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Sbm1301:Basic Calculus And Matrices Question Paper
Sbm1301:Basic Calculus And Matrices
Course:Certificate In Bridging Mathematics
Institution: Meru University Of Science And Technology question papers
Exam Year:2012
QUESTION ONE
a) Find the solution of the system by Cramer’s rule (4 marks)
x+y=5
3x-2y=0
b) Estimate the area enclosed by the curve y=1 2
??2+1,x=0, x=4 and the x-axis using the midordinate rule (4 marks)
c) Evaluate
? ?
?
?
? ? ? ? ? ? ? 3 92 3 lim x x x
(4 marks)
d) Given the A=? ? 7,5,3,1 , list the members of the following sets.
(i) ??3:?? ? ?? (1 mark) (ii) (2?? + 3:?? ? ?? (1 mark)
e) Find the derivatives ??3 3??+1
(4 marks) f) Given the equation of the curve y=x2-1, at point (2,3). Find the equation of
2
(i) tangent (3 marks) (ii) normal (3 marks)
g) Find the inverse of ? ? ? ? ? ? 10 23
(3 marks)
h) Evaluate ? ?dx x? ? 3 2 2 1 (3 marks)
QUESTION TWO a) The displacement s metres of a particle after t seconds is given by s=40t3-t2+3t+3. Find its velocity and acceleration when t=2. (6 marks)
b) Use the matrix method to solve (4 marks)
5x+3y=7
2x+y=5
QUESTION THREE
a) Evaluate ? ?
?
?
? ? ? ?
? ?? ? 4 1682 4 lim x xx x
(4 marks)
b) Given that A=? ? 3,2,1,0,1? list the members of the following sets (4 marks) (i) ? ? Axx ?:2
(ii)
? ? ? ?
? ? ? A x x : 1
3
(iii) ? ? Axx ?:2
(iv) ? ? Axx ?? :14
c) Find the gradient of y=x2 at x=1 (2 marks)
QUESTION FOUR a) Use the trapezium rule to estimate the area under the curve y=2x2+6 the x=1 and x=5 and the x-axis. Use 8 strips (5 marks)
b) The demand for the product of a firm varies with the price that the firm charges for the product. The firm estimates that the annual total revenue R as the function of the price P is given by R=f (p) =100p2+100p. Determine the price, which should be charged in order to maximise total revenue. (5 marks)
QUESTION FIVE
a) Estimate the area enclosed by the curve y=1 2
??2 + 3, x=0, x=5 and the x-axis using the
mid-ordinate rule. (6 marks) b) Given that A is the set of odd numbers less than 20 and B is the set of prime number less than 20, list the members of (4 marks)
(i) A (ii) B (iii) A?B (iv) A?B
4
QUESTION SIX
a) Solve the equation using the determinant method (4 marks) 3x+4y=18 x+2y=8 b) Estimate the area enclosed by the curve y=1 2 ??2 + 1, x=0, x=4 and the x-axis using the trapezium rule (6 marks)
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