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Revision:Mathematics for Business Modelling Sample Questions

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Question 1

Find the inverse of the following matrices using the reduced row echelon technique:

\bf{A} = \begin{pmatrix}2&3&-1\\1&1&1\\0&2&-1\\ \end{pmatrix}


\bf{B} = \begin{pmatrix}0&0&1\\0&1&0\\1&0&0\\ \end{pmatrix}


20 Marks


Question 2

Find the inverse of both

\bf{A} = \begin{pmatrix}1&-4\\2&1\\ \end{pmatrix}


\bf{B} = \begin{pmatrix}1&-2\\3&-2\ \end{pmatrix}


to determine \bf{A}^{-1} - \bf{B}^{-1}


20 Marks


Question 3

Find the limit of:

a) \displaystyle \lim \frac{2x + 5}{x + 6}


5 Marks


b) \lim f(x) when

f(x) = \begin{cases}2x^2 - 3x & \mathrm{if}\ x \neq 1\\5& \mathrm{if}\ x = 1\\ \end{cases}


15 Marks


Question 4

Determine whether the function is continuous at 1:

a) f(x) = \begin{cases}3x - 1 & \mathrm{if}\ x < 1\\4& \mathrm{if}\ x = 1\\2x & \mathrm{if}\ x > 1 \end{cases}


10 Marks


b) f(x) = \begin{cases}3x - 1 & \mathrm{if}\ x < 1\\2& \mathrm{if}\ x = 1\\2x & \mathrm{if}\ x > 1 \end{cases}


10 Marks


Question 5

a) Find the point(s), if any, on the graph of the function y = 4x^2 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 = 2x^2 – 4x + 1. Find the equations of these two lines.

10 Marks


Comments

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