms of M₁ N and T from the formula

(c)Determine the value of x if

3. (a)If the 5^th term of A.P is 23 and 12^th term is 37 find the first term and common difference

(b)How many years would one double one’s investment if Tsh 2500 is invested at 8% compounded semi-annually

4. (a)Find value of x and y if

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

U = {a, b, c, d, e, f, g, h}                    A={c, g, f} and           B= {b, d, h}

(i) Find the number of sub sets of set A'

(ii) Find n (A'n B')

(iii) If an element is picked at random from universal set (U), find the probability that it is an element of set B

5. (a)The coordinate of P, Q and R are (2, m), (-3, 1) and (6, n) respectively. If the length of PQ is  units and midpoint of QR is  find possible value of m and n

(b)The gradient of line L, is – 2, another line L₂ is perpendicular to L₁ and passes through (-3, -2) what is the equation of L₂

6.  

(a)If  = 17cm, =8cm,  = 12cm, and angle ABD = 90°. Calculate the length  

(b)(i) Given  where  and  are the sides of Triangle ABT and  are sides of 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 circle and its area.

7. (a)Rationalize the denominator of

(b)Without using mathematical tables find value of 3 log5 + 5log2 – 2log2

8. (a)Solve for x in the inequality 3x – 4 ≥  x + 16

(b)Solve the following pairs of simultaneous equation by elimination method

9. (a)The sum of first six terms of an AP is 72 and the second term is seven times the fifth term

(i) Find the first term and the common difference 

(ii) Find the sum of first ten terms

(b)Find the sum of the first four terms of a geometric progression which has a first term of 1 and common ration of

10. (a)The gradient of line L₁ is -2, another line L₂ is perpendicular to L₁ and Passes through point (-3, -2) what is the equation of L₂?

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

SECTION B (40 Marks)

Answer all questions

11. (a)The number of workers absent in 52 working days is given in a cumulative frequency table below

Find.

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

(ii) Median 

(b)Find the angle x in figure below

12. (a)The function f is defined as follows

1. Sketch graph of f(x)
2. Determine Domain of f(x)
3. Determine the range of the function

(b)In a triangle ABC the ratio of angle is A: B: C = 2:3:7 the length of shortest side = 5cm. Find the length of longest side.

13. (a)Find the first term and common difference of an AP whose 5^th term is 21 and 8^th term is 30 

(b)Find the 10^th term of a sequence whose first three consecutive terms are 5, 15 and 45. Leave your answer in exponents

14. (a)Mr.Ogango from Kenya visited Tanzania. He had 5,000 Kshs and wanted to change the money into LIS dollar. If 1 Us dollar was equivalent to 2500 Tanzania shillings (Tshs) AND Ksh 1 was equivalent to Tshs 20 how much Us dollars did he get.

(b)A gardene has found that the time cut grass on a square field varies directly on the square of its length (L) and inversely as the number of men (m) doing that job. If 5 men cut grass on field of size 50m in 3 hours, how many more men are required to cut grass on a field of side 100m in 5 hours. Assume