4 Topics Additional Math Has That Elementary Math Does Not
For an overview, Elementary Math (E-Math) helps to develop your child’s logical ability and form connections. The objective of E-Math is to help establish a foundation in everyday math knowledge and skills. On the other hand, Additional Match (A-Math) is a higher study of mathematics. In A-Math, they build analytical skills through complex formulas.
By looking at the overview and names of the subjects, you can tell that E-Math provides the fundamentals of Mathematics, while A-Math will expose your child to additional and more complicated Math concepts.
That is why students who choose to take O-Level A-Math will also be taking O-Level E-Math. There has never been a case where someone could study A-Math without taking E-Math as well. Of course, because A-Math is optional, it’s naturally more in-depth and has other topics that E-Math probably doesn’t.
If you are wondering if your child should take up the optional A-Math, here is a glimpse of some topics and depths that Additional Math will cover, but E-Math will not.
1. Algebraic/Polynomial Long Division
At first glance, this method is similar to the way you would use for division in primary school. The fundamentals are similar; when dividing in primary school, you would be given one number (the divisor) that you will have to divide into another number (the dividend).
You will use the long-division symbol and place the two numbers before figuring out what goes on top of the symbol. Sometimes, you may use it in E-Math as well.
However, for algebraic long division, you are dividing a polynomial by something more complex than a simple number, which forces you to use a different method to simplify. An example of one of the more straightforward questions from an algebraic long division would be something like this:
Divide (x2 − 9x – 10) by (x + 1)
In this case, the dividend is (x2 − 9x – 10), and the divisor is (x + 1).
You would not see this in E-Math, because it focuses on everyday calculations. That is, unless you are pursuing a Mathematics-related career such as an Engineer, you may not run into it again after O/A-Levels.
2. Modulus Function
Modulus function is a topic that focuses on a number's magnitude, regardless of whether it’s positive or negative. It’s also known as the absolute value function. In A-Math, the modulus of a real number is usually in the modulus function, which will look like this: |x|.
Usually, the number inside the modulus function is always a positive value, as it’s considered the number’s distance from the origin, which is zero. Modulus function is written as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R. That’s why if x is a positive number, then f(x) will be equal to x. If there is a minus sign in front, then f(x) will be -x.
This modulus function can be applied in graphs, and while E-Math also has graphs, the formulas would be more straightforward. An interesting thing to note is, the y coordinates in a modulus function graph never go into the negatives.
3. Binomial Theory
To define binomial expansions, it helps to find the expanded value of any algebraic expression of the form (x + y)n. Of course, it’s easy to expand if it’s something like (x + y)2, since all you need to do is multiply the number of times stated at the exponent value.
However, you may be hard-pressed to do the same calculations if it’s something as big as (x + y)16. That is where the binomial theorem comes in, where you can find out these values without the hassle of expanding them one by one.
You can even calculate the exponential value with binomial theory when it’s a negative number or a fraction, which would look something like this:
(x+y)n = nC0 xny0 + nC1 xn-1y1 + nC2 xn-2 y2 + ... + nCn-1 x1yn-1 + nCn x0yn
The binomial theorem helps express the answer as the sum of the terms that will include individual exponents for the variables x and y. Each term in a binomial expansion has a numeric value, which is named a coefficient. When applying the summation notation, the formula for binomial theory will be expressed as
(x+y)n = ∑nk=0nCk xn-kyk = ∑nk=0nCk xkyn-k
An interesting thing to note about binomial theorem is that it can make expanding mathematical formulas easier. E-Math doesn’t cover this, because the value of the power given is not very big, so normal calculations would suffice.
4. Differentiation and Integration
Differentiation and Integration come as a set. It is one of the essential branches in calculus because they can help your child figure out the derivative and integral of a function. Differentiation breaks the function down into simpler parts, while integration combines these parts to form the original function.
To sum up, if the derivative function is integrated, we can get back the first function. Since the integration process is the reverse of differentiation, an integral can be referred to as the antiderivative.
For example, if you are differentiating, the result may look something like this:
d(xn)/dx = nxn-1
On the other hand, if you want to integrate, the end result may look like this:
∫xn dx = xn+1/(n + 1) + C, n ≠ -1
One noteworthy thing is that sometimes, integration may not necessarily be able to come out of the original function’s constant terms. To denote this, the constant C may be added at the end of the integration results.
Think of it geometrically: differentiation will be used to find the curve’s slope, while integration is to identify the area under the curve.
Conclusion
A-Math may seem complicated at first glance, but it is worthwhile if your child manages to master the complicated steps. After all, if they can grasp the in-depth topics of A-Math, they are sure to find E-Math easier to master as well. Then again, A-Math is also systematic, so those who are more rigid in their methods may also thrive in this subject.
If you are looking for A-Math tuition in Singapore, look no further than Glenn Lee Learning Centre. As an online tuition agency in Singapore with a proven track record, we provide personalised tuition and interactive teaching that can suit your child’s learning.
Moreover, we make learning fun so students will be able to grasp topics quicker and be pushed to think out-of-the-box. Check our website or contact our number for more details.