Can you solve this?
My dear students,
I know you had studied hard, worked endlessly and put into so much effort in your studies. I know that you are passionate and committed in doing well and finishing this school term successfully. Undeniably, it was mostly a series of challenges for you since day one. Soon, all your hardwork will bear fruit. You have prepared for this exam, pouring in sleepless nights, doing endless readings and viciously thinking of ways to solve a math problem. You are full of potential and no amount of assessment can tell how successful you will be in the future. I believe that you all have a place in this world and it’s up to you to find that place. When everything is done, tap yourself in the back and say, “I have done well and I am proud.” As your teacher, all I wish is for you to be the best versions of yourselves. You have what it takes to make it to the top. All you have to do is to believe you can because we all do. Diligence, perseverance, learning from failure and facing challenges are important ingredients for you to succeed in whatever endeavor you face. Good luck everyone!
In solving quadratic equations, mathematicians might have constructed a quadratic equation like x2 = – 1. On solving for its roots, the symbol i with i2 = – 1 was invented.
Below is the video that gives you an idea of what complex numbers are.
Probability as a general concept can be defined as the chance of an event occurring. Many people are familiar with probability from observing or playing games of chance, such as card games, slot machines or lotteries. In addition to being used in games of chance, probability theory is used in the fields of investment insurance and weather forecasting. In fact, probability is the basis of inferential statistics. This month, we will tackle some basic concepts involving probability – probability experiments, sample spaces, laws of probability and conditional probabilities.
Geometric shapes and figures abound in nature. The honeycomb of bees is one such example; individual cells have hexagonal openings. The spider web is constructed with a series of polygons anchored in radial thread lines. The orbits of planes and stars are elliptical with some nearly circular. Th cross sections of many fruits and trees are circular. A stone thrown on still water causes the formation of a series of circular waves with increasing circumferences as the ripples move outward. Arc shapes can be found in petals of many flowers. The beautiful rainbow is in the form of arc.
Symmetry is one of the most geometric characteristics in nature. Symmetry brings balance and enhances appearance. The symmetrical and almost perfect cone of Mount Mayon and Mount Fuji make it world famous. We find symmetry abounding in leaves, flowers and fruits.
Artists and builders of all cultures were and are influenced by the geometric shapes and figures observe in nature and have since time immemorial incorporating their observations in their works. This, the pyramids of Egypt and the temples, palaces and churches around the world are wondrously decorated with geometric figures and combinations of them.
Engineers apply triangles in building structures because it is the most stable construction. (You will discover why when you study triangles.) Towers and bridges shape are often constructed with a series of triangles. For rotating motions, the circular shape is a must. The circular shape is applied in innumerable machine parts – wheels, camshafts to name but a few.
Indeed, everybody once in a while applies geometric knowledge in his/her various activities like estimating lengths, areas and/or surface areas and volumes and perhaps the cost of materials.
This month, we will be studying surface areas and volumes of solid/composite figures, properties of triangles and quadrilaterals and congruence and similarities of polygons.
One of the IB Learner Profile states that an IB student is someone who exemplifies honesty, integrity, justice, and respect. Collectively these traits describe a principled learner. How is this learner profile evident in a Math class?
These pictures show how students use their knowledge and skills in the subject in order to solve given math problems successfully. Each student has his/her own unique set of strengths and weaknesses. Every session of Math class is an opportunity for students to develop their strengths and overcome their weaknesses by working independently or through collaboration with other members of the class.
An IB student knows when to persevere until a solution to a problem has been reached but they also recognize the need for guidance or assistance from the teacher or a classmate. This allows them to not only find the solution to the problem but learn the process of how the solution has been reached. Principled learners know when to seek help from others and at the same time offer help to those who may be struggling.
Principled learners are healthy competitors. They exert effort in everything that they do but their mindset is always to bring everyone up with them. They are not threatened with competition rather they use it to inspire and motivate themselves to become better.
An aid for navigation and pilotage at sea is the lighthouse , a tower building or framework very familiar among the navigators, especially to those who sail by boat. This lighthouse serves as the compass for the navigators as it provides travelers and mariners information on the wind direction by displaying a light for their guidance. Lighthouses also provide coordinate location for small aircraft traveling at night.
Because of modern navigational aids, the number of operational lighthouses has declined to less than 1,500 worldwide. Lighthouses are used to mark dangerous coastlines, hazardous shoals away from the coast, and safe entries to harbors.
Just like the lighthouse, you will be introduced to the world of symbols that are used to convey ideas in Algebra. The concept of variables and algebraic expressions are basic in the study of Algebra. The use of variables and symbols become more meaningful when word phrases or verbal phrases are translated to mathematical phrases . Identifying the key phrases in verbal phrases facilitates translating them to mathematical phrases . This process is a prerequisite in solving word problems.
How big is infinity? Can you quantify it?
Trigonometry is a branch of mathematics that deals with properties and applications of ratios associated with angles. It has been used for thousand of years by astronomers, surveyors and cartographers. In modern times, there are applications of trigonometry that involve periodically repetitive phenomena such as wave motions, alternating current, vibrating strings, oscillating pendulum, business cycles and biological rhythms.
This unit introduces you to some concepts necessary to understand trigonometry and eventually apply them in real-life situations.