Mathematics Made Simple

Mathematics Made Simple

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Tired of confusing textbooks? Here, we believe advanced math doesn't have to be complicated. Maths is made to be Simple!

Join us to build a rock-solid foundation, understand the 'why' behind the equations, and transform your confidence in every course. Here is where u will find facts about the world discoveries and records broken....
Life is incomplete without science, so.. explore, record and relate your experience in this trip of science

23/02/2026

Hello, my oga...
This is something I've been working on for a while, as a repository for A-Level students studying Maths...
I'll like you to give it a Like and Subscribe if it suits your fancy, and share with your TL, you never know who needs clarity with Maths...

www.youtube.com/

Thank you!!!

16/10/2025

Full Video Out Now on Youtube!
Watch Here: https://youtu.be/EtGqWEJ15mY
Learn the power representation of the complex variable and so much more
Don't miss a single lesson! We post new, in-depth tutorials every week to help you ace your exams and truly understand advanced mathematics.
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HOW TO DRAW ARGAND DIAGRAM | MODULE TWO 15/10/2025

Full Video Out Now on Youtube!
Watch Here: https://youtu.be/EtGqWEJ15mY
Don't miss a single lesson! We post new, in-depth tutorials every week to help you ace your exams and truly understand advanced mathematics.

Follow us on Tiktok and Subscribe to our Youtube Channel with the link in our Bio.

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HOW TO DRAW ARGAND DIAGRAM | MODULE TWO *LEARN HOW TO DRAW ARGAND DIAGRAMS FOR COMPLEX NUMBERS*In this video, we break down the process of constructing the argand diagram for complex numbers. You'l...

18/09/2024

Over the past years, we have worked behind the scenes to improve the quality of scientific study in schools across Nigeria. Now, we bring to you FREE CLASSES IN OCTOBER, to set you on your way towards excelling in your O-Level Examinations come 2025.
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08/06/2020

EL NIÑO AND LA NIÑA

El Niño and La Niña are complex weather patterns resulting from variations in ocean temperatures in the Equatorial Pacific.
El Niño and La Niña are opposite phases of what is known as the El Niño-Southern Oscillation (ENSO) cycle. The ENSO cycle is a scientific term that describes the fluctuations in temperature between the ocean and atmosphere in the east-central Equatorial Pacific (approximately between the International Date Line and 120 degrees West).

La Niña is sometimes referred to as the cold phase of ENSO and El Niño as the warm phase of ENSO. These deviations from normal surface temperatures can have large-scale impacts not only on ocean processes, but also on global weather and climate.

El Niño and La Niña episodes typically last nine to 12 months, but some prolonged events may last for years. While their frequency can be quite irregular, El Niño and La Niña events occur on average every two to seven years. Typically, El Niño occurs more frequently than La Niña.

El Niño

El Niño means The Little Boy, or Christ Child in Spanish. El Niño was originally recognized by fishermen off the coast of South America in the 1600s, with the appearance of unusually warm water in the Pacific Ocean. The name was chosen based on the time of year (around December) during which these warm waters events tended to occur. During normal weather patterns around the Equator, trade winds carry warm water from the tropical areas of the Pacific Ocean. Moving west, the winds distribute warm water from the Eastern Pacific into the cooler areas of the ocean.

During El Niño, those winds weaken, and the east-west travel of warm water stops. The winds reverse and carry warm water back east, which makes the warm part of the Pacific Ocean even warmer. Sea surface temperatures can increase by 1–3° Fahrenheit for months, or even years.

La Niña
La Niña means The Little Girl in Spanish. La Niña is also sometimes called El Viejo, anti-El Niño, or simply "a cold event."
La Niña episodes represent periods of below-average sea surface temperatures across the east-central Equatorial Pacific. Global climate La Niña impacts tend to be opposite those of El Niño impacts. In the tropics, ocean temperature variations in La Niña also tend to be opposite those of El Niño. The trade winds strengthen, and warm water and rainstorms are pushed to the far western equatorial Pacific over Indonesia. This results in cooler surface water in the equatorial Pacific Ocean, dry conditions in Pacific coastal South America, and much wetter conditions in northern Australia and southeast Asia. La Niña usually impacts U.S. weather by bringing cooler weather to the northwest and warmer weather to the southeast, though just like El Niño, not every La Niña event affects U.S. weather identically.

El Niño and La Niña affect not only ocean temperatures, but also how much it rains on land. Depending on which cycle occurs (and when), this can mean either droughts or flooding.
Typically, El Niño and its warm waters are associated with drought, while La Niña is linked to increased flooding. But, because the global weather system is very complex, this isn’t always the case. For example, in 2015, El Niño caused both flooding and droughts in different places.

Currently, according to the National Oceanic and Atmospheric Administration (NOAA), it’s unclear how the El Niño cycle may change as the world’s temperature increases. “There is evidence for all sorts of outcomes,” they wrote on their ENSO Blog in 2018. “Whether it is more El Niños, stronger overall events, or even a decrease in the number of El Niños or La Niñas. This uncertainty is because of the complicated give-and-take between the atmosphere and ocean with a lot of different tuning k***s that each get adjusted by climate change.”

References:
https://oceanservice.noaa.gov/facts/ninonina.html
https://www.concernusa.org/story/el-nino-and-la-nina/
https://www.americangeosciences.org/critical-issues/faq/what-are-el-nino-and-la-nina

Images from https://www.google.com/search?q=el+nino+and+la+nina&client=ms-android-transsion-infinix-rev1&hl=en&prmd=ivn&sxsrf=ALeKk01RYvF1U_8UYwbQ0o0yzIdP_jxgGA:1591598064696&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiRwZXqzPHpAhWPsBQKHYm5A40Q_AUIFSgB&biw=360&bih=672&dpr=2

08/06/2020

V603 Aquilae (or Nova Aquilae 1918) was a bright nova first observed (from Earth) in the constellation Aquila in 1918. It is a binary system, comprising a white dwarf and donor low-mass star in close orbit to the point of being only semidetached. The white dwarf sucks matter off its companion, which has filled its Roche lobe, onto its accretion disk and surface until the excess material is blown off in a thermonuclear event. This material then forms an expanding shell, which eventually thins out and disappears.

First seen by Zygmunt Laskowski, a medical professor and amateur astronomer, and then confirmed on the night of 8 June 1918 by the UK amateur astronomer Grace Cook at Stowmarket when on the watch for meteors at 9:11 G.M.T., The nova is estimated at between 784 to 839 light years distance from Earth. Nova Aquilae reached a peak magnitude of −0.5; it was the brightest nova recorded in the era of the telescope. It was brighter than all stars but Sirius and Canopus. Tycho's and Kepler's supernovae were brighter, but both occurred before the invention of the telescope.

Other independent discoveries on 8th June were made by Mr. W. F. Denning, at Bristol, and Mr. David Packer, at Birmingham, at 10.00 G.M.T.; Mr. C. L. Brook, at Meltham, at 10.15 G.M.T.; Mr. W. H. Steavenson, at West Norwood, at 10.30 G.M.T.; Mr. H. Thomson, at Newcastle, at 10.44 G. M. T., and Mr. Felix de Roy, at Thornton Heath, at 10.45 G. M. T. It was also noticed at 9.40 G. M. T. by Mr. Witchell, of the Royal Observatory, Greenwich, but not identified as a Nova. On the following day it was also detected independently in Scotland by Dr. Anderson, the discoverer of Nova Persei and Nova Aurigae.

References:
https://en.m.wikipedia.org/wiki/V603_Aquilae
https://www.nature.com/articles/101285a0

Images from https://www.google.com/search?q=Nova+Aquila+1918&client=ms-android-transsion-infinix-rev1&hl=en&prmd=inmv&sxsrf=ALeKk03DNcFDhr4Mll49iPEMAXgGB7vCMQ:1591601024091&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjS1Kjt1_HpAhUZDGMBHbPcBqIQ_AUIFSgB&biw=360&bih=672&dpr=2

07/06/2020

Alan Turing , in full Alan Mathison Turing, (born June 23, 1912, London, England—died June 7, 1954, Wilmslow, Cheshire), was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical computer science, providing a formalisation of the concepts of algorithm and computation with the Turing machine, which can be considered a model of a general-purpose computer. Turing was a highly influential computer scientist and cryptanalyst who developed the Turing machine, one of the most important theoretical models of a computer. In this regard he is considered to be the father of artificial intelligence and of theoretical computer science.

During World War II Turing worked at the UK's code-breaking headquarters at Bletchley Park. Here he played a pivotal role in breaking coded German messages through the Enigma machine, many of which helped the Allies win several crucial battles. One estimate puts the number of lives saved by Turing's work at as many as 14 million.

After the war Turing worked at the National Physical Laboratory, where he designed the Automatic Computing Engine. The Automatic Computing Engine was one of the first designs for a stored-program computer. In 1948, Turing joined Max Newman's Computing Machine Laboratory, at the Victoria University of Manchester, where he helped develop the Manchester computers and became interested in mathematical biology. He wrote a paper on the chemical basis of morphogenesis and predicted oscillating chemical reactions such as the Belousov–Zhabotinsky reaction, first observed in the 1960s.

Turing was never fully recognized during his lifetime due to his homosexuality, which was then a crime in the UK. He was prosecuted in 1952 and underwent forced castration as a punishment. He died in 1954 of cyanide poisoning, at the time ruled as su***de but possibly accidental. In 2009 the British government formally apologized to Turing, and Queen Elizabeth II granted him a pardon in 2013. The Alan Turing law is named after him, which granted pardons to men convicted of homosexuality when it was a crime.

References:

https://www.onthisday.com/people/alan-turing
https://en.m.wikipedia.org/wiki/Alan_Turing
https://www.britannica.com/biography/Alan-Turing

06/06/2020

THE YEAR WITHOUT A SUMMER

The eruption of Mount Tambora was the largest eruption ever witnessed. Its Volcanic Explosivity Index (VEI) was 7, the only known eruption on that scale since the eruption of Lake Taupo in about 180 AD. The eruption blew 150 cubic km into the atmosphere, killing 10,000 people initially. The eruptions' column was so high it reached the stratosphere at an altitude of more than 43 kilometres.

The effects were felt worldwide, 1816 was "the year without a summer". Crops failed across Asia and up to 90,000 people probably died of famine. It was the second-coldest year in the Northern Hemisphere since 1400 and parts of North America experienced frost and snow in June and July.

Mount Tambora, or Tomboro, is an active stratovolcano in the northern part of Sumbawa, one of the Lesser Sunda Islands of Indonesia. It was formed due to the active subduction zones beneath it, and before its eruption, it was more than 4,300 metres (14,100 feet) high, making it one of the tallest peaks in the Indonesian archipelago.

Resettlement of the area began in 1907, and a coffee plantation was established in the 1930s in the Pekat village on the northwestern slope. A dense rain forest of Duabanga moluccana trees had grown at an altitude of 1,000 to 2,800 metres (3,300 to 9,200 ft). It covers an area up to 80,000 hectares (200,000 acres). The rain forest was discovered by a Dutch team, led by Koster and de Voogd in 1933. From their accounts, they started their journey in a "fairly barren, dry and hot country", and then they entered "a mighty jungle" with "huge, majestic forest giants". At 1,100 metres (3,600 ft), the trees became thinner in shape. Above 1,800 metres (5,900 ft), they found Dodonaea viscosa flowering plants dominated by Casuarina trees. On the summit was sparse Edelweiss and Wahlenbergia.

An 1896 survey records 56 species of birds including the crested white-eye. Several other zoological surveys followed and found other bird species, with over 90 bird species discoveries in this period, including yellow-crested cockatoos, Zoothera thrushes, Hill mynas, green junglefowl and rainbow lorikeets are hunted for the cagebird trade by the local people. Orange-footed scrubfowl are hunted for food. This bird exploitation has resulted in population declines, and the yellow-crested cockatoo is nearing extinction on Sumbawa island.

In between the hunting ground and the commercial logging area, there is a designated wildlife reserve where deer, water buffalos, wild pigs, bats, flying foxes and species of reptiles and birds can be found. In 2015, the conservation area protecting the mountain's ecosystem was upgraded to a national park.

References:

https://en.m.wikipedia.org/wiki/Mount_Tambora
https://www.onthisday.com/photos/eruption-of-mount-tambora

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Photos 02/06/2020

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