B. Math District Pree National (Final)

THE UNITED REPUBLIC OF TANZANIA
PRESIDENT’S OFFICE REGIONAL ADMINISTRATIVE AND LOCAL GOVERNMENT

KILOMBERO DISTRICT COUNCIL
FORM FOUR PRE - NATIONAL EXAMINATION
041 BASIC MATHEMATICS
TIME: 3Hours. Wednesday 04th September 2019

Instructions.
1. This paper consists of section A and B.
2. Answer All questions in this paper by showing All necessary Workings and Solutions.
3. Four Figure Mathematical Tables may be used where necessary.
4. Calculators and Cellular Phones are not required in the examination room.
SECTION A.
1. (a) Write 64.962 and correct to:

(i) Four significant figures.
(ii) Two decimal places.
b) Juma and Ally are driving in a circular ground. Juma completes a round in 20 minutes whereas Ally completes
a round in 25 minutes. If they started in the same place and time and go in the same direction. After how many
minutes will they meet again at the starting point?
x
 675
x y
2. (a) Find the value of
y
if 5 .3
(b) Simplify 2log25-3log5+log20
3. (a) In a group of 240 tourists, 80 speak English, 120 speak French but not English, and 60 speak both English and
French. By using Venn diagram, how many tourists speak neither English nor French?
(b) A family has 3 children, find the probability that a family has exactly 2 boys and 1 girl.
4. (a) Find the value of x so that the points A(1,3),B(-2,-3), and C(x,7) are collinear.
(b) Given the vectors a  i  3 j , b  5i  2 j and c  3 a  4 b , find the unit vector in the direction of vector c .
~ ~ ~ ~ ~ ~
5. (a) Find the value of diagonal AC in the figure below, if area is 100 cm2:
(b) In the figure below, calculate the length of the segment AE .
6. (a) Convert 12:00 noon into 24 hours.
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(b)The price of the Radio is Tsh. 120,000 which includes V.A.T. Find the price of the Radio before V.A.T if the rate
of V.A.T is 40%.
7. (a) What do you understand by the word Cash account?

st th
(b)Mr. Paul decided to keep a record of his business from 1 May to 30 May as follows:
May 1 He started the business with cash capital 5000,000

5 Purchased goods 254,000
10 Sold goods 290,000
20 Purchased goods 204.000
25 Expenses 24,000
30 Sold goods 320,000
You are required to prepare cash.
8. (a) Find the next two terms in the sequence 1, 2, 5, 14, ....., ......
(b) The Arithmetic mean and Geometric mean of p and q are 5 and 4 respectively. Find the value of p and q.
sin 150  tan 315 

9. (a) Without using mathematical tables, evaluate .
cos180  sin 270 
(b)A point Q on the ground level is 12m from the base of the flag pole. A wire from point Q is attached to the pole at
16m above the ground. Find the length of the wire.
10. (a) The operation  is define as bellow:
a  b ={
𝑎 − 𝑏 𝑖𝑓 𝑎 > 𝑏
𝑎 + 𝑏 𝑖𝑓 𝑎 < 𝑏
, find the value of 8  6 3
(b) Factorize completely the quadratic expression 2 x 2  x  10 by splitting the middle term.
SECTION B.
11. (a) The table below shows the distribution of marks of 40 form Two C in biology test at Ujamaa secondary school.
Marks(%) 11-15 16-20 21-25 26-30 31-35 36-40
Number of students 5 8 x 12 6 4
(i) Find the value of x
(ii) Prepare the frequency distribution table including the class marks and fx.
(iii) Calculate the mean by using  fx obtained in prepared table above.

(iv) Draw the Histogram and Frequency polygon in the same axes and hence estimate the mode.
(b) In the figure below, find the value of "y":
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12. (a) Below is the right angled triangular pyramid of the base ABCD, vertex V and centre of the base P:
If AB=CD=8cm, AD=BC=6cm and AV=VB=VC=VD=13cm, calculate:
(i)The diagonal DB.
(ii) the height VP.

(b) An aeroplane flies from point A(70 N ,30  E ) to A(30  N ,30  E ) at the speed of 8knots, how long will the
plane reach to point B?
9 7 6  1
13. (a) Given that A=   and   , find:
8 6   2 5 
(i)AB
(ii)BA
(iii)From above (i) and (ii), state whether the matrix multiplication is commutative or not?
(b) Find the enlargement matrix which enlarges the vector r=(3,4) onto r’=(15,20).
14.(a) Find the greatest value of the function f(x ,y)=7x+3y subject to the constraints:
2 x  3 y  12
x  3y  9
x  0, y  o
(b) Given the function f ( x)  x 2  2  4 x , find:
(i) Axis of symmetry
(ii) Maximum or minimum value
(iii) Turning point
(iv) Range
_THE_END_
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THE UNITED REPUBLIC OF TANZANIA

PRESIDENT’S OFFICE REGIONAL ADMINISTRATIVE AND LOCAL GOVERNMENT

041 BASIC MATHEMATICS

TIME: 3Hours. Wednesday 04th September 2019

1. (a) Write 64.962 and correct to:

(b) In the figure below, calculate the length of the segment AE .

6. (a) Convert 12:00 noon into 24 hours.

7. (a) What do you understand by the word Cash account?

May 1 He started the business with cash capital 5000,000

You are required to prepare cash.

sin 150  tan 315 

10. (a) The operation  is define as bellow:

Marks(%) 11-15 16-20 21-25 26-30 31-35 36-40

(i) Find the value of x

(iii) Calculate the mean by using  fx obtained in prepared table above.

(b) In the figure below, find the value of "y":

If AB=CD=8cm, AD=BC=6cm and AV=VB=VC=VD=13cm, calculate:

(i)The diagonal DB.

(ii) the height VP.

(b) Given the function f ( x)  x 2  2  4 x , find:

(i) Axis of symmetry

(ii) Maximum or minimum value

(iii) Turning point

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