Personal response: state whether you enjoyed it and give one or two brief reasons (e.g. challenging, satisfying, improved problem-solving).
Yes. I enjoyed solving the problems because they were challenging and helped me think creatively.
Personal response: indicate difficulty level and give a brief reason or example.
It was moderately hard; some parts were straightforward while others required deeper thought.
Sample concise answer: give 2–3 reasons such as logical thinking, practicality, beauty of patterns.
Yes. Mathematics trains logical thinking, problem-solving and is useful in many real-life applications.
The classmates laughed at Ramanujan’s question.
Ramanujan got S. L. Loney's Trigonometry book from a college library.
Bhaskara proved that zero divided by zero is infinity.
Ramanujan did his mathematical problems on loose sheets of paper or on a slate and jot the results down in notebooks.
Concise factual answer: Ramanujan wrote to G. H. Hardy enclosing a letter filled with his theorems and results (this letter introduced Hardy to Ramanujan's work).
He sent a long letter containing many of his mathematical results and theorems (a collection of original formulae).
Concise answer: The British mathematician G. H. Hardy recognized Ramanujan's exceptional talent.
G. H. Hardy
Ramanujan neglected History, English and Physiology.
The University of Madras granted him a fellowship of R75 a month.
Ramanujan asked a silly question in the class. So the children laughed at him.
The teacher saw Ramanujan's unusual aptitude for mathematics: he solved difficult problems, produced novel results, and showed deep insight. This exceptional talent prompted praise and compliments from his teacher.
Because Ramanujan showed extraordinary mathematical ability—solving problems quickly and presenting original results far beyond his peers.
After studying the trigonometry book, Ramanujan went beyond the exercises: he rediscovered results, extended them, and began formulating his own theorems. This reading stimulated his independent work and led to the many notebooks of identities and formulae he later produced.
He mastered the material and began to produce many original results and formulae on his own, developing deep interest and creativity in mathematics.
Ramanujan became so absorbed in mathematics that he neglected other school subjects. As a result he did not qualify in some formal examinations, which disappointed his father because it reduced his chances of a stable job and social approval.
His father was disappointed when Ramanujan neglected other subjects and failed to pass formal examinations, affecting his prospects for regular employment.
When Ramanujan lacked proper paper, he did not stop working—he recorded results on scraps, backs of documents, and whatever was at hand. Friends and teachers who appreciated his talent sometimes supplied paper and materials so he could continue his work.
He used any available scrap paper and relied on help from friends/teachers who provided paper; he wrote his results wherever he could until better supplies were obtained.
Employers required formal certificates and passed examinations; Ramanujan had not completed conventional courses and so his applications were turned down even though his mathematical talent was exceptional.
Because he lacked formal academic qualifications and had failed some examinations, employers dismissed him despite his mathematical brilliance.
During and after World War I Ramanujan's health worsened. With continuing illness and reduced strength, he returned to India in 1919 for treatment and rest; he died soon after in 1920.
He was sent back because his health deteriorated (illness, tuberculosis) and he needed to return home to recover.
Use 'although' to show contrast: she felt cold despite wearing a winter coat.
although
- A. moreover
- B. although
- C. meanwhile
- D. therefore
- E. because
- F. as long as
- G. thus
- H. above all
- I. for instance
- J. except
Although (B) expresses contrast: she felt cold despite wearing a winter coat.
B
'Moreover' adds information: in addition to having great chefs, their service is also excellent.
moreover
- A. moreover
- B. although
- C. meanwhile
- D. therefore
- E. because
- F. as long as
- G. thus
- H. above all
- I. for instance
- J. except
Moreover (A) is used to add information: besides having excellent chefs, their service is excellent.
A
'Because' explains the reason: I'm not going because I didn't get an invitation.
because
- A. moreover
- B. although
- C. meanwhile
- D. therefore
- E. because
- F. as long as
- G. thus
- H. above all
- I. for instance
- J. except
Because (E) gives the reason for not going: I didn't get an invitation.
E
'Meanwhile' indicates simultaneous actions: while you set the table, I'll start making dinner.
meanwhile
- A. moreover
- B. although
- C. meanwhile
- D. therefore
- E. because
- F. as long as
- G. thus
- H. above all
- I. for instance
- J. except
Meanwhile (C) fits because it shows two actions happening at the same time.
C
'For instance' introduces examples of the instruments the speaker can play.
for instance
- A. moreover
- B. although
- C. meanwhile
- D. therefore
- E. because
- F. as long as
- G. thus
- H. above all
- I. for instance
- J. except
For instance (I) introduces examples: the flute, the guitar and the piano.
I
'Therefore' indicates a consequence: because the store was out of chips, they would need to make a different type of cookie.
therefore
- A. moreover
- B. although
- C. meanwhile
- D. therefore
- E. because
- F. as long as
- G. thus
- H. above all
- I. for instance
- J. except
Therefore (D) expresses the result/consequence: being out of chips leads to needing a different cookie.
D
'Except' fits: the stores are open daily except Sundays.
except
- A. moreover
- B. although
- C. meanwhile
- D. therefore
- E. because
- F. as long as
- G. thus
- H. above all
- I. for instance
- J. except
Except (J) excludes Sundays from the days the stores are open.
J
'As long as' expresses the time-condition: I will stay for the duration that you need me.
as long as
- A. moreover
- B. although
- C. meanwhile
- D. therefore
- E. because
- F. as long as
- G. thus
- H. above all
- I. for instance
- J. except
Use 'as long as' to show duration/condition: "I'll stay as long as you need me."
F
Use 'therefore' to show a logical result: "This detergent is highly concentrated and therefore you will need to dilute it."
D
- A. moreover
- B. although
- C. meanwhile
- D. therefore
- E. because
- F. as long as
- G. thus
- H. above all
- I. for instance
- J. except
'Therefore' indicates the result: "This detergent is highly concentrated and therefore you will need to dilute it." (Option D).
D
Use 'above all': "It was the thing he prized above all."
H
- A. moreover
- B. although
- C. meanwhile
- D. therefore
- E. because
- F. as long as
- G. thus
- H. above all
- I. for instance
- J. except
'Above all' fits the sentence: "It was the thing he prized above all." (Option H).
H
Title: From zero to Infinity
Author: Anonymous (Biography of Ramanujan)
Characters: Ramanujan, Classmates, Teachers and Ramanujan’s Father
Theme: Inborn intelligence with dilegence leads to excellence
Srinivasa Ramanujan was bom in Erode in Tamil Nadu on December 22, 1887. His father was a petty clerk in a cloth shop. From his early childhood, Ramanujan was evidently a prodigy. A question that he had asked as a boy had taken mathematician several centuries to answer. Through out his life in his native Kumbakonam he was always ahead of his mathematics teachers.
Senior students went to his dingy house to get their difficulties in Mathematics solved. At the age of 13, Ramanujan got Loney’s Trignometry from a college library. He mastered the book and began his own research. Ramanujan secured a first class in Mathematics in the Matriculation examination. He was awarded the Subramanyan Scholarship. His father was disappointed when he failed twice in his first year arts examination.
Ramanujan was always scribbling numbers and his father thought that he had gone mad. He began to look for a job. He needed money for food and papers to do his calculations. He started using even scraps of paper lying on the streets. Luckily the Director of Madras Port Trust, Francis Spring was impressed by his note books.
He gave him a clerical job on a monthly salary of ₹25. Later some teachers and educationist interested in Mathematics helped him get a research fellowship. The University of Madras granted him a fellowship of ₹75 even thQugh he had no qualifying degree.
“Genius does what it must, and talent does what it can”
(OR)
Srinivasa Ramanujan was bom on December 22, 1887, in Erode in Tamil Nadu. His father was a petty clerk in a cloth shop. From early childhood, he was a prodigy. Even Mathematicians had taken several centuries to answer his question. He was always ahead of his mathematics teachers.
Senior students went to his house to get their difficulties in Mathematics solved. When he was 13, he got Loney’s Trignometry from a college library. He began his own research, having mastered the book. He secured a first class in Mathematics in the matriculation examination. He was awarded the Sub-Ramayan Scholarship. But he failed twice in his first year arts examination. His father was upset.
As he was always scribbling numbers his father thought that he had gone mad. Ramanujan needed money for food and papers. He started using scraps of paper lying on the streets.
Luckily his note books impressed the Director of Madras Port Trust, Francis Spring. He gave him a clerical job on a salary of ₹25 a month. Later he got a research fellowship. The University of Madras granted him a fellowship of ₹75, though he had no qualifying degree. “There is no great genius without some touch of madness.
In 1913 Ramanujan sent a letter and notebooks containing his theorems to mathematicians in England. Hardy recognized the originality and invited Ramanujan to Cambridge. They worked together on number theory and related areas from about 1914; Hardy mentored him, helped publish his papers and arranged support for Ramanujan during his stay in England.
Ramanujan wrote to G. H. Hardy with samples of his results; Hardy recognized his genius, invited him to Cambridge (1914), collaborated with him, published his work and supported him financially and academically.
- a. will not recognize
- b. will not being recognized
- c. will not be recognized
Passive of future: 'We will not be recognized by her.' (Option c).
c
- a. wasn't invited
- b. wasn't being invited
- c. wasn't inviting
Passive simple past: 'I wasn't invited but I went anyway.' (Option a).
a
- a. broke
- b. had broken
- c. was broken
Passive past: 'The table was broken up for firewood.' (Option c is the closest correct passive form).
c
- a. has won
- b. has been won
- c. had been won
Present perfect passive: 'The first prize has been won by her.' (Option b).
b
- a. is repairing
- b. is repaired
- c. is being repaired
Present continuous passive: 'The car is being repaired by a friend of mine.' (Option c).
c
- a. be begun
- b. begin
- c. is beginning
Imperative to passive: 'Let the work be begun tomorrow.' (Option a).
a
- a. is speaking
- b. is spoken
- c. is being spoken
Simple present passive: 'English is spoken in New Zealand.' (Option b).
b
- a. had shocked
- b. had been shocked
- c. was shocked
Simple past passive: 'I was shocked by his attitude.' (Option c).
c
- a. has already been sent
- b. had already been sent
- c. was already sent
Past perfect passive: 'The parcel had already been sent by her.' (Option b).
b
- a. am worrying by
- b. am worried by
- c. have worried by
Present passive/adjective: 'I am worried by her silence.' (Option b).
b
Match each word to the synonym in the middle column and the antonym in the right column:
1. distribute → circulate (synonym), collect (antonym)
2. infinite → boundless, measurable
3. significant → important, trivial
4. delight → joy, sorrow
5. unkempt → messy, clean
6. initiate → commence, conclude
7. conjecture → guess, fact
1: distribute — circulate — collect; 2: infinite — boundless — measurable; 3: significant — important — trivial; 4: delight — joy — sorrow; 5: unkempt — messy — clean; 6: initiate — commence — conclude; 7: conjecture — guess — fact
Convert each active sentence into the appropriate passive form, keeping the tense and meaning.
1. 'I will never forget this experience.' → 'This experience will never be forgotten by me.' (future passive)
2. 'Mother made a cake yesterday.' → 'A cake was made by mother yesterday.' (simple past passive)
3. 'Have you finished the report?' → 'Has the report been finished by you?' (present perfect passive, interrogative)
4. 'The tiger was chasing the deer.' → 'The deer was being chased by the tiger.' (past continuous → past continuous passive)
5. 'She has written a novel.' → 'A novel has been written by her.' (present perfect passive)
| # | Correct match |
|---|---|
| 1 | This experience will never be forgotten by me. |
| 2 | A cake was made by mother yesterday. |
| 3 | Has the report been finished by you? |
| 4 | The deer was being chased by the tiger. |
| 5 | A novel has been written by her. |
Provide a brief first-person or third-person retelling (4–6 sentences) capturing the main events, characters, and the moral. The sample above can be adapted after listening to the actual audio.
Sample narration: Two brilliant men met and admired each other's talents. One was more practical and the other more theoretical. They discussed a problem, each offering different but complementary approaches, and together they reached a better understanding. The anecdote highlights respect for different kinds of genius and the value of collaboration.
Active: 'Stanley will inform you later.' → Passive: move object 'you' to subject position and use future passive: 'You will be informed by Stanley later.'
You will be informed by Stanley later.
Active (simple present): 'People speak Portuguese in Brazil.' → Passive: 'Portuguese is spoken in Brazil.' (agent 'people' omitted as general subject.)
Portuguese is spoken in Brazil.
Active (simple past): 'My grandfather built this house in 1943.' → Passive: 'This house was built by my grandfather in 1943.'
This house was built by my grandfather in 1943.
Negative imperative passive: 'Do not hurt the animals.' → 'Let the animals not be hurt.' (Alternatively, 'Do not let the animals be hurt.' is also acceptable.)
Let the animals not be hurt.
Modal negative passive: 'You must not drop litter in the streets.' → 'Litter must not be dropped in the streets.' (agent 'you' omitted as general instruction.)
Litter must not be dropped in the streets.
Imperative active → passive: 'Carry it home.' → 'Let it be carried home.' (standard passive form for positive imperatives.)
Let it be carried home.
Present continuous active → passive: 'They are decorating the wall.' → 'The wall is being decorated by them.'
The wall is being decorated by them.
Present perfect active → passive: 'He has already mended the TV set.' → 'The TV set has already been mended by him.'
The TV set has already been mended by him.
Divide class into groups of five. Assign roles: moderator (teacher), leader, timekeeper, note-taker and presenter. Suggested points to discuss (each group may choose some):
- Mathematics is used in daily activities: shopping (bills, discounts), cooking (measuring, proportions), time management, travel (distance, speed, fare).
- Mathematics in technology: mobile phones, computers, internet, banking (ATMs).
- Mathematics in professions: engineering, medicine (dosages), architecture, finance.
- Problem solving and logical thinking developed by mathematics.
- Importance of accuracy, estimation and data interpretation in decision making.
Conclude with each group presenting main ideas; moderator summarizes and highlights real-life examples and moral: mathematics makes life efficient and informed.
Guidelines and sample points for the group discussion.
This is a project task. Follow these steps:
1. Choose five famous personalities (scientists, mathematicians, inventors, artists).
2. Research reliable sources (books, reputable websites) and note key facts: birth/death, education, main contributions, awards.
3. Write a concise biography (6–8 lines) for each person, include a picture and label it, and note one major achievement/invention.
4. Compile into a scrapbook with a title page, index, and references. Decorate and caption pictures.
Examples to consider: Albert Einstein (theory of relativity), Marie Curie (radioactivity), Srinivasa Ramanujan (number theory), Thomas Edison (electric light/phonograph), Leonardo da Vinci (art & inventions).
Suggested plan:
- Collect biographies of at least five figures (examples: Albert Einstein, Marie Curie, Srinivasa Ramanujan, Thomas Edison, Leonardo da Vinci).
- For each person include: a short 6–8 line biography, main achievements/inventions, dates (birth–death), one or two pictures, and one interesting anecdote or quote.
- Arrange pages with a title page, index, and bibliography (sources).
- Add captions for pictures and highlight one key contribution per person.
Shepherd-Barron conceived the idea after realizing people needed cash when banks were closed (for example on Sundays). He combined that need with his experience of vending machines and developed the concept of an automated cash-dispensing machine.
He was inspired when his wife could not withdraw money on a Sunday and by vending-machine technology; he wanted a machine to dispense cash outside bank hours.
The world's first operational cash machine (ATM) was installed by Barclays Bank on 27 June 1967 at its Enfield branch in North London.
27 June 1967, at a Barclays Bank branch in Enfield, London.
Actor Reg Vamey, a celebrity resident of Enfield was the first person to withdraw cash from the ATM.
During trials customers had difficulty remembering a six-digit Personal Identification Number. To make the system user-friendly and reduce errors, the number of digits was shortened to four.
Because users found six digits hard to remember; four digits were easier to recall and practical for customers.
While ATMs physically dispense cash, the security and electronic authorization of ATM transactions rely on modern cryptography, which is built on number theory. Ramanujan's deep contributions to number theory and modular forms contributed to the mathematical foundations that later influenced cryptographic methods used in secure banking systems.
Ramanujan's work in number theory (modular forms and related results) influenced modern number-theoretic developments used in cryptography, which secures ATM transactions.
When I was twelve I entered a local painting competition on a whim. I spent an evening and the following weekend working on a landscape inspired by my grandmother’s garden. On the day of judging I felt nervous because everyone else’s work looked professional. To my surprise the judge praised the composition and use of colour, and announced my painting as one of the winners. The prize was a sketching set and an opportunity to display my painting in the community hall. That recognition gave me confidence to pursue art further; it taught me that quiet passion and steady effort can lead to unexpected rewards.
Sample 100–120 word paragraph describing a memorable incident.
My favourite personality is Marie Curie because of her courage, hard work and pioneering contributions to science. Born in Poland, she overcame financial difficulties and gender prejudice to study physics and chemistry. Her research on radioactivity earned her two Nobel Prizes, and she established laboratories to further scientific study and medical applications. I admire her integrity and dedication to using science for the benefit of humanity, including training young scientists and aiding hospitals during wartime. Her life shows that determination and curiosity can break barriers and leave a lasting legacy that inspires generations.
Sample 100–120 word paragraph about a favourite personality.