**THE UNITED REPUBLIC OF TANZANIA
**

**PRESIDENT’S OFFICE
**

**REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT
**

**KILOSA DISTRICT COUNCIL
**

**FORM FOUR PRE-NATIONAL EXAMINATION
**

**BASIC MATHEMATICS
**

**041
**

**TIME:3:00 Hours** **Thursday 22 ^{nd},August 2019**

**INSTRUCTIONS
**

- This paper consists of section A and B with a total of fourteen questions (14)
- Answer all questions from both sections. Each question in section A carries (6 marks) where as in section B each question carries (10 marks)
- All necessary working and answers for each question done must be shown clearly
- Mathematical table and graph papers may be used
- Calculators, cellular phone and any unauthorised material are not allowed in the examination room
- Write your examination number on every page of your answer sheet/booklets provide

**SECTION A: 60 MARKS
**

- Write a number 699.79 in to:
- Hundreds
- Ones
- Tenth
- Its expanded form

- (a) Solve =
(b) Solve for x: =

- (a) (i) A and B are sets defined as
A =

B =

Find a set of

(ii) Butundwe village has 200 families of which 180 have grown Serena and 165 have grown cassava in their private plots. How many families have grown both food crops if each family has grown at least one of the two crops?

(b) A fair die and a coin are tossed once, what is the probability of tail on the coin and prime number of the die showing up? A line passes through the points (-2, -3) and (-5, 1). Find the equation of the line through (-2, _3) 0perpendicular to the given line.

- (a) (i) A line passes through the points (-2, -3) and (-5, 1). Find the equation of the line through (-2, _3) 0perpendicular to the given line.
(ii) Determine the slope of the line — 4 = 0

(b) Given that; , , . Find

- (a) Find the length of in a figure below if , and

A

E

3cm

C 5cm D 5cm B

(b) Find the radius of the circle inscribed in a regular hexagon with perimeter 500m.

- (a) Madenge bought 60 bottles of water each 350ml for 60 peoples. Write the amount of water Madenge bought in litres

(b) y varies jointly with x and inverse of the square root of z. when and , then . Find y in terms of x and z

- (a) If and evaluate

(b) Find the total amount of money accumulated in 4 years from a principal amount of Tsh.60,000/= deposited in a bank, if the bank pays interest at the rate of 5 per annum.

- (a) Compute the sum of the first 10 terms of the series

(b) The 4

^{th}, 6^{th}and 9^{th}terms of an arithmetic progression forms the first three terms of a geometric progression. If the first term of the Arithmetic progression is 3, determine the common difference and common ratio.- (a) Angle A is acute if, find in simplified form of the value of

(b) Show that, hence find the value of given that

- (a) Factorize completely

(b) Solve for x and y from the equation and , use the substitutions and

SECTION B

- The table below shows the distribution of marks obtained by 40m students in a Mathematics test.

Marks

21-30

31-40

41-50

51-60

61-70

71-80

Frequency

4

3

4

15

12

2

- Use the class mark of the modal class as the assumed mean to calculate the mean mark
- Calculate the mode
- Draw cumulative frequency curve and use it to estimate the median

- (a) The figure below shows a rectangular prism in which
S R

P O 4m

D C

5m

A 6m B

- Calculate the length of diagonal AR
- Find the angle diagonal AR makes with the floor

(b) In the figure below O is the centre of the circle. Find an equation relating x and y.

x

y

O

- (a) Given the matrix; A = , find . Hence find the value of x and y by matrix method given that;

(b) A translation T carries the point (1, 2) to (-2, 8). Find the image of the point

(5, -7) under T.

- A crafts man wishes to decide how many of each type A and B charcoal stove he has to fabricate in order to maximize profit for this Month. Unit profit for type A stove is Tsh.1000/= and Unit profit for type B stove is Tsh.1500/=. Type A stove requires 1m
^{2}of mild steel sheet per unit and type B requires 2m^{2}. He has only 12m^{2}of mild steel sheet available. He can fabricate a total of 8 stoves of either type per month.

(a) How many of each type should he fabricate in order to maximize profit?

(b) What is the maximum profit?