Oh this one, it’s quite hard to remember all. Even more so is the a Maths one. Wait.

Ok.
Any step can remember or can use calculator?

There are six powers of x you must remember for x^n plus one graph of a^x where x is the power this time.

Power 0 is straight forward. This one is a horizontal line y = k.

Power 1 is also straight forward. A typical upsloping line or downsloping line y = mx + c.

Power 2 is your typical quadratic curve which you would have seen frequently in both e and a Maths.

Power 3 is something unusual. The are two shapes for power 3, depending on the parameters used. One is the rise up until 0, then instead of turning back downwards, it continues to go upwards. This one is a typical x3 graph. Another possible cubic graph is a rise-fall-rise graph. This is when b and/or c in the equation y = ax3 + bx2 + cx + d is/are non-zero.

Calculator is not a good way of solving this one. It takes too long to find all the data points just to plot the shape out.

Power -1 is unusual. You will see the graph on opposite diagonals. If one graph appears to be in the ‘first quadrant’, the other side will have a graph in the third quadrant. If one graph appears in the ‘second quadrant’, the other appears in the ‘fourth quadrant’. The difference is that the first and third Quadrants are for the graph of y = a/x where a is positive, while the other two Quadrants are for the case a is negative.

Power -2 has the same shape graphs as power -1, except that this time the graphs appear either in the first and second Quadrants (ie both above the x-axis, for a > 0) or the third and fourth quadrants (ie both below the x-axis, for a < 0).

The last one is where x is the power. You know how to draw the graph of y = e^x and y = e^-x right? e is just a number. The graph of y = a^x, where a is any number more than 1, has the same shape as that of y = e^x, and by analogy, the graph of y = a^-x, where a > 1, had the same shape as that of y = e^-x.

A good rule of thumb is that if the graphs tend to appear disjoint (the graph seems cut in the middle and cannot be connected), then the graph must be power -1 or -2 (at least in your syllabus you only learn -1 and -2).

If you see a graph that starts from near zero and suddenly starts to increase without ever going back down, then x is the power instead of the base.

Otherwise, it’s one of the following cases.

If the graph is a straight line, then power of x is either 0 or 1. Horizontal is for 0, else it’s 1.

Quadratic graphs are just too common.

If the graphs does not meet ANY of the above, it must be a cubic graphx

Additionally, you will learn other powers of x including fractional and real powers, not just whole number powers, grouped into three cases, for a Maths.

Power < 0, to be drawn only for x > 0. This one is same kind as the negative powers, but first quadrant only.

Power 0 < x < 1, to be drawn only for x > 0. This one looks like a ln graph that starts from (0, 0).

Power x > 1, to be drawn only for x > 0. This one is like the right half of a quadratic graph (in fact it is).

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You can post the next question first if you need. Remember, you can study a maths in conjunction with e maths because at least 25 percent of what you learn in e maths appears again in a maths.

Common topics are

1. Simul (obviously)
2. Properties of circles (disguised in a maths as proofs in plane geometry)
3. Coordinate geometry
4. Linear inequalities
5. Indices
6. Toa cah Soh
7. Completing the square (this one must practise because it will affect both papers)