Observe the pattern in figure below

a. If the pattern continues, find the number of letters in the column containing the letter M

b. If the total number of letters in the pattern is 361, which letter will be in the least column? 

A concert hall admits 3 people in the first minute, 5 people in the second, 7 in the third, and so on. After 10 minutes, it is half full. After how many minutes will it be full?

A company offers a starting salary of Birr 28,000 with an annual increase of Birr 1,200.

a. What would the annual salary be in the seventh year?

b. How much would be earned at the firm over the first 7 years? 

A man deposits Birr 5,000 into an account paying 5% interest per year, compounded annually.

Show that the amounts in the account at the end of each year form a geometric sequence. What is the amount after 4 years?

A 500 g radioactive element decays to ¼  of its mass in per years. How much will remain after 12 years

A man was injured an accident at work. He receives a disability grant of 4800 ETB in the first year. This grant increases by fixed amount each year.

a. What is the annual rate of increase  if he received a total of 143,500 ETB over 20 years?

b. His initial annual expenses are 2600 ETB, which increases at a rate of 400 ETB per year. After how many years will his expense exceed his income?

A bamboo plant is initially 50 cm tall. After one year, it grows to 65 cm. Each year, the growth is half the growth of the previous year.

a) What is the maximum height it can reach?

b) Show the height after 5 years.

Given square with side length a. The side of the second square is half of its diagonal. The side of the third square is half of the diagonal of the second square, and so on, as shown in the  figure below. Find the sum of the areas of all these squares.

 

 

1. A person is scheduled to get a raise of Birr 250 every 6 months during his/her first 5 years on the job. If his/her starting salary is Birr 25,250 per year, what will his/her annual salary be at the end of the 3rd year?

2. Bontu begins a saving program in which she will save Birr 1,000 the first year,   and each subsequent year she will save 200 more than she did the previous year. How much will she save during the eighth year ? 

1. A certain item loses one-tenth of its value each year. If the item is worth Birr 28,000 today, how much will it be worth 4 years from now?

2.  A boat is now worth Birr 34,000 and loses 12% of its value each year. What will it    be worth after 5 years?

3. The population of a certain town is increasing at a rate of 2.5% per year. If the population is currently 100,000, what will the population be 10 years from now?

4) A woman deposits Birr 3,500 in a bank account paying an annual interest at a rate of 6%. Show that the amounts she has in the account at the end of each year form a geometric sequence 

Find the amount she has at the end of

a.the first year  

b. the second year        

c. the third year

d. the fourth year   

  

e. the nth year

f. Do the amounts she has at the end of each year form a geometric sequence? 

 

 

1. A job applicant finds that a firm A offers a starting salary of Birr 31,100 with a guaranteed raise of Birr 1,200 per year, whereas firm B offers a higher starting salary of Birr 35,100 but will guarantee a yearly raise of only Birr 900.

a. What would the annual salary be in the 11th  year at firm A?

b. What would the annual salary be in the 11th  year at firm B?

c. Over the first 11 years, how much would be earned at firm A?

d. Over the first 11 years, how much would be earned at firm B?

e.  Compare the amount earned in 11 years in firms A and B

2.  A contest offers a total of 18 prizes. The first prize is worth Birr 10,000, and each   consecutive prize is worth Birr 500 less than the next higher prize. Find the value of   the eighteenth prize and the total value of the prizes.

3. A contest offers 10 prizes with a total value of Birr 13,250. If the difference in value   between consecutive prizes is Birr 250, what is the value of the first prize? 

 

1. Suppose a ball is dropped from a height of h m and always rebounds to r% of the height from which it falls. Show that the total vertical distance that could be covered by the ball is h((r+1)/(1-r))m .Assume that the ball will never stop bouncing.

2. Given an equilateral triangle with side length a, its height is the side of another  equilateral triangle. The height of this triangle is then the side of the third equilateral triangle and so on, as shown in the diagram below. Find the sum of the areas of all these triangles. 

Last modified: Jimaata, 31 Onkoloolessa 2025, 10:01 AM