H2 Math is a beast.
Okay, maybe not. Just ask my students who improved under my tutelage.
But then H2 Math vectors is definitely a beast.
Okay, maybe not too. Just ask my students who've been trained to view the question from my perspective.
It is true, though, that most students struggle with vectors. I was no different when I was a JC2. The only recollection I had of studying was for vectors just months before my prelim exams. Fortunately, vector is a stand-alone chapter. It does not overlap with other topics such as calculus. In other words, if you struggle with vectors, it is unlikely that it will affect other chapters in the syllabus.
However, do not take the above as a pretext to brush vectors aside. We will still need to master vectors if we want to stand a higher chance of securing that elusive distinction. In order to master any technique, you will first need to understand where the common pitfalls are.
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Table of Content:
Too Many Aspects
There are a total of 3 chapters to vectors.
First, you learn about vectors in 2D. This is mainly your O level E math refresher while introducing you to ratio theorem, dot product, and cross product.
Subsequently, you will be taught lines. This would range from introduction to the equation of lines in its 3 forms to introduction to the relationships between point and line, line and line.
Finally, you will then be taught to appreciate vectors in a 3D model completely through the introduction of planes. In this chapter, you will be taught the relationship between point and plane, line and plane, and plane and plane.
The above would intimidate any student. Most students, at the start, would try to memorize all the concepts learned. After all, that is the easiest way to begin your revision. However, the sheer amount of content would make it challenging for any student to memorize them all. What most students fail to realize is, that vectors can be broken down into just 2 simple concepts. Dot and cross product.
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Inability to Visualize
In H2 Math vectors, due to the presence of the 3 axis (x, y, and z), questions involve 3D models, and hence, an ability to visualize is required. For the lazy, your refusal to sketch a diagram is going to hurt you.
In lectures, students are taught the various relationships between various components in vectors. However, the questions are hardly straightforward. Questions do not blatantly mention the relationship between a line and a plane. You are expected to discover that on your own through answering the preceding parts and a simple sketch of a diagram.
Most students struggle to get the correct visualization due to poor sketching. Personally, I explain to students using pens to represent lines, paper to represent planes, and coins to represent a point. You may look silly in the hall but at least you get your distinction. Your call.
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The hardest type of question is the application question. Most of us are experienced with application questions by now. In calculus, we have found the maximum volume of a cone, rate of change, etcetera. In vectors, application questions are monstrous.
Most application questions in vectors would be accompanied by a diagram. Guidance would be given in terms of how to interpret the coordinates with respect to the x, y, and z-axis. However, such unfamiliar territory is precisely what throws students off. Students are unsure and therefore, afraid to proceed with the question.
Furthermore, students are expected to apply equations of planes to walls, grounds, and surfaces of cliffs. At the same time, the projectile of objects is now modeled by the equation of a line. Contextual questions tend to throw students off. Vectors, without context, are confusing in themselves. Combine vectors with application and you have many students scoring zeroes.
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I used to hate vectors too
We, at VANTAGE TUTOR, have struggled and walked through a similar path to students when they were students themselves. We understand where you fall short and in hindsight, we also realized how we could have done better for our A Math and E Math coordinate geometry.
Currently, as Math and Physics tutors, we don’t want you to walk the same path we did with no one to direct us. We would direct you toward the right path and also set you up for success by going at your pace during class. We will achieve basic mastery before applying to problem-based questions. Furthermore, our Math and Physics tutors have a track record in helping students improve in Math for N level, O level, A level, and even IP!
I personally pride myself on my ability to solve vector questions easily and to teach vectors now.
So hesitate no more, contact us today!