Mathematics by Siyabonga Khoza

📢📢!
Trial Exams Revision by Khoza
2021
This one is ONLY for Ladysmith Matriculants.

For reinforcement of the Calculus Concept I uploaded Today, go through these Key🔑 Points I made🙏❤️.
Also take Note of the (Food for Thought) pointers at the end! 😁😁

NB: It's possible for Examiners to Give us Parabolic Function in Calculus(High Order Question) and ask you to reverse it to Cubic Function, If you Don not Understand the Last Paragraph on this Post it will be difficult for you to ANSWER THE QUESTIONS.


Grade 12

to Matric 2020 Finals.
Studying🤗.
"Genius is 1% talent and 99% hard work" Albert Einstein.

Pointers to look out For in Cubic Functions.

1.Plotting(These are free Marks no one should miss!!).

1.1 First decide of the shape of your graph(that's where the first mark goes). Ask yourself :Will it start with a Max. Turning Point or Minimum Turning point? The answer to that you'll find by checking the sign of your (a). Negative (a) = Max. Tp first. Positive (a)=Min. Tp first.

1.2 Given an equation: look for X-intercepts of a Cubic Function, as usual Equate your Equation to zero(y) and factorise either by using Long division, inspection, rational roots .e.t.c
Plot your X-intercepts (X;0).

1.3 Given an equation: look for Y-intercepts of your Cubic function. Make X=0 and subtitute that value. However if you remember the rules well!! You should know that your Y-intercept is your Constant value🤗.

1.4 Given an Equation : look for your Turning Points. Remember 💭! At a turning point your Gradient/First derivative is equal to zero(hence called stationary points). Therefore if I'm looking for coordinates of a Turning Point I have to:

1.derive my original Equation.
2. Equate the deritive to zero.
3. Solve for X(factorise your quadratic Equation).
4.Substitute Your X-coordinates to the original Equation(cubic function). NB: Do not substitute on the derivative, Please 🙏.

1.5 Lastly For Plotting, look for your Point of Infection:
1. Get the second derivative of the cubic function.
2. Equate your second to zero and solve for X.
3. Substitute that x-value to your original equation.
NB: It is very rare to find a Question paper not asking about change in Concavity of a cubic function. Whenever you see the word Concavity, don't even think twice!!! 😅 They are looking for point of inflection!
👍❤️There you have it!! Plotted💯

2. Food for thoughts:💭
2.1 The X-values of the turning points of a Cubic Function are equal to the x-intercepts of the parabolic function(first derivative of that Cubic function).
2.2 The X-value of a point of inflection is equal to the x-value of the Turning point of a Parabolic Function (first derivative of that cubic function). 👌😅
2.3 The same x-value of a point of inflection is equal to the x-intercept of a straight line(2nd derivative of that cubic function). 😁
2.4 The same x-value of a point of inflection is equal to the value of the Constant Graph(3rd derivative of that cubic function). 😅❤️.