[Exercise- page 185]
E.9.1. The geometrical figures below are made up of lines of equal length.
a) Make the fourth diagram and find the number of lines.
b) Which mathematical formula or rule is satisfied by the number of lines, explain with logic.
c) Find out the number of lines required to make the 1st 100 diagrams
Solution:
E.9.2. Anowara Begum saves Tk 500 in the first month from her salary and in the following month she saves Tk 100 more than the previous month.
a) Express, with explanation, the account of savings with a mathematical formula or rule.
b) How much does she save on the 30th month?
c) What are her total savings in the first 3 years?
Solution:
E.9.3. Aurobindu Chakma bought 3 yearly savings certificates with 3 monthly interests, for 5 lac taka from his pension money. The rate of interest is 8% per annum.
a) Find a Mathematical formula or rule, with explanation, to find the interest.
b) How much interest will he get in the first installment i.e. that is after the first 3 months, use your formula to find that.
c) How much interest will he get at the end of 3 years?
Solution:
E.9.4. You are told to donate 100 kg rice. But you cannot donate the whole amount at a time. On the 1st day you can donate half of 100 kg, i.e. 50 kg; on 2nd day can donate half of 50 kg, i.e., 25 kg. In this way, every day you must donate half the remaining rice. How many days will you take to donate the entire amount of rice in this way?
[N.B. you cannot donate less than 1 kg in any way]
Solution:
E.9.5. The following trapezium shaped floor has to be covered by 12 inch square tiles. The number of tiles in each row will be 1 less than the previous row.
a. How many tiles in total will be required to cover the floor?
b. If the cost of tiles is Tk 75 per square feet, how much will be spent for the tiles?
Solution:
E.9.6. A mason/bricklayer got some bricks from a heap of bricks and arranged them in 15 steps. He made two rows in the lowest step and kept 30 bricks on each row.
Then for each following step above, he kept 2 less bricks from each row of the step below.
a) How many bricks will be there at the topmost step?
b) Express the process of brick arrangements using a mathematical formula or rule, with logical explanations.
c) How many bricks has he arranged?
Solution:
E.9.7. Make square tiles of edge 2 cm by cutting paper. Then arrange the tiles as the following diagrams using gum.
a) Make the next diagram
b) Fill up the following table by counting the tiles of each diagram.
c) Express the number of diagrams and the tiles with a common formula.
d) Draw a line graph using graph paper, taking the diagram number along the x-axis and number of tiles along the y-axis.
Solution:
E.9.8. Mondira sowed 2 sunflower saplings in the courtyard of her home on a Friday. During the sowing, the heights of two plants were 10 cm and 15 cm respectively. She measures the heights of the plants at a fixed time every week. Mondira noticed that the height of the 10 cm high sapling increases 2 cm per week and the 15 cm high sapling increases 1.5 cm every week.
a) Make a list of the increments of heights for two months, of the two saplings from the day they were sown.
b) Express the growth of the two saplings by a Mathematical formula with the definitions of the variables.
c) Draw a line graph taking the weeks along the x-axis and the heights of the two saplings along the y-axis for the data of the first 3 months.
d) Find the point of intersection of the two graphs from the line graph. Explain what is meant by the point of intersection with reference to the two plants.
e) Solving the Mathematical formula obtained in part (b), justify the accuracy of the point of intersection obtained from the graph in part (d).
Solution:
E.9.9. The heights of 10 students of class six are as follows (in centimeter):
a) If the average height of the students is 120 cm, find the value of x.
b) Find the median and the mode of the heights of the students.
Solution:
E.9.10. . The picture is a water tank, whose base is square. Length of the base is 3 meter and the height is x meter.
a) Express the volume V of the tank with a Mathematical formula or rule.
b) Fill up the following table for different values of x:
c) Draw a line graph using the table obtained in part (b)
d) What height of the tank will give its volume 15
Solution:
E.9.11. . Kamal thought of a three digit number. He gave Shihab few hints to find the number. The hints are:
> The number is less than half of 1212.
> It lies between 502 and 606
> It is not possible to draw a triangle with sides of lengths equal to the three digits of the number.
> The digit in the units place of the number multiplied by the digit in the units place gives a number whose sum of digits will be equal to the digit in the units place.
> The tenth and the units digits are relatively prime.
> Like Shihab, you also solve the case of the secret number of Kamal.
Solution:
E.9.12. a) In the picture below, how many oranges are there in the lowest layer?
b) What is the total number of oranges in the picture?
c) Have you seen any other fruits or vegetables arranged like this in shops?
Find few more examples like this and draw pictures.
Solution:
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