Last Minute Reminder for Mathematics T
Chapter 7
Remember all indeterminate form of limits
Know how to evaluate limit (direct substitution, factorisation, rationalisation, divide by highest power of x in denominator, L' Hospital's rule)
Know how to show existence of limit
Know how to show continuity of function at a point and in the interval (never come out)
Chapter 8
Know how to differentiate using first principle (never come out)
Remember all derivatives
Know how to use all rules of differentiation
Know how to perform implicit and parametric differentiation
Know how to use first derivative test and second derivative test
Application (curve sketching, rate of change and optimisation problem)
Chapter 9
Remember all antiderivatives
Know all trigonometric identities (double angle formula, compound angle formula, pythagoras identities, sum and difference of sine and cosine and etc)
Know how to decompose partial fractions
Know how to determine u and dv in integration by parts (LIATE)
Remember all substitution methods
Remember formula to find area and volume
Chapter 10
Know how to identify types of differential equations (separable, linear and homogenous)
Know how to integrate separately for separable DE
Know how to integrate by mean of integrating factor for linear DE
Know how to substitute to transform homogeneous DE into linear or separable DE
Know how to find general solutions
Know how to use boundary condition to find particular solutions
Chapter 11
Remember Maclaurin Theorem
Know how to use standard series
Know how to evaluate limit, differentiate and integrate using Maclaurin expansion
Chapter 12
Intermediate answer in more than 1/2 dp/sf from required dp/sf in question
Know how to determine iteration converges or diverges
Remember ≈ for the Trapezium rule
State dp/sf in final answer
Know how to determine overestimate and underestimate of the Trapezium rule
Good luck to all sem 2 students that take Mathematics T. Wish you all the best and meet you all in sem 3 (statistics).
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