Tuesday, December 5, 2023

Mat 1033 Intermediate Algebra

Intermediate Algebra Final Exam Study Guide

;Four hours lecture per week. Prerequisite: MAT 0024, MAT 0028, MAT 0057 or equivalent. This course includes an introduction to functions, the study of real numbers, linear and quadratic equations, linear inequalities, systems of linear equations, exponents, polynomials, factoring, rational expressions and related equations, radicals, quadratic formula, complex numbers, graphing and applications. This course includes the study of real numbers, linear and quadratic equations, linear inequalities, systems of linear equations, exponents, polynomials, factoring, rational expressions and related equations, radicals, quadratic formula, completing the square, complex numbers, absolute value, graphing and applications. Additional special fees are required.

Questions From Chapters 4 To 6

• \begin \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &2x&+&5y&=&-18 \\ +&-2x&+&y&=&6 \\ \hline &&&\dfrac&=&\dfrac \\ \\ &&&y&=&-2 \\ \\ &\therefore y&-&6&=&2x \\ &-2&-&6&=&2x \\ &&&2x&=&-8 \\ &&&x&=&-4 \endAnswer:
• \begin \begin \\ \\ \\ \\ \\ \\ \\ \\ \\ & \\ & \\ \\ &-16x&-&14y&=&-102 \\ +&35x&+&14y&=&\phantom140 \\ \hline &&&\dfrac&=&\dfrac \\ \\ &&&x&=&2 \\ \\ \end & \hspace \begin \\ \\ \\ \\ \\ \therefore 5x&+&2y&=&20 \\ 5&+&2y&=&20 \\ 10&+&2y&=&20 \\ -10&&&&-10 \\ \hline &&2y&=&10 \\ &&y&=&5 \end \endAnswer:
• \begin \\ \\ \\ \\ \\ \\ \begin \\ \\ \\ \\ &-2x&-&2y&-&12z&=&-10 \\ +&2x&&&-&3z&=&\phantom4 \\ \hline &&& \\ &&& \\ \\ &&&-6y&-&45z&=&-18 \\ &&+&6y&+&8z&=&\phantom18 \\ \hline &&&&&-37z&=&0 \\ &&&&&z&=&0 \\ \\ \end &\hspace \begin 2x&-&\cancel0&=&4 \\ &&x&=&\dfrac\text2 \\ \\ 3y&+&\cancel0&=&9 \\ &&y&=&\dfrac\text3 \end \endAnswer
• \begin \\ \\ 24+\1\}+3x \\ 24-3x-1+3x \\ 23 \end
• 2ab^3\Rightarrow 2a^3b^3-32ab^3
• \begin \\ \\ \\ \\ \\ \\ ^ \\ \\ ^ \\ \\ x^y^7 \\ \\ \dfrac \end
• \begin \\ \\ 3x^2+3x+8x+8 \\ 3x+8 \\ \end
• ^3-y^3\Rightarrow
• \begin \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ & \\ & \\ \\ &-370A&-&370B&=&-18500 \\ +&395A&+&370B&=&\phantom19125 \\ \hline &&&25A&=&625 \\ \\ &&&A&=&\dfrac\text25 \\ \\ &A&+&B&=&50 \\ &25&+&B&=&50 \\ &&&B&=&25 \\ \end
• \begin \\ \\ \\ \\ \\ \\ \\ \\ \\ & \\ &10d&+&25q&=&235 \\ \\ &-10d&-&10q&=&-160 \\ +&10d&+&25q&=&\phantom235 \\ \hline &&&\dfrac&=&\dfrac \\ \\ &&&q&=&5 \\ &&&\therefore d&=&16-5=11 \\ \end
• Questions From Chapters 7 To 10

• \dfrac3s^2}}1}\cdot \dfrac1\cancel}1\cancel}\cdot \dfrac}2\cancel}\Rightarrow \dfrac
• \begin \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \text= \\ \\ \dfrac \\ \\ \dfrac \\ \\ \dfrac \\ \\ \dfrac \end
• \begin \dfrac-9\right)y^3}\right)y^3}\Rightarrow \dfrac\Rightarrow \dfrac\Rightarrow \dfrac}} \\ \\ \Rightarrow y \end
• \begin \\ \\ \\ \\ 3\cdot 5\sqrt-2\sqrt-\sqrt \\ \\ 15\sqrt-2\cdot 6\sqrt-4x\sqrt \\ \\ 15\sqrt-12\sqrt-4x\sqrt \end
• \dfrac}}}}\Rightarrow \dfrac}\cdot \dfrac}}\Rightarrow \dfrac}
• \left^}\Rightarrow \dfrac}}}d^}}\Rightarrow \dfrac}\Rightarrow \dfrac
• \begin \\ =0 \\ x=5,-1 \end
• \begin \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &&&^2&=&^2 \\ \\ &x^2&-&6x&+&9&=&\phantomx^2 \\ -&x^2&&&&&&-x^2 \\ \hline &&&-6x&+&9&=&0 \\ \\ &&&&&\dfrac&=&\dfrac \\ \\ &&&&&x&=&\dfrac \end
• \begin \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ A&=&\dfracbh \\ \\ 20&=&\dfrach \\ \\ 40&=&h^2+6h \\ \\ 0&=&h^2+6h-40 \\ 0&=&h^2+10h-4h-40 \\ 0&=&h-4 \\ 0&=& \\ \\ h&=&4, \cancel \\ b&=&4+6=10 \end
• \phantomx, x+2, x+4 \\\begin &&&&x&=&\phantom8&+&6 \\ x^2&+&2x&&&&&=&\phantom8&+&6x&+&24 \\ &-&6x&-&8&-&24&&-8&-&6x&-&24 \\ \hline &&x^2&-&4x&-&32&=&0&&&& \\ \\ x^2&+&4x&-&8x&-&32&=&0&&&& \\ x&-&8&=&0&&&& \\ &&&=&0&&&& \\ &&&&&&x&=&-4,8&&&& \end\phantom
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Questions From Chapters 1 To 3

• \begin \\ \\ \\ \\ \\ \\ –\sqrt \\ \\ -6-\sqrt \\ \\ -6-\sqrt \\ \\ -6-2=-8 \end
• \begin \\ \\ \\ \\ 6x&+&24&=&35&-&5x&-&8&+&12x \\ 6x&+&24&=&27&+&7x&&&& \\ -7x&-&24&&-24&-&7x&&&& \\ \hline &&-x&=&3&&&&&& \\ &&\therefore x&=&-3&&&&&& \\ \end
• \phantom\left \\\begin 2&-&1&=&x&+&2 \\ 2x&+&8&-&2&=&x&+&2 \\ -x&-&8&+&2&&-x&-&8+2 \\ \hline &&&&x&=&-4&& \end
• x=-2
• \begin \\ \\ \\ \\ \\ \\ d^2&=&\Delta x^2+\Delta y^2 \\ &=&^2+^2 \\ &=&6^2+8^2 \\ &=&36+64 \\ &=&100 \\ \\ \therefore d&=&\sqrt=10 \end
• 2x-3y=6
• \text7,9
• Questions From Chapters 7 To 9

In problems 13, perform the indicated operations and simplify.

For questions 46, simplify each expression.

For questions 7 and 8, solve by any convenient method.

In problems 9 and 10, find the solution set of each system by any convenient method.

• The length of a rectangle is 5 cm longer than twice the width. If the area of the rectangle is 75 cm2, find its length and width.
• Find three consecutive odd integers such that the product of the first and the second is 25 less than 8 times the third.
• <a class=internal href=/intermediatealgebraberg/back-matter/final-exam-version-b-answer-key/>Final Exam: Version B

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