INTRODUCTION TO MATHEMATICS

1. a) Given the following sets:

A= (5, 6, 7, 9)

B= (6, 8, 13, 14)

C= (6, 7)

Find

i)AuB            ii) AnB               iii) AuBuC              iv) AnBnC                            (4mks)

1. ii) Represent the above solutions using venn diagrams          (6mks)
2. c) Compute the y and the x intercepts for the following:
3. i) y= 3+1/3x  (2mks

ii)y= -4 + 3x                                                                                                          (2mks)

iii) y= -8 -2x                                                                                                           (2mks)

 

d)Solve by graphical method and comment on your results

1. i) x + z =12 ii)4x – 2y =5

x – z =0                                                   x-2y =-4

x +y =10                                                    (9mks)

2. A single commodity market model is defined by the following equations:

Q_d =25 -3/4p

Q_s = -8 + 5/8p

1. Find the equilibrium quantity and price                      (5mks)
2. Explain what is likely to happen when the price level is at p=27 and p= 20,

and when Q_s is at q_s =10 and q_s =5 and q_d=10                                                                 (10mks)

 

3. Solve the following simultaneous equations using both elimination and substitution techniques
4. i) 5x + 2y = -5 ii)1/y – 3/x = 4      iii) 3x + y = 15

-3x + 4y =29                               3/y -4/x = -14                       x + 1/3 y = 2                  (15mks)

4. Determine the derivative of:
5. i) y = 13 + 2x² ii) y = x^-1 iii) y = 3x² – x + 17   iv) y = 5x ^1/5 –x +3
6. v) y = x³ – 2x⁴ + 16                  (15mks)
7. Find the 1^st,2^nd and 3^rd leading principal sub-matrices of the following
8. i) A =2 1 0 ii) A= aij     ij= 1,2,…4                iii) B=3  1  1

3   2   1                                                                         2  1  2

1   2   4                                                                        4   0   3                              (15mks)

 

6. Find the determinants of:
7. i) A= 12 3                       ii) A =  1  2  3                  iii) A =  3  0  0

5   10                                   4  0  5                                2  2  0

2  1  6                               4  3  1                             (15mks)