Tips & Challenges – Page 6 – JC A Level H2 Math Tuition Singapore

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”

detect asymptotoes 1.jpg

detect asymptotoes 2

detect asymptotoes

Checking Summation results

Suppose we want to check whether our answers for the following is correct:

results

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.

Cancellation tip

Approximation in series expansion

This question was posed by a student.

question

Explanation

Exact versus approximation. The two curves depart from each other at x=pi/5

approximation

When we use the approximation to compute the volume, it differs significantly from the exact volume.

volume

Advanced graph transformation

Advanced graph transformation can be done in stages, using the replacement method. Each time, we replace x or y.

advanced transformation 1

advanced transformation 2

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:

sum and difference of two cubes

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

gc to find normal

normal to plane

Using GC in Differential Equations

The following example illustrates how we can use GC in Differential equations, and avoid the need to do integration to solve differential equation.

2016 RI MCT

Solution for part ii

Using GC in DE

Challenging graphing technique question 1

This question was posted by a student at Singapore JC maths.

question

Solution for Part ii

Methods to determine whether a line is on a plane

lineplane1

lineplane2