Mathematics for Business Modelling Sample Questions
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1. Find the inverse of the following matrices using the reduced row echelon technique:

2 3 -1 0 0 1

A = 1 1 1 B = 0 1 0

0 2 -1 1 0 0

20 Marks

2. Find the inverse of both

1 -4 1 -2

A = B =

2 -1 3 -2

to determine A^-1 - B^-1

20 Marks

3. Find the limit of:

a) lim ( (2x + 5 )/ x + 6))

5 Marks

2x² – 3x if x ¹ 1

b) lim f(x) when f(x) =

5 if x = 1

15 Marks

4. Determine whether the function is continuous at 1:

3x – 1 if x < 1

a) f(x) = 4 if x = 1

2x if x > 1

10 Marks

3x – 1 if x < 1

b) f(x) = 2 if x = 1

2x if x > 1

10 Marks

5. a) Find the point(s), if any, on the graph of the function y = 4x² at which the tangent line is parallel to the line 2x – y – 6 = 0.

10 Marks

b) Two lines through the point (0,2) are tangent to the graph of the function y = 2x² – 4x + 1. Find the equations of these two lines.

10 Marks

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1. Mathematics for Business Modelling Sample Questions

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