# Section 12.2 Answers - Mathematics

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1. (u(x,t)=frac{4}{3pi ^{3}} sum_{n=1}^{infty}frac{(-1)^{n+1}}{(2n-1)^{3}}sin 3(2n-1)pi tsin (2n-1)pi x)

2. (u(x,t)=frac{8}{pi ^{3}} sum_{n=1}^{infty}frac{1}{(2n-1)^{3}}cos 3(2n-1)pi tsin (2n-1)pi x)

3. (u(x,t)=-frac{4}{pi ^{3}} sum_{n=1}^{infty}frac{(1+(-1)^{n}2)}{n^{3}}cos nsqrt{7}pi tsin npi x)

4. (u(x,t)=frac{8}{3pi ^{4}} sum_{n=1}^{infty}frac{1}{(2n-1)^{4}}sin 3(2n-1)pi tsin (2n-1)pi x)

5. (u(x,t)=-frac{4}{sqrt{7}pi ^{4}} sum_{n=1}^{infty}frac{(1+(-1)^{n}2)}{n^{4}}sin nsqrt{7}pi tsin npi x)

6. (u(x,t)=frac{324}{pi ^{3}} sum_{n=1}^{infty}frac{(-1)^{n}}{n^{3}}cosfrac{8npi t}{3}sinfrac{npi x}{3})

7. (u(x,t)=frac{96}{pi ^{5}} sum_{n=1}^{infty}frac{1}{(2n-1)^{5}}cos 2(2n-1)pi tsin (2n-1)pi x)

8. (u(x,t)=frac{243}{2pi ^{4}} sum_{n=1}^{infty}frac{(-1)^{n}}{n^{4}}sinfrac{8npi t}{3}sinfrac{npi x}{3})

9. (u(x,t)=frac{48}{pi ^{6}} sum_{n=1}^{infty}frac{1}{(2n-1)^{6}}sin 2(2n-1)pi tsin (2n-1)pi x)

10. (u(x,t)=frac{pi }{2}cossqrt{5}tsin x-frac{16}{pi} sum_{n=1}^{infty}frac{n}{(4n^{2}-1)^{2}}cos 2nsqrt{5}tsin 2nx)

11. (u(x,t)=-frac{240}{pi ^{5}} sum_{n=1}^{infty}frac{1+(-1)^{n}2}{n^{5}}cos npi tsin npi x)

12. (u(x,t)=frac{pi }{2sqrt{5}}sinsqrt{5}tsin x-frac{8}{pisqrt{5}} sum_{n=1}^{infty}frac{1}{(4n^{2}-1)^{2}}sin 2nsqrt{5}tsin 2nx)

13. (u(x,t)=-frac{240}{pi ^{6}} sum_{n=1}^{infty}frac{1+(-1)^{n}2}{n^{6}}sin npi tsin npi x)

14. (u(x,t)=-frac{720}{pi ^{5}} sum_{n=1}^{infty}frac{(-1)^{n}}{n^{5}}cos 2npi tsin npi x)

15. (u(x,t)=-frac{240}{pi ^{6}} sum_{n=1}^{infty}frac{(-1)^{n}}{n^{6}}sin 3npi tsin npi x)

18. (u(x,t)=-frac{128}{pi ^{3}} sum_{n=1}^{infty}frac{(-1)^{n}}{(2n-1)^{3}}cosfrac{3(2n-1)pi t}{4}cos frac{(2n-1)pi x}{4})

19. (u(x,t)=-frac{64}{pi ^{3}} sum_{n=1}^{infty}frac{1}{(2n-1)^{3}}left[(-1)^{n}+frac{3}{(2n-1)pi} ight]cos (2n-1)pi tcosfrac{(2n-1)pi x}{2})

20. (u(x,t)=-frac{512}{3pi ^{4}} sum_{n=1}^{infty}frac{(-1)^{n}}{(2n-1)^{4}}sinfrac{3(2n-1)pi t}{4}cosfrac{(2n-1)pi x}{4})

21. (u(x,t)=-frac{64}{pi ^{4}} sum_{n=1}^{infty}frac{1}{(2n-1)^{4}}left[(-1)^{n}+frac{3}{(2n-1)pi} ight]sin (2n-1)pi tcosfrac{(2n-1)pi x}{2})

22. (u(x,t)=frac{96}{pi ^{3}} sum_{n=1}^{infty}frac{1}{(2n-1)^{3}}left[(-1)^{n}3+frac{4}{(2n-1)pi} ight]cosfrac{(2n-1)sqrt{5}pi t}{2}cosfrac{(2n-1)pi x}{2})

23. (u(x,t)=-96sum_{n=1}^{infty}frac{1}{(2n-1)^{3}}left[(-1)^{n}+frac{2}{(2n-1)pi} ight]cosfrac{(2n-1)sqrt{3} t}{2}cosfrac{(2n-1) x}{2})

24. (u(x,t)=frac{192}{pi ^{4}sqrt{5}}sum_{n=1}^{infty}frac{1}{(2n-1)^{4}}left[(-1)^{n}3+frac{4}{(2n-1)pi} ight]sinfrac{(2n-1)sqrt{5}pi t}{2}cosfrac{(2n-1)pi x}{2})

25. (u(x,t)=-frac{192}{sqrt{3}}sum_{n=1}^{infty}frac{1}{(2n-1)^{4}}left[(-1)^{n}+frac{2}{(2n-1)pi} ight]sinfrac{(2n-1)sqrt{3}t}{2}sinfrac{(2n-1)x}{2})

26. (u(x,t)=-frac{384}{pi ^{4}} sum_{n=1}^{infty}frac{1}{(2n-1)^{4}}left[1+frac{(-1)^{n}4}{(2n-1)pi} ight]cosfrac{3(2n-1)pi t}{2}cosfrac{(2n-1)pi x}{2})

27. (u(x,t)=frac{96}{pi ^{3}} sum_{n=1}^{infty}frac{1}{(2n-1)^{3}}left[(-1)^{n}5+frac{8}{(2n-1)pi} ight]cosfrac{(2n-1)sqrt{7}pi t}{2}cosfrac{(2n-1)pi x}{2})

28. (u(x,t)=-frac{768}{3pi ^{5}} sum_{n=1}^{infty}frac{1}{(2n-1)^{5}}left[1+frac{(-1)^{n}4}{(2n-1)pi} ight]sinfrac{3(2n-1)pi t}{2}cosfrac{(2n-1)pi x}{2})

29. (u(x,t)=frac{192}{pi ^{4}sqrt{7}} sum_{n=1}^{infty}frac{1}{(2n-1)^{4}}left[(-1)^{n}5+frac{8}{(2n-1)pi} ight]sinfrac{(2n-1)sqrt{7}pi t}{2}cosfrac{(2n-1)pi x}{2})

30. (u(x,t)=-frac{768}{pi ^{4}} sum_{n=1}^{infty}frac{1}{(2n-1)^{4}}left[1+frac{(-1)^{n}2}{(2n-1)pi} ight]cosfrac{(2n-1)pi t}{2}cosfrac{(2n-1)pi x}{2})

31. (u(x,t)=-frac{1536}{pi ^{5}} sum_{n=1}^{infty}frac{1}{(2n-1)^{5}}left[1+frac{(-1)^{n}2}{(2n-1)pi} ight]sinfrac{(2n-1)pi t}{2}cosfrac{(2n-1)pi x}{2})

32. (u(x,t)=frac{1}{2}left[C_{Mf}(x+at)+C_{Mf}(x-at) ight]+frac{1}{2a} int_{x-at} ^{x+at} C_{Mg}( au )d au )

35. (u(x,t)=frac{32}{pi} sum_{n=1}^{infty}frac{1}{(2n-1)^{3}}cos 4(2n-1)tsinfrac{(2n-1)x}{2})

36. (u(x,t)=-frac{96}{pi ^{3}} sum_{n=1}^{infty}frac{1}{(2n-1)^{3}}left[ 1+(-1)^{n}frac{4}{(2n-1)pi} ight]cosfrac{3(2n-1)pi t}{2}sinfrac{(2n-1)pi x}{2})

37. (u(x,t)=frac{8}{pi} sum_{n=1}^{infty}frac{1}{(2n-1)^{4}}sin 4(2n-1)tsinfrac{(2n-1)x}{2})

38. (u(x,t)=-frac{64}{pi ^{4}} sum_{n=1}^{infty}frac{1}{(2n-1)^{4}}left[1+(-1)^{n}frac{4}{(2n-1)pi} ight]sinfrac{3(2n-1)pi t}{2}sinfrac{(2n-1)pi x}{2})

39. (u(x,t)=frac{96}{pi ^{3}} sum_{n=1}^{infty}frac{1}{(2n-1)^{3}}left[1+(-1)^{n}frac{2}{(2n-1)pi} ight]cosfrac{3(2n-1)pi t}{2}sinfrac{(2n-1)pi x}{2})

40. (u(x,t)=frac{192}{pi} sum_{n=1}^{infty}frac{(-1)^{n}}{(2n-1)^{4}}cosfrac{(2n-1)sqrt{3}t}{2}sinfrac{(2n-1)x}{2})

41. (u(x,t)=frac{64}{pi ^{4}} sum_{n=1}^{infty} frac{1}{(2n-1)^{4}}left[1+(-1)^{n}frac{2}{(2n-1)pi} ight]sinfrac{3(2n-1)pi t}{2}sinfrac{(2n-1)pi x}{2})

42. (u(x,t)=frac{384}{sqrt{3}pi} sum_{n=1}^{infty}frac{(-1)^{n}}{(2n-1)^{5}}sinfrac{(2n-1)sqrt{3}t}{2}sinfrac{(2n-1)x}{2})

43. (u(x,t)=frac{1536}{pi^{4}} sum_{n=1}^{infty}frac{1}{(2n-1)^{4}}left[(-1)^{n}+frac{3}{(2n-1)pi} ight]cosfrac{(2n-1)sqrt{5}pi t}{2}sinfrac{(2n-1)pi x}{2})

44. (u(x,t)=frac{384}{pi ^{4}} sum_{n=1}^{infty}frac{1}{(2n-1)^{4}}left[(-1)^{n}+frac{4}{(2n-1)pi} ight]cos (2n-1)pi tsinfrac{(2n-1)pi x}{2})

45. (u(x,t)=frac{3072}{sqrt{5}pi ^{5}} sum_{n=1}^{infty}frac{1}{(2n-1)^{5}}left[(-1)^{n}+frac{3}{(2n-1)pi} ight]sinfrac{(2n-1)sqrt{5}pi t}{2}sinfrac{(2n-1)pi x}{2})

46. (u(x,t)=frac{384}{pi ^{5}} sum_{n=1}^{infty}frac{1}{(2n-1)^{5}}left[(-1)^{n}+frac{4}{(2n-1)pi} ight]sin (2n-1)pi tsin frac{(2n-1)pi x}{2})

47. (u(x,t)=frac{1}{2}[S_{Mf}(x+at)+S_{Mf}(x-at)]+frac{1}{2a} int_{x-at} ^{x+at} S_{Mg}( au )d au )

50. (u(x,t)=4-frac{768}{pi^{4}} sum_{n=1}^{infty}frac{1}{(2n-1)^{4}}cosfrac{sqrt{5}(2n-1)pi t}{2}cosfrac{(2n-1)pi x}{2})

51. (u(x,t)=4t-frac{1536}{sqrt{5}pi ^{5}} sum_{n=1}^{infty}frac{1}{(2n-1)^{5}}sinfrac{sqrt{5}(2n-1)pi t}{2}cosfrac{(2n-1)pi x}{2})

52. (u(x,t)=-frac{2pi ^{4}}{5}-48 sum_{n=1}^{infty}frac{1+(-1)^{n}2}{n^{4}}cos 2ntcos nx)

53. (u(x,t)=-frac{7}{5}-frac{144}{pi ^{4}} sum_{n=1}^{infty}frac{(-1)^{n}}{n^{4}}cos nsqrt{7}pi tcos npi x)

54. (u(x,t)=-frac{2pi ^{4}t}{5}-24sum_{n=1}^{infty}frac{1+(-1)^{n}2}{n^{5}}sin 2ntcos nx)

55. (u(x,t)=-frac{7t}{5}-frac{144}{pi ^{5}sqrt{7}}sum_{n=1}^{infty}frac{(-1)^{n}}{n^{5}}sin nsqrt{7}pi tcos npi x)

56. (u(x,t)=frac{pi ^{4}}{30}-3sum_{n=1}^{infty}frac{1}{n^{4}}cos 8ntcos 2nx)

57. (u(x,t)=frac{3}{5}-frac{48}{pi ^{4}}sum_{n=1}^{infty}frac{2+(-1)^{n}}{n^{4}}cos npi tcos npi x)

58. (u(x,t)=frac{pi ^{4}t}{30}-frac{3}{8}sum_{n=1}^{infty}frac{1}{n^{5}}sin 8ntcos 2nx)

59. (u(x,t)=frac{3t}{5}-frac{48}{pi ^{5}}sum_{n=1}^{infty}frac{2+(-1)^{n}}{n^{5}}sin npi tcos npi x)

60. (u(x,t)=frac{1}{2}left[ C_{f}(x+at)+C_{f}(x-at) ight] +frac{1}{2a} int _{x-at}^{x+at} C_{g}( au )d au )

63. c. (u(x,t)=frac{f(x+at)+f(x-at)}{2}+frac{1}{2}int_{x-at}^{x+at} g(u)du)

64. (u(x,t)=x(1+4at)

65. (u(x,t)=x^{2}+a^{2}t^{2}+t)

66. (u(x,t)=sin (x+at))

67. (u(x,t)=x^{3}+6tx^{2}+3a^{2}t^{2}x+2a^{2}t^{3})

68. (u(x,t)=xsin xcos at+atcos xsin at+frac{sin xsin at}{a})

## Higher Secondary Plus One/Plus Two Mathematics Previous Questions

i am very happy to get the question bank of maths. but when will the remaining parts publishing. exam is approaching.

Yes. I am expecting to complete it within 2 weeks. Question bank is a model. You should prepare the NCERT Text Book also to score maximum mark.

Thank you sir. Your contributions deserves lots of appreciation. pls attach answer keys also-it is not possible to ask teachers for answer in this last minute

Sir please publish the remaining parts as fast you can.The published items are very useful.(expecting answer key also)

Sir ,could u please tell me what preparations should I take for ma maths exam..and what all texts should I refer. .

Sir, could you please tell me what preparations should I take for ma maths exam. ..and what books should I refer. ..

Pls publish the remaining ones so fast

Kerala plus2 exam time table pulish cheyyunnathennanu.March ennu kandirunnu any change in date ?pls publish the date Sir

To know more about Higher Secondary Examination 2016 and Time Table, copy the following link, paste it in the address bar and click the link:

Can I get the solutions of question bank

Please publish the remaining part.exam is approching

Dear student, you should try to find the answers. If you find any difficulty, please ask your teacher. You know, to learn Mathematics is to do mathematics. Otherwise our skill will not developed.

But if i would like to check my answers how will it be possible without an answer key

Sir..pls give me the chapter wise mark disribution for maths (science)

Plz post all question bank of chapters

Will questions come from micelenius

Some times. But you should study miscellaneous examples.

The questions of first and second chapters are not opening. Please fix it.

Sir, I want all answes of maths previous question papers.Iam requesting you to publish the answers of previous question papers answers of X1

This comment has been removed by the author.

1. Consider the statement
 
n n P n  7  3
is divisible by 4.
a) Show that
P򖆑
is true.
b) Verify, by the method of Mathematical induction that
Pn
is true for all
n N

how to find volume of triangle with circular edges

Hi, question has some problem. we cannot find the volume of a triangle. Solid has only volume.

This comment has been removed by the author.

Hi student, don’t be nervous for the examination. Be happy and confident. Then you can achieve A+ in all subjects. You have got 70 marks in the first year. Is it Theory Mark or Theory + CE mark. If it is theory mark (out of 80), then it is easy for you to get A+ for Mathematics. In the II year, you score 74 marks (for theory paper out of 80). A systematic approach will help you to do this. You have to study all chapters. Nothing will be avoided. Chapter wise examples, exercises and miscellaneous examples are necessary. Previous years questions will help you to understand the pattern of examination.
Chapter wise scores will be:
Ch 1: 5, Ch 2: 4, Ch 3: 6, Ch 4: 5, Ch 5: 6, Ch 6: 5, Ch 7: 10, Ch 8: 6, Ch 9: 6, Ch 10: 8, Ch11: 8, Ch 12: 6, Ch 13: 5.
All the best.

## Math Riddles

A collection of Math Riddles for fun and pleasure! Tease your brain with these riddles, then click to show or hide the answer. (Note: You may need to enable JavaScript on your browser for the answers to show properly.)

1. Why should you never mention the number 288 in front of anyone? Because it is too gross (2 x 144 - two gross).
2. Which weighs more? A pound of iron or a pound of feathers? Both weigh the same.
3. How is the moon like a dollar? They both have 4 quarters.
4. What is alive and has only 1 foot? A leg.
5. When do giraffes have 8 feet? When there are two of them.
6. How many eggs can you put in an empty basket? Only one, after that the basket is not empty.
7. What coin doubles in value when half is deducted? A half dollar.
8. What is the difference between a new penny and an old quarter? 24 cents.
9. If you can buy eight eggs for 26 cents, how many can you buy for a cent and a quarter? 8.
10. Where can you buy a ruler that is 3 feet long? At a yard sale.

1. If there were 9 cats on a bridge and one jumped over the edge, how many would be left? None - they are copycats.
2. If you take three apples from five apples, how many do you have? You have three apples.
3. What has 4 legs and only 1 foot? A bed.
4. How many times can you subtract 6 from 30? Once after that it is no longer 30 (Don't try this in a test!)
5. If one nickel is worth five cents, how much is half of one half of a nickel worth? .0125
6. How many 9's between 1 and 100? 20.
7. Which is more valuable - one pound of $10 gold coins or half a pound of$20 gold coins? It is the same. One pound is twice of half pound.
8. It happens once in a minute, twice in a week, and once in a year. What is it? The letter 'e'.
9. How can half of 12 be 7? Cut XII into two halves horizontally. You get VII on the top half.
10. When things go wrong, what can you always count on? Your fingers.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

### Product description for parents

Mental Arithmetic provides rich and varied practice to develop pupils&rsquo essential maths skills and prepare them for all aspects of the Key Stage 2 national tests. It may also be used as preparation for the 11+, and with older students for consolidation and recovery.

Tailored to meet the requirements of the National Curriculum for primary mathematics, each book contains 36 one-page tests designed to build confidence and fluency and keep skills sharp. Each test is presented in a unique three-part format comprising:

• Part A: questions where use of language is kept to a minimum
• Part B: questions using number vocabulary
• Part C: questions focusing on one- and two-step word problems.

Structured according to ability rather than age, the series allows children to work at their own pace, building confidence and fluency. Two Entry Tests are available in the Mental Arithmetic Teacher&rsquos Guide and on the Schofield & Sims website, enabling teachers, parents and tutors to select the appropriate book for each child. All the books can be used flexibly for individual, paired, group or whole-class maths practice, as well as for homework and one-to-one intervention.

Mental Arithmetic 2 Answers contains answers to all the questions included in Mental Arithmetic 2, as well as guidance on how to use the series and mark results. Answers are clearly laid out in the format of a correctly completed pupil book making marking quick and easy, while a card cover ensures durability.

Dimensions: 21 x 0.4 x 29.7 cm

• Mental Arithmetic Book 2 Certificate
• Mental Arithmetic Entry Test A
• Mental Arithmetic Entry Test B
• Mental Arithmetic Entry Test Group record sheet
• Mental Arithmetic Entry Test Marking Keys
• Mental Arithmetic Maths Facts: Area
• Mental Arithmetic Maths Facts: Fractions Chart
• Mental Arithmetic Maths Facts: Fractions Equivalencies
• Mental Arithmetic Maths Facts: Imperial Units of Measurement
• Mental Arithmetic Maths Facts: Months of the Year
• Mental Arithmetic Maths Facts: Multiplication Square
• Mental Arithmetic Maths Facts: Number Line 0 to 100
• Mental Arithmetic Maths Facts: Perimeter
• Mental Arithmetic Maths Facts: Time
• Mental Arithmetic Maths Facts: Two and Three-dimensional Shapes
• Mental Arithmetic Maths Facts: Units of Measurement and Money
• Mental Arithmetic National Curriculum Chart
• Mental Arithmetic Selecting the Appropriate Pupil Book

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Column integrity.
User-defined integrity.

9. Column integrity refers to:

Columns always having values.
Columns always containing positive numbers.
Columns always containing values consistent with the defined data format.
Columns always containing text data less than 255 characters.

10. The explanation below defines which constraint type:

A primary key must be unique, and no part of the primary key can be null.

Entity integrity.
Referential integrity.
Column integrity.
User-defined integrity.

Test: Quiz: Basic Mapping: The Transformation Process

1. In a physical data model, an entity becomes a _____________.

Attribute
Table
Constraint
Column

2. In a physical data model, a relationship is represented as a:

Column
Primary Key
Unique Identifier
Foreign Key

3. The transformation from an ER diagram to a physical design involves changing terminology. Relationships in the ER diagram become __________ , and primary unique identifiers become ____________.

Foreign keys, primary keys
Primary keys, foreign keys

4. Attributes become columns in a database table. True or False?

True
False

5. Why would this table name NOT work in an Oracle database?
2007_EMPLOYEES

Numbers cannot be incorporated into table names
Underscores “_” are not allowed in table names
None of the above

6. In an Oracle database, why would the following table name not be allowed ‘EMPLOYEE JOBS’?

The database does not understand all capital letters
EMPLOYEE is a reserved word
JOBS is a reserved word
You cannot have spaces between words in a table name

7. The transformation from an ER diagram to a physical design involves changing terminology. Entities in the ER diagram become __________ , and attributes become ____________.

Columns, Tables
Tables, Columns
Foreign Keys, Columns
Tables, Foreign Keys

Test: Quiz: Relationship Mapping

1. One-to-One relationships are transformed into Foreign Keys in the tables created at either end of that relationship? True or False?

True
False

2. One-to-Many Optional to Mandatory becomes a _______________ on the Master table.

Mandatory Foreign Key
Nothing (There are no new columns created on the Master table)
Optional Foreign Key
Primary Key

3. What do you create when you transform a many to many relationship from your ER diagram into a physical design?

Foreign key constraints
Intersection entity
Intersection table
Primary key constraints

4. Two entities A and B have an optional (A) to Mandatory (B) One-to-One relationship. When they are transformed, the Foreign Key(s) is placed on:

The table BS
The Table AS
Nowhere, One-to-One are not transformed
Both tables As and Bs get a new column and a Foreign Key.

5. Relationships on an ERD can only be transformed into UIDs in the physical model? True or False?

True
False

6. A barrred Relationship will result in a Foreign Key column that also is part of:

The Table Name
The Column Name
The Check Constraint
The Primary Key

Test: Quiz: Subtype Mapping

1. When translating an arc relationship to a physical design, you must turn the arc relationships into foreign keys. What additional step must you take with the created foreign keys to ensure the exclusivity principle of arc relationships? (Assume that you are implementing an Exclusive Design) (Choose Two)

Make all relationships mandatory
Make all relationships optional
Create an additional check constraint to verify that one foreign key is populated and the others are not

All the above

2. Which of the following are reasons you should consider when using a Subtype Implementation? (Choose Two)

When the common access paths for the subtypes are similar.
When the common access paths for the subtypes are different.
Most of the relationships are at the subtype level

3. The “Arc Implementation” is a synonym for what type of implementation?

Supertype Implementation
Subtype Implementation
Supertype and Subtype Implementation

4. When mapping supertypes, relationships at the supertype level transform as usual. Relationships at subtype level are implemented as foreign keys, but the foreign key columns all become optional. True or False?

### The headline of the passage: Flying tortoises

In this question type, IELTS candidates are provided with a list of headings, usually identified with lower-case Roman numerals (i, ii, iii, etc,). A heading will refer to the main idea of the paragraph or section of the text. Candidates must find out the equivalent heading to the correct paragraphs or sections, which are marked with alphabets A, B, C and so forth. Candidates need to write the appropriate Roman numerals in the boxes on their answer sheets. There will always be two or three more headings than there are paragraphs or sections. So, some of the headings will not be used. It is also likely that some paragraphs or sections may not be included in the task. Generally, the first paragraph is an example paragraph that will be done for the candidates for their understanding of the task.

TIPS: Skimming is the best reading technique. You need not understand every word here. Just try to gather the gist of the sentences. That’s all. Read quickly and don’t stop until you finish each sentence.

Question 1: Paragraph A

In paragraph A, the answer is found in line 7 where the writer says, “…. . .. the islands were colonized by one or two tortoises from mainland South America…”. And then continues, “……. .. . giving rise to at least 14 different subspecies…” These lines suggest that tortoises were populating the islands.

So, the answer is: v Tortoises populate the islands

Question 2: Paragraph B

In paragraph B, line 3-4 says, “….. saw this exploitation grow exponentially.” The previous lines say that tortoises were taken on ships by pirates as food supply. Then line 3-4 talks about the increase of the exploitation.

So, the answer is: iii Developments to the disadvantages of tortoise populations

Question 3: Paragraph C

For Paragraph C, the answer lies in line 2, where the author mentions, “….. In 1989, work began on a tortoise breeding centre……” suggesting that some people had started a conservation project to protect the tortoises.

So, the answer is: viii The start of the conservation project

Question 4: Paragraph D

As for paragraph D, the answer is found in lines 4-5. Here, the writer states, “…. .. if people wait too long after that point, the tortoises eventually become too large to transport.” This means that if the timing is wrong, there is a big price to pay or they have to face a big problem.

So, the answer is: i The importance of getting the timing right

Question 5: Paragraph E

The answer for paragraph E lies in lines 6-7. Here, the author says, “….to work out more ambitious reintroduction. The aim was to use a helicopter to move 300 of the breeding centre’s tortoises to various locations close to Sierra Negra.” It means that the plan is a very big one which is yet to occur.

So, the answer is: iv Planning a bigger idea

Question 6: Paragraph F

In Paragraph F, the writer mentions the procedures which were taken to complete the transportation of 33 tortoises to relocate them to different parts of Galapagos Island. All the procedures indicate that the operation was carefully prepared.

So, the answer is: vi Carrying out a carefully prepared operation

Question 7: Paragraph G

The answer for paragraph G is in line 3, where the author mentions, “Eventually, one tiny tortoise came across a fully grown giant …..”.

So, the answer is: ii Young meets old

Questions 8-13 (Completing sentences with ONE WORD ONLY):

In this type of question, candidates are asked to write only one word to complete the sentence. For this type of question, first, skim the passage to find the keywords in the paragraph concerned with the answer, and then scan to find the exact word.

Question 8: 17th Century: small numbers taken onto ships used by 8 _____________.

Keywords for this answer: 17th Century, small numbers, ships used by

For this question, we look at the paragraph where 17 th century is mentioned. Start skimming from the beginning of the text. You’ll find the mention of 17 th century in paragraph B. So, we can be sure that the answer will be in this paragraph. In line 2-3 the writer says, “… From 17 th century onwards, pirates took a few on board for food, … … .”. Here, a few = small numbers. So, we can understand that those ships were used by pirates, who took small numbers of tortoises on their ships (on board) for food supply.

Question 9 and 10: 1790s: very large numbers taken onto whaling ships kept for 9 _______ and also used to produce 10 _______.

Keywords for these answers: 1790s, very large numbers, whaling ships, kept for, to produce

For these questions, we have to look at paragraph 2 line 3. Here we find 1790s, which is our first clue. Then, when we read further, we find in lines 5 and 6, “…. The tortoises were taken on board these ships tq act as food supplies during long ocean passages. Sometimes, their bodies were processed into high-grade oil.”

*Kept for = act as

*To produce = processed

So the answer for Q 9 is: food

The answer for Q 10 is : oil

Question 11: Hunted by 11 _________ on the islands

In paragraph 2, the word ‘hunted’ is directly found in line 10—-“They hunted the tortoises……”. As ‘they’ is a pronoun, we have to read the previous line to learn what noun ‘they’ is referring to. “This historical exploitation was then exacerbated when settlers came to the islands.” Here, ‘they’ is referring to settlers.

Questions 12 and 13: Habitat destruction: for the establishment of agriculture and by various 12 ______ not native to the islands, which also fed on baby tortoises and tortoise’s 13 ______

Keywords for these answers: Habitat destruction, establishment of agriculture, not native, also fed on, baby tortoises and tortoise’s

Continue reading from the previous lines. The word ‘habitat’ is found in line 9, ‘establishment of agriculture’ in line 10. Then, in line 10, the author says, “They also introduced alien species- ranging from …..”. Here the word ‘alien’ is a match with ‘not native’.

So the answer for Q 12 is: species

After that, in line 11, we find, “- that either prey on the eggs and young tortoises… .. ..”. Here, prey on means fed on, young tortoises means baby tortoises.

So the answer for Q 13 is: eggs

3. What command can be used to show information about the structure of a table?

ALTER
SELECT
DESCRIBE
INSERT

4. Examine the follolowing SELECT statement.

SELECT *
FROM employees
This statement will retrieve all the rows in the employees table. True or False?

True
False

5. What command can be added to a select statement to return a subset of the data?

WHERE
WHEN
ALL
EVERYONE

Test: Quiz: Basic Table Modifications

1. The f_customers table contains the following data:

ID Name Address City State Zip
1 Cole Bee 123 Main Street Orlando FL 32838
2 Zoe Twee 1009 Oliver Avenue Boston MA 02116
3 Sandra Lee 22 Main Street Tampa FL 32444

If you run the following statement,

DELETE FROM F_CUSTOMERS
WHERE STATE=’FL’

how many rows will be left in the table?

2. The SQL statement ALTER TABLE EMPLOYEES DROP COLUMN SALARY will delete all of the rows in the employees table. True or False?

True
False

3. What will the following statement do to the employee table?

ALTER TABLE employees ADD (gender VARCHAR2(1))

Add a new row to the EMPLOYEES table
Rename a column in the EMPLOYEES table
Change the datatype of the GENDER column
Add a new column called GENDER to the EMPLOYEES table

If my printer could literally print out money, would it have that big an effect on the world?

You can fit four bills on an 8.5”x11” sheet of paper:

If your printer can manage one page (front and back) of full-color high-quality printing per minute, that’s $200 million dollars a year. This is enough to make you very rich, but not enough to put any kind of dent in the world economy. Since there are 7.8 billion$100 bills in circulation, and the lifetime of a $100 bill is about 90 months, that means there are about a billion produced each year. Your extra two million bills a year would barely be enough to notice. What would happen if you exploded a nuclear bomb in the eye of a hurricane? Would the storm cell be immediately vaporized? —Rupert Bainbridge (and hundreds of others) This question gets submitted a lot. It turns out the National Oceanic and Atmospheric Administration—the agency which runs the National Hurricane Center—gets it a lot, too. In fact, they’re asked about it so often that they’ve published a response. I recommend you read the whole thing, but I think the last sentence of the first paragraph says it all: “Needless to say, this is not a good idea.” It makes me happy that an arm of the US government has, in some official capacity, issued an opinion on the subject of firing nuclear missiles into hurricanes. If everyone put little turbine generators on the downspouts of their houses and businesses, how much power would we generate? Would we ever generate enough power to offset the cost of the generators? A house in a very rainy place, like the Alaska panhandle, might receive close to four meters of rain per year. Water turbines can be pretty efficient. If the house has a footprint of 1,500 square feet and gutters five meters off the ground, it would generate an average of less than a watt of power from rainfall, and the maximum electricity savings would be: The rainiest hour on record occurred in 1947 in Holt, Missouri, where about 30 centimeters of rain fell in 42 minutes. For those 42 minutes, our hypothetical house could generate up to 800 watts of electricity, which might be enough to power everything inside it. For the rest of the year, it wouldn’t come close. If the generator rig cost$100, residents of the rainiest place in the US—Ketchikan, Alaska—could potentially offset the cost in under a century.

Using only pronounceable letter combinations, how long would names have to be to give each star in the universe a unique one word name?

There are about 300,000,000,000,000,000,000,000 stars in the universe. If you make a word pronounceable by alternating vowels and consonants (there are better ways to make pronounceable words, but this will do for an approximation), then every pair of letters you add lets you name 105 times as many stars (21 consonants times 5 vowels). 105 possibilities per two characters is about the same information density that numbers have, which suggests the name will end up being about as long as the total number of stars written out:

I like doing math that involves measuring the lengths of numbers written out on the page—which is really just a way of loosely estimating log

x. It works, but it feels so wrong.

I bike to class sometimes. It's annoying biking in the wintertime, because it's so cold. How fast would I have to bike for my skin to warm up the way a spacecraft heats up during reentry?

Reentering spacecraft heat up because they’re compressing the air in front of them (not, as is commonly believed, because of air friction).

According to this calculator, to increase the temperature of the air layer in front of your body by twenty degrees Celsius (enough to go from freezing to room temperature), you would need to be biking at 200 m/s.

The fastest human-powered vehicles at sea levels are recumbent bicycles enclosed in streamlined aerodynamic shells. These vehicles have an upper speed limit near 40 m/s. This is the speed at which the human can just barely produce enough thrust to balance the drag force from the air.

Since drag increases with the square of the speed, this limit would be pretty hard to push any further. Biking at 200 m/s would require at least 25 times the power output needed to go 40 m/s.

At those speeds, you don’t really have to worry about the heating from the air—a quick back-of-the-envelope calculation suggests that if your body were doing that much work, your core temperature would reach fatal levels in a matter of seconds.

How much physical space does the internet take up?

There are a lot of ways to estimate the amount of information stored on the internet, but we can put an interesting upper bound on the number just by looking at how much storage space we (as a species) have purchased.

The storage industry produces in the neighborhood of 650 million hard drives per year. If most of them are 3.5” drives, then that’s eight liters (two gallons) of hard drive per second.

This means the last few years of hard drive production—which, thanks to increasing size, represent a large chunk of global storage capacity—would just about fill an oil tanker. So, by that measure, the internet is smaller than an oil tanker.

What if you strapped C4 to a boomerang? Could this be an effective weapon, or would it be as stupid as it sounds?

Aerodynamics aside, I’m curious what tactical advantage you’re expecting to gain by having the high explosive fly back at you if it misses the target.

## WAEC Past Questions for Mathematics

Click on the year you want to start your revision.

Do you have any other past question(s) other than the ones listed here? If yes, don’t hesitate to share them with others by sending it to [email protected].

You have to keep trying more than one exam to increase your success in the forthcoming WAEC Exam.

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