RTQF Level 4 QP_FUNDAMENTAL MATHEMATICS ANALYSIS.pdf

RTQF L4 – FUNDAMENTAL MATHEMATICAL ANALYSIS DATE: THURSDAY 07 JULY 2022 PERIOD: 08H30 – 11H30 PM END OF TERM III EXAMINATIONS SECTOR: Agriculture and Food Processing, Construction and Building Services, ICT and Multimedia, Manufacturing and Mining, Energy, Transport and Logistics,...

RTQF L4 – FUNDAMENTAL MATHEMATICAL ANALYSIS DATE: THURSDAY 07 JULY 2022 PERIOD: 08H30 – 11H30 PM END OF TERM III EXAMINATIONS SECTOR: Agriculture and Food Processing, Construction and Building Services, ICT and Multimedia, Manufacturing and Mining, Energy, Transport and Logistics, Technical Services TRADES: Animal Health, Crop Production, Food Processing, Forestry, Irrigation and Drainage, Carpentry, Interior Design, Land surveying, Masonry, Plumbing, Road Construction, Hydropower Energy, Industrial Electricity, Solar Energy, Software Development, Networking, Production Technology, Welding, Multimedia, Electronics, Telecommunication, Auto electricity and Electronic Systems, Auto Mobile Transmission and Control System Technology RTQF LEVEL: 4 MODULE CODE AND TITLE: Fundamental mathematical analysis MARKS: /100 DURATION: 3 HOURS INSTRUCTIONS TO CANDIDATES: This Exam paper is composed of one section. Follow the instructions given below, and answer the indicated questions for a total of 100marks Section A: Fifteen (15) questions, all Compulsory. 100 marks Allowed materials: Mathematical Non-programmable Calculator Blue pen or black pens RTQF LEVEL 4 – Fundamental Mathematics Analysis – Page 1 of 2 – Marking guides Section A: Answer all questions (100marks) All questions are compulsory 01. Find the domain of definition of f(x)= (5marks) x3 02. Find the following limits, if they exist lim x  4 (5marks) x2 03. Determine the derivative of the following function f ( x)  x  x 3 (4marks) 04. State whether the following function is even or odd: f(x)=x2+1 (6marks) 05. Find the range of the function for the domain = (6marks) 06. Find the equation of the oblique asymptote to the curve representing f(x)= (10marks) 07. Calculate: a) lim x (e2 x  e x  4) (7marks) 08. Find the vertical asymptote for f(x)= (5marks)  3x 2 09. Evaluate the following limits: lim x x 0 x (7marks) 10. Sketch the following function (10marks) 11. Differentiate the tangent with the normal line formulas at the point (6marks) 12. Find the derivative of function f ( x)  2ln x (6marks) 13. Find the derivative of f ( x)  34 x 2 (7marks) x 1 14. Find the domain of the function f ( x)  3 x2 (6marks) 15. Calculate lim x0 f ( x) such that f ( x)  x ln x (10marks) RTQF LEVEL 4 – Fundamental Mathematics Analysis – Page 2 of 2 – Marking guides