Questions and Answers of Financial Accounting Information For Decisions

a. Expand (3 + x)4.b. Use your answer to part a to express (3 + √5)4 in the form a + b√5.
a. Write down, in ascending powers of x, the first 4 terms in the expansion of (1 – 3x)10.b. Find the coefficient of x3 in the expansions of (1 - 4x) (1 - 3x)10.
The first two terms in an arithmetic progression are -2 and 5. The last term in the progression is the only number in the progression that is greater than 200. Find the sum of all the terms in the
Three consecutive terms of a geometric progression are x, x + 6 and x + 9. Find the value of x.
The second term of a geometric progression is – 96 and the fifth term is 40 ½.a. Find the common ratio and the first term.b. Find the sum to infinity.
The first two terms of a progression are 5x and x2 respectively.a. For the case where the progression is arithmetic with a common difference of 24, find the two possible values of x and the
a. i. Use the Binomial Theorem to expand (a + b)4, giving each term in its simplest form.ii. Hence find the term independent of x in the expansion of (2x + 1/5x)4.b. The coefficient of x3 in the
a. Expand (1 + x)5.b. Use your answer to part a to expressi. (1 + √3)5 in the form a + b√3,ii. (1 - √3)5 in the form c + d√3.c. Use your answers to part b to simplify (1 + √3)5 + (1 -
a. Find, in ascending powers of x, the first 3 terms in the expansion of (1 + 2x)7.b. Find the coefficient of x2 in the expansions of (1 + 2x)7 (1 – 3x + 5x2).
The first term of an arithmetic progression is 8 and the last term is 34. The sum of the first sic terms is 58. Find the number of terms in this progression.
In the geometric sequence ¼, ½, 1, 2, 4, … which is the first term to exceed 500000?
The first three terms of a geometric progression are 175, k and 63. Given that all the terms in the progression are positive, finda. The value of kb. The sum to infinity.
a. Expand (2 – x2)4.b. Find the coefficient of x6 in the expansion of (1 + 3x2) (2 – x2)4.
The first term of a geometric progression is 35 and the second term is – 14.a. Find the fourth term.b. Find the sum to infinity.
a. Find, in ascending powers of x, the first 4 terms in the expansion of (1 + x)7.b. Hence find the coefficient of y3 in the expansions of (1 + y – y2)7.
Find the sum of all the integers between 100 and 400 that are multiples of 6.
In the geometric sequence 256, 128, 64, 32, … which is the first term that is less than 0.001?
The second term of a geometric progression is 18 and the fourth term is 1.62. Given that the common ratio is positive, finda. The common ratio and the first termb. The sum to infinity.
The first three terms of a geometric progression are 2k + 6, k + 12 and k respectively. All the terms in the progression are positive.a. Find value of k.b. Find the sum to infinity.
Find the coefficient of x in the expansion (c – 3/x)5.
Find the coefficient of x in the binomial expansion of (x – 3/x)7.
The first term of an arithmetic progression is 7 and the eleventh term is 32. The sum of all the terms in the progression is 2790. Find the number of terms in the progression.
Find the sum of the first eight terms of each of these geometric series.a. 4 + 8 + 16 + 32 + …b. 729 + 243 + 81 + 27 + …c. 2 – 6 + 18 – 54 + …d. – 5000 + 1000 – 200 + 40 - … …
The first three terms of a geometric progression are k + 15, k and k – 12 respectively, finda. The value of kb. The sum to infinity.
An arithmetic progression has first term a and common difference d. Give that the sum of the first 100 terms is 25 times the sum of the first 20 terms.a. Find d in term of a.b. Write down an
Find the term independent of x in the expansion of (x2 + 1/2x)3.
Find the term independent of x in the binomial expansion of (x + 1/2x2)9.
Rafiu buys a boat for $15,500. He pays for this boat by making monthly payments that are in arithmetic progression. The first that he makes is $140 and the debt is fully repaid after 31 payments.
The first four terms of a geometric progression are 1, 3, 9 and 27. Find the smallest number of terms that will give a sum greater than 2,000,000.
The fourth term of a geometric progression is 48 and the sum to infinity is three times the first term. Find the first term.
The 15th term of an arithmetic progression is 3 and the sum of the first 8 terms is 194.a. Fid the first term of the progression and the common difference.b. Given that the nth term of the
a. Find the first three terms, in ascending powers of y, in the expansion of (2 + y)5.b. By replacing y with 3x – 4x2, find the coefficient of x2 in the expansion of (2 + 3x – 4x2)5.
When (1 + ax)n is expanded the coefficients of x2 and x3 are equal. Find a in terms of n.
The eight term of an arithmetic progression is – 10 and the sum of the first twenty terms is – 350.a. Find the first term and the common difference.b. given that the nth term of this progression
A ball is thrown vertically upwards from the ground. The ball rises to a height of 10m and then falls and bounces. After each bounce it rises to 4/5 of the height of the previous bounce.a. Write down
A geometric progression has first term a and common ratio r. The sum of the first three terms is 62 and the sum to infinity is 62.5. Find the value of a and the value of r.
The second term of a geometric progression is – 576 and the fifth term is 243. Finda. The common ratiob. The first termc. The sum to infinity.
The coefficient of x3 in the expansion of (3 + ax)5 is 12 times the coefficient of x2 in the expansion of (1 + ax/2)4. Find the value of a.
The sum of the first n terms, Sn, of a particular arithmetic progression is given by Sn = 4n2 + 2n. Find the first term and the common difference.
The sum of the first n terms, Sn, of a particular arithmetic progression is given by Sn = - 3n2 – 2n. Find the first term and the common difference.
The third term of a geometric progression is nine times the first term. The sum of the first four terms is k times the first term. Find the possible values of k.
The first term of a geometric progression is 1 and the second term is 2 sin x where – π/2 < x < π/2. Find the set of values of x for which this progression convergent.
a. The sixth term of an arithmetic progression is 35 and the sum of the first ten terms is 335. Find the eighth term.b. A geometric progression has first term 8 and common ratio r. A second geometric
a. Given that (x2 + 4/x)3 – (x2 – 4/x)3 = ax3 + b/x3, find the value of a and the value of b.b. Hence, without using a calculator, find the exact value of (2 + 4/√2)3 – (2 – 4/√2)3.
The sum of the first n terms, Sn, of a particular arithmetic progression is given by Sn = n/12(4n + 5). Find an expression for the nth term.
John competes in a 10 km race. He completed the first kilometer in 4 minutes. He reduces his speed in such a way that each kilometer takes him 1.05 times the time taken for the preceding kilometer.
A ball is dropped from a height of 12 m. After each bounce it rises to ¾ of the height of the previous bounce. Find the total vertical distance that the ball travels.
a. The 10th term of an arithmetic progression is 4 and the sum of the first 7 terms is – 28. Find the first term and the common difference.b. The first term of a geometric progression is 40 and the
Given that y = x + 1/x, expressa. x3 + a/x3 in terms of yb. x5 + a/x5 in terms of y.
A circle is divided into twelve sectors. The sizes of the angles of the sectors are in arithmetic progression. The angle of the largest sector is 6.5 times the angle of the smallest sector. Find the
A geometric progression has first term a, common ratio r and sum to n terms, Sn.Show that 2n 2n S.
Starting with an equilateral triangle, a Koch snowflake pattern can be constructed using the following steps:Step 1: Divide each line segment into three equal segments.Step 2: Draw an equilateral
a. A geometric progression has first term a, common ratio r and sum to infinity S. A second geometric progression has first term 3a, common ratio 2r and sum to infinity 4S. Find the value of r.b. An
An arithmetic sequence has first term a and common difference d. The sum of the first 25 terms is 15 sums of the first 4 terms.a. Find a in terms of d.b. Find the 55th term in terms of a.
1, 1, 3, 1/3, 9, 1/9, 27, 1/27, 81, 1/81, …Show that the sum of the first 2n terms of this sequence is ½(3n – 31-n + 2).
A circle of radius 1 unit is drawn touching the three edges of an equilateral triangle.Three smaller circle are then drawn at each corner to touch the original circle and two edges of the
The eight term in an arithmetic progression is three times the third term. Show that the sum of the first eight terms is four times the sum of the first four terms.
Sn = 6 + 66 + 666 + 6666 + 66666 + …Find the sum of the first n terms of this sequence.
The first term of an arithmetic progression is cos2 x and the second term is 1.a. Write down an expression, in terms of cos x, for the seventh term of this progression.b. Show that the sum of the
The sum of the digits in the number 56 is 11. (5 + 6 = 11)a. Show that the sum of the digits of the integers from 15 to 18 is 30.b. Find the sum of the digits of the integers from 1 to 100.
Rafiu has a collection of 10 CDs.4 of the CDs are classical, 3 are jazz and 3 are rock.He selects 5 of the CDs from his collections.Find the number of ways he can make his selection ifa. There are no
Without using a calculator, find the value of each of the following.Use the x! key on your calculator to check your answers.a. 7!b. 4!/2!c. 7!/3!d. 8!/5!e. 4!/2!2!f. 6!/3!2!g. 6!/(3!)2h. 5!/3! ×
Find the number of different arrangementsa. 4 people sitting in a row on benchb. 7 different books on a shelf.
Without using a calculator, find the value of each of the following.Use the nPr key on you calculator to check your answers.a. 8P5b. 6P4c. 11P8d. 7P7
Without using a calculator find the value of each of the following, and then use the nCr key on your calculator to check your answers.a. 5C1b. 6C3c. 4C4d.e.f. 4)
a. How many even numbers less than 500 can be formed using the digits 1, 2, 3, 4 and 5?Each digit may be used only one in any number.b. A committee of 8 people is to be chosen from 7 men and 5
Rewrite each of the following using factorial notation.a. 2 × 1b. 6 × 5 × 4 × 3 × 2 × 1c. 5 × 4 × 3d. 17 × 16 × 15 × 14e. 10 × 9 × 8/3 × 2 × 1f. 12 × 11 × 10 × 9 × 8/4 × 3 ×
Find the number of different arrangements of letters in each of the following words.a. Tigerb. Olympicsc. Paintbrush
Find the number of different ways that 4 books, chosen from 6 books be arranged on a shelf.
Show that 8C3 = 8C5.
a. An art gallery displays 10 paintings in a row.Of these paintings, 5 are by Picasso, 4 by Monet and 1 by turner.i. Find the number of different ways the paintings can be displayed if there are no
Rewrite each of the following using factorial notation.a. n(n – 1) (n – 2) (n – 3)b. n(n – 1) (n – 2) (n – 3) (n – 4) (n – 5)c. n(n – 1)(n – 2)/5 × 4 × 3 × 2 × 1d. n(n- 1) (n
a. Find the number of different four-digit numbers that can be formed using the digits 3, 5, 7 and 8 without repetition.b. How many of these four-digit numbers arei. Evenii. Greater than 8000?
How many different five-digit numbers can be formed from the digits 1 ,2, 3, 4, 5, 6, 7, 8, 9 if no digit can be repeated?
How many different ways are there of selecting?a. 3 photographs from 10 photographsb. 5 books from 7 booksc. A team of 11 footballers from 14 footballers?
a. Arrangements containing 5 different letters from the word AMPLITUDE are to be made.Findi. The number of 5-letter arrangements if there are no restrictions,ii. The number of 5-letter arrangements
A shelf holds 7 different books.4 of the books are cookery books and 3 of the books are history books.a. Find the number of ways the books can be arranged if there are no restrictions.b. Find the
There are 8 competitors in a long jump competition.In how many different ways can the first, second and third prizes be awarded?
How many different combinations of 3 letters can be chosen from the letters P, Q, R, S, T?
Six-digit numbers are to be formed using the digits 3, 4, 5, 6, 7 and 9.Each digit may only be used once in any number.a. Find how many different six-digit numbers can be formed.Find how many of
Five-digit numbers are to be formed using the digits 2, 3, 4, 5 and 6.Each digit may only be used once in any number.a. Find how many different five-digit numbers can be formed.How many of these
Find how many different four-digit numbers greater than 4000 that can be formed using the digits 1, 2, 3, 4, 5, 6 and 7 if no digit can be used more than once.
The diagram shows 2 different boxes, A and B.8 different toys are to be placed in the boxes.Find the number of ways in which the 8 toys can be placed in the boxes so that 5 toys are in box. A and 3
a. A shelf contains 8 different travel books, of which 5 are about Europe and 3 are about Africa.i. Find the number of different ways the books can be arranged if there are no restrictions.ii. Find
Three girls and two boys are to be seated in a row.Find the number of different ways that his can be done ifa. The girls and boys sit alternatelyb. A girl sits at each end of the rowc. The girls sit
Find how many even number between 5000 and 6000 can be formed from the digits 2, 4, 5, 7, 8, if no digit can be used more than once.
4 pencils and 3 pens are to be selected from a collection of 8 pencils and 5 pens.Find the number of different selections that can be made.
A 4-digit number is formed by using four of the seven digits 1, 3, 4, 5, 7, 8 and 9.No digit can be used more than once in any number.Find how many different 4-digit numbers can be formed ifa. There
a. Find the number of different arrangements of the letters in the word ORANGE.Find the number of these arrangements thatb. Begin with the letter Oc. Have the letter O at one end and the letter E at
A four-digit number is formed using four of the eight digits 1, 2, 3, 4, 5, 6, 7 and 8. No digit can be used more than once.Find how many different four-digit numbers can be formed ifa. There are no
Four of the letters of the word PAINTBRUSH are selected at random.Find the number of different combinations ifa. There is no restriction on the letters selectedb. The letter T must be selected.
a. Jean has nine different flags.i. Find the number of different ways in which Jean can choose three flags from her nine flags.ii. Jean has five flagpoles in a row. She puts one of her nine flags on
a. Find the number of different six-digit numbers which can be made using the digits 0, 1, 2, 3, 4 and 5 without repetition. Assume that a number cannot begin with 0.b. How many of the six-digit
Numbers are formed using the digits 3, 5, 6, 8 and 9.No digit can be used more than once.Find how many differenta. Three-digit numbers can be formedb. Numbers using three or more digits can be formed.
A test consists of 30 questions.Each answer is either correct or incorrect.Find the number of different ways in which it is possible to answera. Exactly 10 questions correctly.b. Exactly 25 questions
a. A lock can be opened using only the number 4351. State whether this is a permutation or a combination of digits, giving a reason for your answer.b. There are twenty numbered balls in a bag. Two of
6 girls and 2 boys are to be seated in a row.Find the number of ways that this can be done if the 2 boys must have exactly 4 girls seated between them.
Find how many different even four-digit numbers greater than 2000 can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8 if no digit may be used more than once.
An athletics club has 10 long distance runners, 8 sprinters and 5 jumpers.A team of 3 long distance runners, 5 sprinters and 2 jumpers is to be selected.Find the number of ways in which the team can
a. 6 books are to be chosen at random from 8 different books.i. Find the number of different selections of 6 books that could be made.A clock is to be displayed on a shelf with S of the 8 different

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