HOLIDAY HOMEWORK ANC/SRT/CSG IB DP MAY 2017 BATCHHolidays Homework (Summer 2015)Subject: Mathematics Form: S IB HLNote:1. All the students must revise the syllabus completed in this term.1. All the students must solve the questions of the worksheet given below.1. The solutions of this worksheet (to be done in thin exercise booklets by the students) will be collected by the respective teachers by the end of the first week of next term. 1. This worksheet will be checked by the respective teachers and considered for the assessment of autumn 2014 Report Card. Worksheet:1.

Solve for : 2.

Solve for : 3.

Solve for : 4.

Solve for and : and 5.

Solve for : 6.

Solve for : 7.

An endangered species of animal is placed into the game reserve. 150 such animals have been introduced into the reserve. The number of animals alive after being placed in this reserve is predicted by the exponential growth model.(a) The number of animals alive after (i) 1 year(ii) 2 years(iii) 5 years(b) How long will it take the population to double?(c) How long is it before there are 400 of this species in the reserve?8.

The height of a tree is given by is the height of the tree measured in metres and is the age of the tree (in years) since it was planted.(a) Determine the height of the tree when planted.(b) By how much will the tree have grown in the first year?(c) How tall will the tree be after 10 years?(d) How tall will it be after 100 years?(e) How long will it take for the tree to grow to the height of (i) 10 m?(ii) 20 m? (iii) 30 m?(f) What is the maximum height that the tree can reach? Explain your answer.9.

The sum of the first eight terms of the sequence is given by .Find and.10.

If and form an arithmetic sequence, find the first term and the common difference.11. Find the number of terms in the sequence 12.

Find and given that are the first four terms of an arithmetic sequence.13.

A family decided to save some money in an account that pays annual interest calculated at the end of each year. They put into the account at the beginning of each year. All interest is added to the account and no withdrawals are made. How much money will they have in the account on the day after they made their tenth payment?14. A geometric sequence has the same first term as an arithmetic sequence. The third term of the geometric sequence is the same as the tenth term of the arithmetic sequence with both being 48. The tenth term of the arithmetic sequence is four times the second term of the geometric sequence. Find the common difference of the arithmetic sequence and the common ratio of the geometric sequence.15. Find a number which when added to each of 2, 6 and 13 gives three numbers in geometric sequence.16.

If, find the value of.17.

Find the total number of terms in the 1st brackets of the series where the bracket contains terms. Hence find the sum of the numbers in the first brackets.18. The product of first three terms of a G.P. is 1000. If we add 6 to its second term and 7 to its third term, the resulting three terms form an A.P. Find the terms of the G.P.19. A bouncing tennis ball rebounds each time to a height equal to half the height of the previous bounce. If it is dropped from a height of 16 metres, find the total distance it travelled when it hits the ground the tenth time.20. The sum of an infinite G.P. is 16 and the sum of the squares of its terms is. Find the common ratio and the fourth term of the progression.21. If , prove that

, 22.

(a) In an arithmetic sequence the first term is 8 and the common difference is. If the sum of the first terms is equal to the sum of next terms, find.

(b) If are the terms of a geometric sequence with a common ratio, show that 23.

The sum , of the first terms of a geometric sequence , whose term is , is given by (a) Find an expression for.(b) Find the first term and the common ratio of the sequence.(c) Consider the sum of infinity of the sequence(i) Determine the value of such that sum to infinity exists.(ii) Find the sum to infinity when it exists.24. Find the sum of multiples of 3 between 100 and 500.25. Each time a ball bounces, it reaches 95% of the height reached on the previous bounce. Initially, it is dropped from a height of 4 metres.(a) What height does the ball reach after its fourth bounce?(b) How many times does the ball bounce before it no longer reaches a height of 1 metre?(c) What is the total distance travelled by the ball?26. In how many ways can Susan get dressed if she has 3 skirts, 5 blouses, 6 pairs of socks and 3 pair of shoes to choose from?27. Three Italian, two Chemistry and four Physics books are to be arranged on a shelf. How many ways can this be done(a) If there are no restrictions?(b) If the Chemistry books must remain together?(c) If the books must stay together by subject?28.

Find if.29.

Find if.30. In how many ways can a jury of 12 be selected from 9 men and 6 women so that there are at least 6 men and 4 women in the jury?31.

If, find.32.

If, find.33. How many arrangements of the letters of the word COMMISSION are possible?34. Prove that 35. Find the 10th term in the expansion of.36.

Find the coefficient of in the expansion of.37.

Find the term independent of in the expansion of.38.

Find the term independent of in the expansion of.39. .40.

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