# A Peek Into the H2 Mathematics Syllabus

## Singapore Junior College H2 Math Syllabus

For the H2 Maths Syllabus, students are taught basic functions in Year 1 and the implementation of more complex functions in Year 2, followed by the A-levels exam. The syllabus covers 6 main “strands” which are described as functions and graphs, sequences and series, vectors, complex numbers, calculus, probability, and statistics.

To understand more about what each of these topics’ entails, here is a glimpse of the H2 Math Syllabus!

## Examples of Syllabus Chapters

Quadratic Equations: Following the teachings of functions and graphs in the “O” levels syllabus, the H2 math syllabus begins with an understanding of quadratic equations.

A quadratic equation is a second-degree polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and a ≠ 0. Through this, students will be taught methods such as factorization, completing the square, and the quadratic formula.

Graphical Representation: In addition to quadratic equations, at the H2 Math level, students are equipped with a graphing calculator that would be capable of deriving values.

Specifically, Students learn to graph quadratic functions by identifying key features such as the vertex, intercepts, and the concavity of the graph. They also study the relationship between the coefficients a, b, and c and how they affect the shape and position of the graph.

Calculus

For both quadratics and calculus, algebraic functions serve as the basic building block, to move a step further the following section will elaborate more about calculus.

Differentiation: In essence, differentiation allows us to analyze how quantities change and understand the relationship between different variables. It is often used in physics, engineering, economics, and other fields to model and predict various phenomena.

As Calculus is one of the core teachings of the H2 Maths syllabus, students are taught various functions, such as trigonometric functions, exponential functions, and logarithmic functions.

The basics of the Differentiation rules are as follows:

1. Power Rule: If you have a function of the form f(x) = x^n, where n is a constant, the derivative is given by: f'(x) = n * x^(n-1)

For example:

• If f(x) = x^2, then f'(x) = 2x
• If g(x) = x^3, then g'(x) = 3x^2
1. Constant Rule: If you have a constant function, f(x) = c, where c is a constant, the derivative is always zero: f'(x) = 0
2. Sum/Difference Rule: If you have a function that is the sum or difference of two functions, f(x) = u(x) ± v(x), then the derivative is the sum or difference of the derivatives of the individual functions: f'(x) = u'(x) ± v'(x)
3. Product Rule: If you have a product of two functions, f(x) = u(x) * v(x), then the derivative is given by: f'(x) = u'(x) * v(x) + u(x) * v'(x)
4. Quotient Rule: If you have a quotient of two functions, f(x) = u(x) / v(x), then the derivative is given by: f'(x) = (u'(x) * v(x) – u(x) * v'(x)) / (v(x))^2
5. Chain Rule: If you have a composition of functions, f(x) = g(h(x)), then the derivative is given by: f'(x) = g'(h(x)) * h'(x)

Integration:  Integration is the reverse process of differentiation. It involves finding the accumulated or total value of a quantity over an interval. It is commonly used to calculate areas, volumes, and accumulated sums.

When you integrate a function, you are essentially adding up infinitesimally small changes in the quantity represented by the function. This process is represented by the integral symbol (∫) in mathematics. While integration can be used for several purposes, in simple terms, integration calculates the area under a curve.

With the rules in mind for differentiation and integration, here is an example of integration in action.

Consider the function f(x) = 2x. To find the integral of this function with respect to x, we can use the power rule of integration:

∫(2x) dx = x^2 + C

In this formula, the symbol ∫ represents integration, (2x) is the function we want to integrate, dx represents the differential element (infinitesimally small change in x), and C is the constant of integration.

Now, let’s solve the integral:

∫(2x) dx = x^2 + C

The integral of 2x with respect to x is x^2, and we add the constant of integration C.

So, for example, if we want to find the integral of 2x with respect to x from x = 0 to x = 3, we can use the definite integral:

∫[0 to 3] (2x) dx = [(x^2 + C)] [0 to 3] = (3^2 + C) – (0^2 + C) = 9 – 0 = 9

The definite integral gives us the accumulated area under the curve of the function from x = 0 to x = 3, which in this case is equal to 9.