MAT102 GEOMETRYa KCA Certificate Past Paper

UNIVERSITY EXAMINATIONS: 2016/2017
EXAMINATION FOR THE CERTIFICATE IN BRIDGING
MATHEMATICS
MAT103 CALCULUS
DATE: AUGUST, 2017 TIME: 2 HOURS
INSTRUCTIONS: Answer Question One & ANY OTHER TWO questions.

QUESTION ONE
a) Differentiate the following expressions with respect to the independent variables

b) Determine

Determine
i) The distance travelled after 6 seconds (4 Marks)
ii) The velocity of the particle after 3 seconds (3 Marks)
iii) The acceleration of the particle after 4 seconds (3 Marks)
QUESTION TWO
a) A stone is thrown vertically upwards at a velocity of 20m/s. Assuming no air
resistance, find / determine;
i) The velocity at the highest point reached (2 Marks)
ii) The time it takes to reach this highest point (3 Marks)
iii) The distance from the ground to the highest point reached (3 Marks)
iv) the velocity after 1.5seconds (3 Marks)
b) determine the area bounded within the curve y = x2 +3x + 2 and the x – axis between
x = 3 and x = 5 (9 Marks)
QUESTION THREE

QUESTION FOUR
a) Define the following terms as used in calculus
i) Calculus (2 Marks)
ii) Variable (2 Marks)
iii) Function (2 Marks)
iv) Limit (2 Marks)
b) Briefly discuss the following types of functions. Use graphical sketches for each
i) Linear function (3Marks)
ii) Quadratic functions (3 Marks)
iii) Exponential functions (3 Marks)
iv) Logarithmic functions (3 Marks)
QUESTION FIVE

 

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