endobj endobj 36 0 obj /Type /Annot Helpful Websites . << /S /GoTo /D (section.4) >> /Font << /F17 55 0 R /F18 56 0 R >> /A << /S /GoTo /D (section.12) >> << /S /GoTo /D (section.12) >> What is Algebra Algebraic thinking spans all areas of mathematics. In this chapter, the basic algebraic structures (groups, rings, fields, vector spaces) are reviewed, with a major emphasis on vector spaces. endobj >> /A << /S /GoTo /D (section.7) >> Working with fractions is a very important foundation to algebra. << /S /GoTo /D (section.10) >> 49 0 obj /Rect [71.004 361.793 349.72 374.412] (Linear Inequalities and Their Graphs) 13 0 obj Glossary 3. /Rect [71.004 506.997 287.952 519.617] /Rect [71.004 332.752 310.076 345.371] Y�e@�$��('��x��{��P(�gѦH3zU�Y�5b�"_y��r05K>��*���\�G���`C��҃K��#_�@�zɀ2�`\�! Writing reinforces Maths learnt. /MediaBox [0 0 612 792] Simplifying Equations: Using Expansion 7. Linear algebra is one of the most applicable areas of mathematics. 1034 0 obj <>stream /Subtype /Link Coordinates The plane of points that can be graphed in 2 dimensions is called the Rectangular Coordinate Plane or the Cartesian This book is directed more at the former audience than the latter, but it is hoped that the writing is sufficiently clear with ����B��Kj1��2B�Ocy��u���G%��>1 g��� 8��>T! Introduction to School Algebra [Draft] H. Wu July 24, 2010 Department of Mathematics, #3840 University of California Berkeley, CA 94720-3840 wu@math.berkeley.edu << /S /GoTo /D [50 0 R /Fit ] >> 17 0 obj /D [73 0 R /XYZ 110.851 721 null] (Quadratic Functions and Their Graphs) /Subtype /Link /A << /S /GoTo /D (section.3) >> /Filter /FlateDecode /A << /S /GoTo /D (section.4) >> endobj o��K�C�1h��,TU�ò%W�R0_*V�����ʗ�u�Y�DVp�c��8g�|�K�� �P����#J�+^�q��p����a��.lw~�����n���߁&�vqu�ď����[mw��ua��8'���n���O�|��T��8~�]����7z����+|\��� >> endobj /Type /Annot Algebra Basics Words and symbols Algebra uses letters or symbols called variables. /A << /S /GoTo /D (section.5) >> endobj /Rect [71.004 274.67 320.295 287.289] /Border[0 0 1]/H/I/C[1 0 0] You probably always understood this, even as a little baby. Simplifying Equations with Exponents 8. 63 0 obj << 37 0 obj /Border[0 0 1]/H/I/C[1 0 0] 12 0 obj endobj h�b```�NV�z!��2�0p400I0H8|� (Some Word Problems) 21 0 obj /Length 380 25 0 obj 80 0 obj << >> endobj /Type /Annot /Subtype /Link Addition & Multiplication Properties 5. endobj 32 0 obj /Border[0 0 1]/H/I/C[1 0 0] Special thanks to: My beautiful wife, Nicole Wallace who spent countless hours typing problems and my two wonderful kids for their patience and support during this project Another thanks goes to the faculty reviewers who reviewed this text: Donna Brown, Michelle /Type /Annot /Border[0 0 1]/H/I/C[1 0 0] If you were told that +4=10, you can probably see straight away that =6. >> endobj xڅXK�ܸ��W����ޛĀX ��!΁+�[�Hb/I��9䷧^��X�\D�X,ɯ^��뇗�e���i�����ᩨ��,ڧ��Ӽ+�^��$�8}P�����//���)��}]���7]�6��sѤMS������s��Il7^��=0a�}X���b�~���]�,��M���gh���]D\�S#��I����7'�� A����l�a�#�ڴ��Ԗpt�D�m����%�v>�=�]�| 8U%��uF�Oq�X�>Oz8j&ṱ=9�L��jNؕ�>�o��^X�Yd�Qd�sLXr ��,��L�]�M�xܑ�8�~~y�U����ڽ���/;8k����?��4 ��� ��d8. What is Algebra 2. As this is a review, concepts will not be explained in detail as other lessons are. endobj >> endobj 66 0 obj << /Subtype /Link endobj 62 0 obj << 44 0 obj /Type /Annot /Contents 74 0 R %%EOF 75 0 obj << (Linear Equations in One Variable) /Type /Annot xڕT���0��+r��G@�h�J�����M��R;8���g\���Y�\b;�y���o�ūk�ʂc%�v�I�UJ���&� /Subtype /Link Algebraic expressions with an equals sign ‘=’ are called equations. /Rect [71.004 451.24 218.788 461.535] %PDF-1.4 74 0 obj << endobj Basic notions of linear algebra such as vector spaces, subspaces, linear combinations, linear independence, /Subtype /Link endobj Answers 9. (Transcription of Verbal Information into Symbolic Language) endobj (Simultaneous Linear Equations) h��X[S�8������&����d' 2[(%��ayp5�:v�vJ�����M�exه�dN$��')R8�a�3����J`�'��� �g;��Î R���D�vq����+m�!���AÞ�� Let's look at another similar expression. Special thanks to: My beautiful wife, Nicole Wallace who spent countless hours typing problems and my two wonderful kids for their patience and :zy��V���Ud�O�N�] �2�*�t^n5t�* �% ��?nܣGF/�wIBƢc��P�A8-�)��̭�n�|_�r�9���p:�O�E=B�w���|v��E%�L�=�]��v��)�e���. These worksheets contain pre-algebra & Algebra exercises suitable for preschool, kindergarten, first grade to eigth graders levels . 72 0 obj << (Exponents) endobj endobj 995 0 obj <> endobj /Type /Annot If you were told that −7=5, you can probably see straight away that =12. /Type /Annot endobj 45 0 obj /Border[0 0 1]/H/I/C[1 0 0] In fact the first mathematical concepts we ever encounter are the foundation of the subject. << /S /GoTo /D (section.11) >> >> endobj Chapter 1 Basics Algebra Graphing with Coordinates Graphs in two dimensions are very common in algebra and are one of the most common algebra applications in real life.