CONTINUOUS ASSESSMENT LEARNING ACTIVITY (CALA) LEARNING AREA: MATHEMATICS LEVEL: A - LEVEL SYLLABUS TOPIC: FIRST ORDER DIFFERENTIAL EQUATIONS SUB-TOPIC: DIFFERENTIAL EQUATIONS TITLE: DETERMINING THE NUMBER OF PEOPLE INFECTED BY COVID-19 COMPETENCE SKILLS: Formulate a DE Solve the DE BACKGROUND In 2019, a new virus was found and it spread all over the world. The spread of the covid-19 occurs at a rate proportional to the product of the number of people infected and the number not infected. Initially 50 out of a population of 1050 are infected and the virus is spreading at a rate of 10 new cases per day. You are therefore required to determine the number of people affected by the virus at a certain day THE CALA You are to carry out the activities in three parts. i.e Part A, Part B and Part C PART A If n is the number infected after day t, write down the DE that describes the situation. PART B solve this DE to find the number of people affected after t days. How long will it take for 250 people to be affected Part C Explain why everyone in the population will eventually be infected. HOW YOU WILL BE ASSESSED You are to be assessed based on your ability to perform the following activities: Coming up with the correct D.E General solution of the D.E Number of days it will take to infect 250 people Solid reason CALA TIPS - Remember to use correct tools and formulas [4] [7] [2] [3] LEARNER GUIDE LEARNING AREA: MATHEMATICS LEVEL: A - LEVEL SYLLABUS TOPIC: FIRST ORDER DIFFERENTIAL EQUATIONS SUB-TOPIC: DIFFERENTIAL EQUATIONS TITLE: DETERMINING THE NUMBER OF PEOPLE INFECTED BY COVID-19 NAME SCHOOL CLASS DATE GRASSLANDS HIGH SCHOOL CALA CONTENT In 2019, a new virus was found and it spread all over the world. The spread of the covid-19 occurs at a rate proportional to the product of the number of people infected and the number not infected. Initially 50 out of a population of 1050 are infected and the virus is spreading at a rate of 10 new cases per day. You are therefore required to determine the number of people affected by the virus at a certain day CALA DESCRIPTION Formulate a DE Solve the DE CALA TIPS - Remember to Use correct tools and formulas TEACHER GUIDE BACKGROUND In 2019, a new virus was found and it spread all over the world. The spread of the covid-19 occurs at a rate proportional to the product of the number of people infected and the number not infected. Initially 50 out of a population of 1050 are infected and the virus is spreading at a rate of 10 new cases per day. You are therefore required to determine the number of people affected by the virus at a certain day You are to carry out the activities in three parts. i.e Part A, Part B and Part C You are to carry out the activities in three parts. i.e Part A, Part B and Part C PART A If n is the number infected after day t, write down the DE that describes the situation. PART B solve this DE to find the number of people affected after t days. How long will it take for 250 people to be affected Part C Explain why everyone in the population will eventually be infected. CALA TIPS: Remember to u se correct tools and formulas A - LEVEL SYLLABUS TOPIC: FIRST ORDER DIFFERENTIAL EQUATIONS SUB-TOPIC: DIFFERENTIAL EQUATIONS TITLE: DETERMINING THE NUMBER OF PEOPLE INFECTED BY COVID-19 DIMENSIONS/ CRITERIA 4 Formulating a D.E EXCELLENT 4 Correct D.E with the true value of k 7 6-7 General Obtaining a solution of the correct D.E D.E showing all working 2 Calculating number of days 3 Conclusion TOTAL GOOD FAIR MARK LEVEL: MARK MATHEMATICS MARK LEARNING AREA: UNSATISFACTORY 3 Correct D.E with the incorrect value for k 2 Not simplified D.E 0-1 Wrong D.E 4-5 Correct D.E but with missing steps in calculations 2-3 Incomplete solution 0-1 Wrong solution 2 1 0 Correct calculation with a correct number of days Correct calculation with incorrect number of days Wrong calculations with incorrect number of days 3 2 A conclusion with a solid reason Good conclusion without a good reason 1 Poor conclusion and reason 0 No conclusion given MARK ACHIEVEMENT STANDARDS
