Synthetic division in complex numbers
Tips & Challenges
How to check Sequence of Transformation?
Using GC to calculate Expectation and Variance of Discrete Random Variable
Example 1
Solution
Enter the data in the GC as follows:
Variance can also calculated using the GC as follows:
Example 2
GC setting for faster graph plot
Method 1: Change Xres to 3
The Xres button refers to pixel resolution (1 through 8). At Xres = 1, functions are evaluated and graphed at each pixel on the x-axis. At Xres = 8, functions are evaluated and graphed at every eighth pixel along the x-axis. Small Xres values improve graph resolution but may cause the calculator to draw graphs more slowly. Setting Xres to 3 provides good balance between speed and resolution.
Example
Xres= 1
Time taken to plot= 23.4 s
Xres= 3
Time taken to plot= 3.6 s
Savings of almost 20 seconds! Which is crucial in exams
Method 2: Turn off “Detect Asymptotes”
Checking Summation results
Suppose we want to check whether our answers for the following is correct:
We can use our GC to check as follows:
Since both expressions give the same values, the answer is correct.
How to spot the Cancellation Pattern in Method of Difference
Tips: Write the terms using functions. For bottom rows, write from last row and then write the last 2nd row.
Approximation in series expansion
This question was posed by a student.
Explanation
Exact versus approximation. The two curves depart from each other at x=pi/5
When we use the approximation to compute the volume, it differs significantly from the exact volume.
Advanced graph transformation
Advanced graph transformation can be done in stages, using the replacement method. Each time, we replace x or y.
Sum and Difference of Two cubes
In 2013 alevel, factorisation of the difference of two cubes can be used in one of the questions
Here are the formulas students should remember:
Students can use the mnemonic “SOAP” to help them remember the formula.
S: Same sign
O: Opposite sign
A: Always
P: Positive
Using GC to find the Normal vector to planes
JC A Level H2 Math Tuition Singapore 
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