Apps. and Interpretation for IBDP Maths Ebook 1 | Page 76

Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 21
1. The lengths of the sides of a 10-sided polygon form a geometric sequence. The three
shortest sides are 1 m, 1.1 m and 1.21 m respectively.
(a) Write down the exact length of the fourth shortest side of the polygon.
[1]
(b) Find the length of the longest side of the polygon.
[2]
(c) Find the perimeter of the polygon.
[3]
2. In the theatre of a town hall, there are 12 rows in total. Each row consists of 30 seats. The
price of a seat in the first row is $100. The prices of a seat in the following rows continue
to decrease in the same ratio, such that the price of a seat in the second row is $90, and
the price of a seat in the third row is $81, and so on. Give the answers correct to the
nearest dollar in this question.
(a) Find the price of a seat in the sixth row.
[2]
(b) Find the price of a seat in the n th row.
[2]
(c) Find the total income of the theatre if all tickets are sold.
[3]
3. In a souvenir market in Khabarovsk located in East Russia, a set of 20 wooden dolls is
displayed in a row and arranged in descending doll sizes. The volume of the largest doll
is
3
24000 cm . The volume of the second largest doll is 95% of the previous doll, and this
pattern continues.
(a)
(b)
Find the total volume of all wooden dolls when they are displayed in a single row.
[3]
Find the number of wooden dolls with volume less than
3
10000 cm .
4. A car is travelling in a journey. On 1st February the car travels 120 km. The distance
travelled is expected to decrease by 10% each day.
[3]
(a)
(b)
(c)
Find the distance travelled on the fifth day.
[2]
Find the difference between the distance travelled on the fifth day and the one on
the sixth day.
[2]
The car needs to refuel for every 500 km travelled. Find the date when the car
refuels for the second time of this journey.
[3]
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