THE UNITED REPUBLIC OF TANZANIA NATIONAL EXAMINATIONS COUNCIL OF TANZANIA

FORM TWO NATIONAL ASSESSMENT

041 BASIC MATHEMATICS

Time: 2:30 Hours YEAR 2023

INSTRUCTIONS

1. This paper consists of ten (10) compulsory questions.
2. Show clearly all the working and answers in the space provided.
3. All writing must be in blue or black ink except drawings which must be in pencil.
4. Four figure mathematical tables, geometric instruments and graph papers may b used where necessary
5. All communication devices, calculators and any unauthorized materials are not allowed in the examination room
6. Write your examination Number at the top right corner of every page.

1.(a) List first twelve multiples of 4 and 5 and hence identify the common multiples 

(b) Evaluate

 correct to;

(i) One significant figure

(ii) Three decimal places

2.(a) Arrange the given fractions in ascending order of magnitude:

(b) In the year 2016 the population of Mericho village was 2,800. In 2017 the population increased by 8%. What was the population in 2017?

3.(a) If 1,000 tonnes of maize were shared equally among 25 schools, how many kilograms did each school get.

(b) A shopkeeper bought a radio for sh. 80,000/= and sold it at a profit of 20%. What were the profit and selling price?

4. (a) If ABCD is a trapezium, find the values of angles marked a, b and c 

(b) The floor of a room is a square of length 5 metres. Find its perimeter and area 

5. (a) If

Find the value of y correct to three significant figures.

(b) Solve the equation 3x² - 7x - 6 = 0

6.(a) Find the gradient of a straight line joining the points (-1 , 2) and (3 , -5).

(b) Find the image of point P(-3 , 7) after a reflection in the x-axis and y-axis.

7.(a) Solve for n in the equation

Leave the answer in improper fraction.

(b) Find the value of x in the equation log(2x² + 1) + log4 = log(7x² + 8) 

8.(a) In the given figure:  and . Find the length of

(b) ABC is a triangle in which  and D is the mid-point of  prove that

9.(a) The angle of elevation of the top of a building from a point on the ground is 25⁰. If the point on the ground is 80m from the base of the building. Find the height of the building correct to one decimal place.

(b) Calculate the length of ???????? IN the following Figure:

10.(a) At a certain school, 250 students attended on the first day of re-opening of the school, 350 students attended on the second day and 150 students attended on both first and second day. It was further noted that 10 students were absent on both days. If all registered students were supposed to attend the school on both days, how many students does the school have? Do not use venn diagram.

(b)The given Pie chart represents the number of students who passed a Qualifying Test in mathematics, Chemistry and Kiswahili

Find:

(i) The fraction of students who passed Kiswahili

(ii) The percentage of students who passed Mathematics.

(iii) The percentage of students who passed Mathematics and Kiswahili