Category: Physics

The Grade 9 to Senior School selection process in Kenya involves students choosing their preferred pathways. They also choose subject combinations and schools. This is done through an online system managed by the Ministry of Education. 

This process is part of the transition to Senior School under the Competency-Based Education (CBE) framework. Students will select their pathways and subject combinations and they will also choose up to 12 schools across four clusters. STEM is a mandatory pathway.

SELECTION OF PATHWAYS AND SENIOR SCHOOLS

• Determination of pathways per senior school
• Determination of vacancies for boarding and day schooling in senior schools
• Selection of pathways, subjects’ combination and schools by grade 9 learners

Selection based on pathway

The learner will select 12 schools for their chosen pathway as follows.

• 4 schools in first choice track and subject combination
• Four (4) schools in second choice subject combination
• Four (4) schools in third choice subject combination (Total 12 schools)

Selection based on accommodation

Out of the 12 schools selected based on pathway:

• 9 will be boarding schools; 3 from the learners’ home county, 6 from outside their home
  county/county of residence.
• Three (3) day schools in their home sub county/sub county of residence. (Total 12 schools)
  Pre selection – A school that does not allow open placement can apply to be pre-select if it meets the criteria defined by the Ministry of Education.

Accommodation- Based Breakdown

Top 6 learners per gender in each STEM track per sub-county will be placed for Boarding in
schools of choice

• Top 3 learners per gender in each Social Science track per sub-county will be placed for
  Boarding in schools of choice
• Top 2 learners per gender in each Arts and Sports Science track per sub-county be placed to
  Boarding schools of their choice
• Placement of Candidates with Achievement Level of averaging 7 and 8 per track to boarding
  schools of their choice

To get the form, click below:

GRADE 9 TO SENIOR SCHOOL SELECTION FORM

LEANER’S FULL NAME__________________________________________________

ASSESSMENT NUMBER (KPSEA) __________________________________________

DATE OF BIRTH____________________________GENDER ([] Male [] Female)

CURRENT School NAME:_________________________________________________

COUNTY OF Residence: _______________Sub-County of Residence_________________

Parent/Guardian Name__________________________________________________

Parent/Guardian Phone Number _____________________ID No___________________

B. Selected Pathway & Subject Track

[] STEM (Science, Tech, Eng., Math) __________________________________________

[] Social Sciences______________________________________________________

[] Arts & Sports Science__________________________________________________

 C. School Choices – Based on Pathways

    First choice (4 schools):

1. School Name & County_______________________________________________
2. School Name & County_______________________________________________
3. School Name & County _______________________________________________
4. School Name & County________________________________________________

 Second choice (4 schools):

1. School Name & County________________________________________________
2. School Name & County________________________________________________
3. School Name & County_______________________________________________
4. School Name & County________________________________________________

     Third choice (4 schools):

• School Name & County _______________________________________________
• School Name & County _______________________________________________
• School Name & County _______________________________________________
• School Name & County _______________________________________________

   D. Accommodation- Based Breakdown

       [] 3 Boarding Schools within home county

      [] 6 Boarding Schools outside home county

      [] 3 Day schools in home sub-county

E. Teacher’s recommendation

___________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________________________________________________________

 F. Learner’s Signature

               Signature_________________________Date____________________________

 G. Parent/Guardian Consent

 I confirm that the above choices were made in consultations with the learner and based on MoE  guidance.

   Name_______________________________________________________

    Signature________________________ Date _________________________

Download Microsoft word format free

Related topics

• Isaac Newton
• Albert Einstein
• Hans Oersted
• calculus
• Errors and approximations

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The Fundamental Theorem of Calculus  establishes a crucial link between differentiation and integration.

 It essentially states that these two operations are inverses of each other, and it provides a way to evaluate definite integrals using anti-derivatives.

Suppose that f is continuous at a closed interval [a, b] . If the function F is defined on a closed interval [a, b] by:

where a is a real number, Then F is the anti-derivative of f. in other words, F'(x) = f(x)

consider the relationships:

then

f(x) = x² and

Note: We use the dummy variable (t) in the integrand to avoid confusion with the upper limit x.

Sometimes the fundamental theorem of calculus is interpreted to mean that:

differentiation and integration are inverse processes to each other.

It follows that:

The fundamental theorem of calculus states that:

if f is continous on an open interval containing a and x and then we first integrate the function f and then differentiate with respect to x, then the result we get is the function f again.

In other words, the fundamental theorem of calculus argues that differentiation cancels the effect of intergration of continous f(x’).

in short:

For example

Example problem1

Use the fundamental theorem of calculus to find derivative of the following functions

(a)

solution

NOTE: The best way to benefit from this examples is trying the problem first before looking for answers and attempting again after checking your work against the answer.

Example problem2

(b)

solution to problem 2

Example problem 3

Find h'(x) given that :

solution

let y=h(x) and u=x² and hence:

since u=x²;

and therefore:

By use of chain rule:

which implies u³sinu(2x) = (x²)³sin(x²)2x resulting to:

=2x⁷sin(x²)

Example problem 4

Consider the expression below, we exchange the limits in the intergral and then change the sign from positive to negative before using the fundamental theorem to solve it.

Example problems on fundamental theorem of calculus

We exchange limits and so the sign of the integral so that the upper limit is the valuable x.

Example problem 6

Use the fundamental theorem of calculus to solve:

Solution

splitting the integral about point zero we have:

and then exchanging limits in the first integral;

let u=-x; first part of the expression above becomes;

from laws of differentiation du/dx=-1 and using chain rule;

and hence

and finally

Revision Exercise

Answers to revision exercise

Related topics

• Basic Integration rules
• The second fundamental theorem of calculus

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The most common calculator used by high school learners is ms fx-82 model. Calculator has many scientific functions that can help a student work out many scientific computations. However, ms fx-82 calculator is non-programmable.

Casio fx-82MS Scientific Calculator

The Casio fx-82 MS is a widely used scientific calculator. It is especially favored by students and professionals for its reliability. It also complies with exam requirements.

Key Features of fx-82 calculator:

• 240 Functions: Includes trigonometric, statistical, fractional, and exponential calculations.
• Natural Textbook Display: Shows expressions as they appear in textbooks for easy comprehension.
• Two-Line Display: Simultaneously displays input and output for clarity.
• Multi-Replay Function: Allows quick recall and editing of previous formulas.
• STAT-Data Editor: Supports mean, standard deviation, and regression analysis.
• 9 Variable Memories: Stores and recalls up to 9 data sets for efficiency.
• Durable Design: Features robust plastic keys and a protective slide-on hard case.
• Battery Powered: Operates on a single AAA battery.
• Non-Programmable: Compliant with exam standards for academic use.
• Portable and Lightweight: Compact design for easy everyday use.

Handling Precautions

• Even if the calculator is operating normally, replace the battery at least after every two years. Continued use after the specified number of years can result to abnormal operation.
• You should replace the battery immediately after display figures become dim.
• A dead battery can leak, causing damage to and malfunction of the calculator. Never leave a dead battery in the calculator.
• The battery that comes with the calculator is for factory testing, and it discharges slightly during shipment and storage. Because of these reasons, its battery life can be shorter than normal. For that reason, consider replacing the battery sooner.
• Avoid use and storage of the calculator in areas subjected to temperature extremes, and large amounts of humidity and dust.
• Do not subject the calculator to excessive impact, pressure, or bending.
• Never try to take the calculator apart.
• Use a soft, dry cloth to clean the exterior of the calculator
• Do not use a nickel-based primary battery with this product.
• use of incompatible batteries such as nickel-based primary battery with fx-82ms calculator can result in shorter battery life and product malfunctioning.

Turning Power On and Off

• In order turn on the calculator. Press:

• to turn off the calculator: press (OFF). that is;

Adjusting Display Contrast

To show the display setup screen, press:

A scree appears as shown:

press 2 and the use > and < to adjust display contrast. when satisfied with the display settings, press AC button

use of calculator keys

To use the alternate function of a key, press [SHIFT] key followed by the key. The alternate function is indicated by the text printed above the key. The alternate function is usually marked with a different color from the main key.

Basic operations in calculator

• use AC button to clear all values.

• To clear memory press shift then mode . Three screens will display as follow:

• to clear memory press:

• If your calculator has FIX or SCI on the display press mode three times to get the following screens:

pressing 3 followed by 2 takes you to a normal mode.

• If your calculator has RAD or GRAD on the display, then press mode two times to get the following on the screen:

DEG represents Degree mode and you get there by pressing 1.

• To display a decimal point as a dot or a comma such as 200.678 or 200, 678, you can press mode button 4 times until DISP 1 is displayed.

press 1 then forward button once.

press 1 to separate thousands with a comma(,) or press 2 to separate thousands with dot (.)

• To initialize the calculator and return the calculation mode and setup to their initial default settings. use the following procedure:

This operation also clears all data currently in calculator memory.

Related topics

• mathematics
• Integrating products of trigonometric functions 1