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12/03/2024

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01/06/2022

Calculus

They are 5 things you need to
Know
1. Derivative by first principle
2. Differentiation by rules
3. sketching cubic function
4. Interpretation of cubic function
5. Optimisation

1. Derivative by first principle

Step1: write a formula as it from
formula
f(x)=lim f(x+h)
h->0 h
Step2: find f(x+h)
Step3: find f(x+h)-f(x)
Step4: substitute to the formula
Then simplify

Example
Given f(x)= 4x^2

Step1
f(x)= lim f(x-h)-f(x)
h->0 h
Step2
f(x+h)= 4(x+h)^2
=4(x^2+2xh+h^2)
= 4x^2+8xh+4h^2
Step3
F(x+h)-f(x)=4x^2+8xh+4h^2-4x^2
= 8xh+4h^2
Step4
f'(x)= lim 8xh+4h^2
h->0 h
=lim h(8x+4h)
h->0 h
=lim 8x+4h
h->0
=8x+h(0)
=8x

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23/04/2022

Gr11 and Gr12

Energy
* Kinetic energy- energy due to movement. Ek=1/2mv^2

*Gravitational energy- energy due to position. Ep=mgh

*Mechanical energy- sum of Ek and Ep. Emech=Ek+Ep

* Principle of conservation of mechanical energy in an isolated system remain constant. Emech(initial)=Emech(final)
Ep(i)+Ek(i)=Ep(f)+Ek(f)
Mgh(i)+1/2mv^2(i)=mgh(f)+1/2mv^2(f)

2. work done by non-conservative force
Wnc=change in Ek+change in Ep
Wnc=1/2m(Vf^2-Vi^2)+mg(hf-hi)

3. Step in calculating work done by each force and net work done

Step1: draw a free body diagram
Step2: calculate work done by each force considering the direction and theta
Step3 combine the work done by each force to get net work done

4. Different methods to calculate the work done by the gravitational force
Method1- use the formula Wfg=fg/\xcos theta
Object moving up the inclined theta=90+angle of incline
Object moving down the inclined theta=90-angle of the incline
Fg=mg
/\x is the displacement
Method 2-use the formula
Wfg//=fg//
*/\x*cos theta

Fg//=mgsin angle of incline
/\x is displacement
Theta=0°( if the object moving down the inclined) and theta= 180°(if object moving up the inclined)

Power
- Power is the rate at which work is done or the rate at which energy is transferred
P=W/ change in time P-( watt-W), W-( joules-J) and T-( second- s)

Avarage power
- the avarage power needed to keep an object moving at constant velocity it can be calculated using formula
Pavarage= Favarage=F( change in velocity÷change in time)

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24/02/2022

Sequence GR12 and GR11

1. Linear pattern/sequence
- is a sequence which has a constant difference in the first difference
This sequence has a general term Tn= an+b / Tn=a+(n-1)d

How to determine Tn of linear sequence using general term
Tn=an+b
Step1: find the value of a
* a- is a first constant difference which is equal to T²-T¹=T³-T²

Step2: use the fact that a+b=first term of the sequence.
Using general term Tn=a+(n-1)d
Step1: find the values of a&d
a- first term of the sequence
d- first constant difference
T²-T¹=T³-T²
Step2: substitute the value of a &d in the standard equation and simplify

2. Quadratic pattern/sequence
-is a sequence which has a constant difference in the second difference
This sequence has a general term Tn=an^+bn+c

How to determine Tn of quadratic sequence

Step1: find the value of a using
2a=second constant difference
Step2: find the value of b using
3a+b=first term of the 1st difference
Step3: find the value of c using a+b+c= first term in the sequence

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17/02/2022

Gr12
Maths term 1

Number pattern

Part 1: revision
1. Revision from GR10 linear pattern
2. Revision from GR11 quadratic pattern

Part 2 : GR12 work
1. Arithmetic sequence and series
2. Geometric sequence and series
3. Sigma notation
4. Derivation and application of formula for sum of arithmetic and geometric series

Euclidean geometry
1. Revise conditions of polygons
2. Proof for proportionality theorem and midpoint theorem
3. Similarity theorem
4. Pythagoras theorem
5. Application of those theorems

Trigonometry
1. Angle identities
2. Double angle identities
3. 2D and 3D diagram

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25/01/2022

Hello family
Year has been started so does the work

Rules For Asking Your Questions ON Our Inbox

1. Please don't greet us just go straight to the question as we receive a lot of message, replying to greeting will take us lot of time, just greet and ask in one massage

2. Do send your assignment or homework for us to do for you as that amount of cheating, just do the task and only ask where you're stacked then definitely we will help you

3. Do not ask us for upcoming question papers or what in your exam as that cheating and we do not have access to question papers to be written. Study your own work

4. Ask specific questions and precise questions not generally ones please, your question must be clear and on point

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24/08/2021

Properties of cubic function

-The main concepts involved with this function are as follows
*Intercept with the axes
-fo x-intercept let Y=0, for y-intercept let X=0
*Stationary with the axes
-at stationary points, the gradient of the tangent is zero, i.e f '(x)=0
-determine f '(x), equate it to zero and solve for X
-then substitute the x-value of the stationary points into the original equation to obtain the corresponding y-value
-if the function has two stationary points astablis whether they are maximum or minimum turning points
* Points of inflection
- points of inflection are points where the cubic graph changes it concavity
-for points of inflection, find f "(x), equate it to zero and solve for X
-you can also add up the x-values of the turning point and divide by 2 to get the x-value of the point of inflection

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19/06/2021

Euclidean geometry
Just use Doctor Cape Town (DR CPT) method to master Euclidean

D- all theorems associated with diameter ( angle subtended by diameter is 90°)
R-all theorems associated with radii( angle at centre is twice angle at the circumference and radii can also form triangle with 2 equal sides, two equal base angles)
C- all theorems associated with cyclic quad and chord( opposite angle of a cyclic quad are sumplimentary, exterior angle equal to interior opposite angle)
P- all things associated with parallel lines ( alt angle, corr angles and co-int angles)
T- all theorems associated with tangents ( tan chord theorem, tan from the same point and radius perpendicular to tangent)

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