|
|
|
|
|
|
|
¸ñÂ÷ |
|
Preface 2
ÀúÀÚ ¼Ò°³ 3
ÀÌ Ã¥ÀÇ ±¸¼º°ú Ư¡ 4
Topic 1 Basic Elements of Geometry
1.1 Points, Lines, and Planes................................................... 10
1.2 Collinear or Coplanar Points.............................................. 11
1.3 Line, Segment, and Ray..................................................... 12
1.4 Midpoint and Bisector of a Segment.................................. 14
1.5 Coordinate Plane................................................................ 16
1.6 Angle and Its Measure....................................................... 18
1.7 Congruent Angles.............................................................. 19
1.8 Bisector of an Angle.......................................................... 20
1.9 Angle Relationship............................................................ 21
Topic 2 Relationship between Point, Line, and Plane
2.1 Point and Line.................................................................... 24
2.2 Two Lines on a Plane......................................................... 25
2.3 What forms a Plane?.......................................................... 26
2.4 Two Lines in a Space......................................................... 27
2.5 Plane and Line in a Space.................................................. 28
2.6 Plane and Plane in a Space................................................. 29
2.7 Summary : Postulates about Points, Lines, and Planes...... 30
Topic 3 Mathematical Reasoning
3.1 Induction and Deduction.................................................... 32
3.2 Truth Tables....................................................................... 33
3.3 Tools for Deduction : Law of Detachment and of Syllogism. 36
3.4 Algebraic Proof and Geometric Proof................................ 37
3.5 Proving Segment Relationships......................................... 38
3.6 Proving Angle Relationships.............................................. 40
Topic 4 Parallel and Perpendicular Lines
4.1 Parallel Lines and Transversal........................................... 48
4.2 Parallel Line Property........................................................ 49
4.3 Slope of Lines.................................................................... 52
4.4 Proof about Parallel Lines.................................................. 54
4.5 Distance Formula Revisited............................................... 57
Topic 5 Congruent Triangles
5.1 Basic Classification of Triangles........................................ 60
5.2 Interior Angle Sum / Exterior Angle Theorem................... 61
5.3 Congruent Triangles........................................................... 63
5.4 Congruence Postulates....................................................... 65
5.5 Finding Congruent Triangles in Isosceles Triangle............ 69
Topic 6 Triangle Properties............................................... 73
6.1 Angle Bisector Theorem.................................................... 74
6.2 Points of Concurrency....................................................... 76
6.3 Properties of Right Triangle............................................... 81
6.4 Triangular Inequality......................................................... 83
Topic 7 Similar Triangles
7.1 Similar Triangles................................................................ 88
7.2 Attacking Similar Triangle Problems................................. 90
7.3 Ratio of Similar Figures..................................................... 92
Topic 8 Quadrilateral
8.1 Quadrilateral...................................................................... 94
8.2 Trapezoid........................................................................... 95
8.3 Parallelogram..................................................................... 97
8.4 Rhombus............................................................................ 99
8.5 Rectangle........................................................................... 101
8.6 Square................................................................................ 103
Topic 9 Polygons
9.1 Polygon.............................................................................. 106
9.2 Finding Angles................................................................... 107
9.3 Area of Polygon................................................................. 109
9.4 Diagonals of Polygons....................................................... 113
Topic 10 Circles
10.1 Terminology....................................................................... 116
10.2 Arcs, Angles and Chords.................................................... 117
10.3 Power of a Point Theorem................................................. 127
Topic 11 Transformation
11.1 Translation......................................................................... 130
11.2 Rotation............................................................................. 132
11.3 Reflection........................................................................... 135
11.4 Dilation.............................................................................. 138
Topic 12 Solid Figures
12.1 Polyhedron......................................................................... 142
12.2 Solid of Revolution............................................................ 144
Topic 13 Surface Area and Volume
13.1 Surface Area...................................................................... 150
13.2 Volume............................................................................... 153
Topic 14 Trigonometric Ratio
14.1 Basic Ratio......................................................................... 156
14.2 Extension of Basic Ratio.................................................... 158
Solution to 120 Exercises 161 |
|
|
|
ÀúÀÚ
|
|
À¯Çϸ²
¹Ì±¹ Northwestern University, B.A. in Mathematics and Economics (³ë½º¿þ½ºÅÏ ´ëÇб³ ¼öÇаú/°æÁ¦Çаú Á¹¾÷) ¸¶½ºÅÍÇÁ·¾ ¼öÇпµ¿ª ´ëÇ¥°»ç ¾Ð±¸Á¤ ÇöÀå°ÀÇ ReachPrep ¿øÀå
°íµîÇб³ ½ÃÀý ¹®°ú¿´´Ù°¡, ¹Ì±¹ ³ë½º¿þ½ºÅÏ ´ëÇб³ ÇкΠ½ÃÀý ÀçÇÐ Áß ¼öÇп¡ ¸Å ·áµÇ¾î, Calculus ¹× Multivariable Calculus Á¶±³ È°µ¿ ¹× ¼öÇÐ °ÀÇ È°µ¿À» ÇØ¿Â ¹®/ÀÌ°ú¸¦ ¾Æ¿ì¸£´Â µ¶Æ¯ÇÑ ÀÌ·ÂÀ» °¡Áø °»çÀÌ´Ù. ÇöÀç ¾Ð±¸Á¤ ¹Ì±¹¼öÇÐ/°úÇÐÀü¹® ÇпøÀ¸·Î ReachPrep(¸®Ä¡ÇÁ·¾)À» ¿î¿µ ÁßÀ̸ç, ¹Ì±¹ ¸í¹® º¸µù½ºÄð Çлýµé°ú ±¹³» ¿Ü±¹ÀÎÇб³ ¹× ±¹Á¦Çб³ ÇлýµéÀ» ²ÙÁØÈ÷ ÁöµµÇÏ¸é¼ ¸í¼ºÀ» ½×¾Æ°¡°í ÀÖ´Ù. 2010³â ÀÚ±âÁÖµµÇнÀ¼ÀÎ ¡°¸ôÀÔ°øºÎ¡±¸¦ ÁýÇÊÇÑ ÀÌÈÄ, ¹Ì±¹ Áß°í±³¼öÇп¡ °ü½ÉÀ» º» °ÝÀûÀ¸·Î °¡Áö°Ô µÇ¾ú°í, ÇöÀç À¯Çϸ²Ä¿¸®Å§·³ Essential Math Series¸¦ ÁýÇÊÇÏ¿©, ¾Ð±¸Á¤ ÇöÀå°ÀÇ ¹Ì±¹¼öÇÐÇÁ¸®Æнº¸¦ ÅëÇØ, ¾ÐµµÀûÀ¸·Î ¸¹Àº ÇлýµéÀÇ Çǵå¹éÀ» Åë ÇØ, ¹ßÀüÀûÀ¸·Î ±³Àç ÁýÇÊ¿¡ Èû¾²°í ÀÖ´Ù. À¯ÇÐºÐ¾ß ÀÎÅÍ³Ý °ÀÇ 1À§ »çÀÌÆ®ÀÎ ¸¶½ºÅÍÇÁ·¾ ¼öÇпµ¿ª ´ëÇ¥°»ç Áß ÇÑ ¸íÀ¸·Î ¹Ì ±¹ ¼öÇÐ Ä¿¸®Å§·³ÀÇ ±âÃʼöÇкÎÅÍ °æ½Ã¼öÇбîÁö ¸ðµÎ ¿µ¾î¿Í Çѱ¹¾î·Î °ÀÇÇϸé¼, ½ÇÀü °æÇèÀ» ½×¾Æ ±× Àü¹®¼ºÀ» È®°íÈ÷ ÇÏ°í ÀÖ´Ù.
[Àú ¼] ¸ôÀÔ°øºÎ The Essential Workbook for SAT Math Level 2
Essential Math Series ½Ã¸®Áî
|
¸ôÀÔ°øºÎ | À¯Çϸ² | ·£´ýÇϿ콺ÄÚ¸®¾Æ
The Essential Guide to Precalculus | À¯Çϸ² | Ç츣¸óÇϿ콺
The Essential Guide to Competition Math | À¯Çϸ² | Ç츣¸óÇϿ콺
The Essential Guide to Prealgebra | À¯Çϸ² | Ç츣¸óÇϿ콺
The Essential Workbook for SAT MATH LEVEL 2 | À¯Çϸ² | ÀÌ´ãºÏ½º
|
|
À¯Çϸ²
À¯Çϸ²Àº 2009³â °ø±³À° ¼º°ø»ç·Ê ¼ö±â°ø¸ðÀü ¿ì¼ö»óÀ» ¹Þ°í, ³ë½º¿þ½ºÅÏ ´ëÇб³ (Northwestern University) °æÁ¦Çаú/¼öÇаú º¹¼ö Àü°øÀ¸·Î 2012³â Çлç Á¹¾÷ÇÏ¿´´Ù. ÀÚ±âÁÖµµÀû ¹Ì±¹ ÇкΠÀ¯ÇÐ Áغñ¼ "¸ôÀÔ°øºÎ" (·£´ýÇϿ콺, 2010) ÀúÀÚ·Î, ¼¿ï ´ëÄ¡µ¿/¾Ð±¸Á¤ SAT Àü¹®Çпø ¼öÇÐ °»ç·Î È°µ¿Çϸç, ¾Æ¸¶Á¸´åÄÄ¿¡¼ ¹Ì±¹ Áß/°í±³¼öÇÐ Àü¹®±³Àç ½Ã¸®Áî Essential Math Series ÁýÇÊÀ» ÇÏ°í ÀÖ´Ù. ÇöÀç ¸¶½ºÅÍÇÁ·¾ (MasterPrep) Àΰ °»ç·Î È°µ¿ÇÏ°í, ¾Ð±¸Á¤ ¸®Ä¡ÇÁ·¾(Reach Prep) ¿øÀåÀÌ´Ù
|
The Essential Guide to Prealgebra | À¯Çϸ² | Ç츣¸óÇϿ콺
Number Theory | À¯Çϸ² | Ç츣¸óÇϿ콺
Counting and Probability | À¯Çϸ² | Ç츣¸óÇϿ콺
|
|
|
|
|
|
|
Ãâ°í¾È³» |
|
|
Ãâ°í¶õ ÀÎÅÍÆÄÅ© ¹°·ùâ°í¿¡¼ µµ¼°¡ Æ÷ÀåµÇ¾î ³ª°¡´Â ½ÃÁ¡À» ¸»Çϸç, ½ÇÁ¦ °í°´´Ô²²¼ ¼ö·ÉÇϽô ½Ã°£Àº »óÇ°Áغñ¿Ï·áÇØ Ãâ°íÇÑ ³¯Â¥ + Åùè»ç ¹è¼ÛÀÏÀÔ´Ï´Ù. |
|
ÀÎÅÍÆÄÅ© µµ¼´Â ¸ðµç »óÇ°ÀÇ Àç°í°¡ ÃæÁ·ÇÒ ½Ã¿¡ ÀÏ°ý Ãâ°í¸¦ ÇÕ´Ï´Ù. |
|
ÀϺΠÀç°í¿¡ ´ëÇÑ Ãâ°í°¡ ÇÊ¿äÇÒ ½Ã¿¡´Â ´ã´çÀÚ¿¡°Ô Á÷Á¢ ¿¬¶ôÇϽðųª, °í°´¼¾ÅÍ(°í°´¼¾ÅÍ(1577-2555)·Î ¿¬¶ôÁֽñ⠹ٶø´Ï´Ù. |
|
¹è¼Ûºñ ¾È³» |
|
|
ÀÎÅÍÆÄÅ© µµ¼ ´ë·®±¸¸Å´Â ¹è¼Û·á°¡ ¹«·áÀÔ´Ï´Ù. |
|
´Ü, 1°³ÀÇ »óÇ°À» ´Ù¼öÀÇ ¹è¼ÛÁö·Î ÀÏ°ý ¹ß¼Û½Ã¿¡´Â 1°³ÀÇ ¹è¼ÛÁö´ç 2,000¿øÀÇ ¹è¼Ûºñ°¡ ºÎ°úµË´Ï´Ù. |
¾Ë¾ÆµÎ¼¼¿ä! |
|
|
°í°´´Ô²²¼ ÁÖ¹®ÇϽŠµµ¼¶óµµ µµ¸Å»ó ¹× ÃâÆÇ»ç »çÁ¤¿¡ µû¶ó Ç°Àý/ÀýÆÇ µîÀÇ »çÀ¯·Î Ãë¼ÒµÉ ¼ö ÀÖ½À´Ï´Ù. |
|
Åùè»ç ¹è¼ÛÀÏÀÎ ¼¿ï ¹× ¼öµµ±ÇÀº 1~2ÀÏ, Áö¹æÀº 2~3ÀÏ, µµ¼, »ê°£, ±ººÎ´ë´Â 3ÀÏ ÀÌ»óÀÇ ½Ã°£ÀÌ ¼Ò¿äµË´Ï´Ù.
(´Ü, Åä/ÀÏ¿äÀÏ Á¦¿Ü) |
|
|
|
|
ÀÎÅÍÆÄÅ©µµ¼´Â °í°´´ÔÀÇ ´Ü¼ø º¯½É¿¡ ÀÇÇÑ ±³È¯°ú ¹ÝÇ°¿¡ µå´Â ºñ¿ëÀº °í°´´ÔÀÌ ÁöºÒÄÉ µË´Ï´Ù.
´Ü, »óÇ°À̳ª ¼ºñ½º ÀÚüÀÇ ÇÏÀÚ·Î ÀÎÇÑ ±³È¯ ¹× ¹ÝÇ°Àº ¹«·á·Î ¹ÝÇ° µË´Ï´Ù.
±³È¯/¹ÝÇ°/º¸ÁõÁ¶°Ç ¹× Ç°Áúº¸Áõ ±âÁØÀº ¼ÒºñÀڱ⺻¹ý¿¡ µû¸¥ ¼ÒºñÀÚ ºÐÀï ÇØ°á ±âÁØ¿¡ µû¶ó ÇÇÇظ¦ º¸»ó ¹ÞÀ» ¼ö ÀÖ½À´Ï´Ù.
Á¤È®ÇÑ È¯ºÒ ¹æ¹ý ¹× ȯºÒÀÌ Áö¿¬µÉ °æ¿ì 1:1¹®ÀÇ °Ô½ÃÆÇ ¶Ç´Â °í°´¼¾ÅÍ(1577-2555)·Î ¿¬¶ô Áֽñ⠹ٶø´Ï´Ù.
¼ÒºñÀÚ ÇÇÇغ¸»óÀÇ ºÐÀïó¸® µî¿¡ °üÇÑ »çÇ×Àº ¼ÒºñÀÚºÐÀïÇØ°á±âÁØ(°øÁ¤°Å·¡À§¿øȸ °í½Ã)¿¡ µû¶ó ºñÇØ º¸»ó ¹ÞÀ» ¼ö ÀÖ½À´Ï´Ù.
|
±³È¯ ¹× ¹ÝÇ°ÀÌ °¡´ÉÇÑ °æ¿ì |
|
|
»óÇ°À» °ø±Þ ¹ÞÀ¸½Å ³¯·ÎºÎÅÍ 7ÀÏÀ̳» °¡´ÉÇÕ´Ï´Ù. |
|
°ø±Þ¹ÞÀ¸½Å »óÇ°ÀÇ ³»¿ëÀÌ Ç¥½Ã, ±¤°í ³»¿ë°ú ´Ù¸£°Å³ª ´Ù¸£°Ô ÀÌÇàµÈ °æ¿ì¿¡´Â °ø±Þ¹ÞÀº ³¯·ÎºÎÅÍ 3°³¿ùÀ̳», ±×»ç½ÇÀ» ¾Ë°Ô µÈ ³¯ ¶Ç´Â ¾Ë ¼ö ÀÖ¾ú´ø ³¯·ÎºÎÅÍ 30ÀÏÀ̳» °¡´ÉÇÕ´Ï´Ù. |
|
»óÇ°¿¡ ¾Æ¹«·± ÇÏÀÚ°¡ ¾ø´Â °æ¿ì ¼ÒºñÀÚÀÇ °í°´º¯½É¿¡ ÀÇÇÑ ±³È¯Àº »óÇ°ÀÇ Æ÷Àå»óÅ µîÀÌ ÀüÇô ¼Õ»óµÇÁö ¾ÊÀº °æ¿ì¿¡ ÇÑÇÏ¿© °¡´ÉÇÕ´Ï´Ù.
|
|
|
|
±³È¯ ¹× ¹ÝÇ°ÀÌ ºÒ°¡´ÉÇÑ °æ¿ì |
|
|
|
°í°´´ÔÀÇ Ã¥ÀÓ ÀÖ´Â »çÀ¯·Î »óÇ° µîÀÌ ¸ê½Ç ¶Ç´Â ÈÑ¼ÕµÈ °æ¿ì´Â ºÒ°¡´ÉÇÕ´Ï´Ù. (´Ü, »óÇ°ÀÇ ³»¿ëÀ» È®ÀÎÇϱâ À§ÇÏ¿© Æ÷Àå µîÀ» ÈѼÕÇÑ °æ¿ì´Â Á¦¿Ü) |
|
½Ã°£ÀÌ Áö³²¿¡ µû¶ó ÀçÆǸŰ¡ °ï¶õÇÒ Á¤µµ·Î ¹°Ç°ÀÇ °¡Ä¡°¡ ¶³¾îÁø °æ¿ì´Â ºÒ°¡´ÉÇÕ´Ï´Ù. |
|
Æ÷Àå °³ºÀµÇ¾î »óÇ° °¡Ä¡°¡ ÈÑ¼ÕµÈ °æ¿ì´Â ºÒ°¡´ÉÇÕ´Ï´Ù. |
|
|
´Ù¹è¼ÛÁöÀÇ °æ¿ì ¹ÝÇ° ȯºÒ |
|
|
|
´Ù¹è¼ÛÁöÀÇ °æ¿ì ´Ù¸¥ Áö¿ªÀÇ ¹ÝÇ°À» µ¿½Ã¿¡ ÁøÇàÇÒ ¼ö ¾ø½À´Ï´Ù. |
|
1°³ Áö¿ªÀÇ ¹ÝÇ°ÀÌ ¿Ï·áµÈ ÈÄ ´Ù¸¥ Áö¿ª ¹ÝÇ°À» ÁøÇàÇÒ ¼ö ÀÖÀ¸¹Ç·Î, ÀÌÁ¡ ¾çÇØÇØ Áֽñ⠹ٶø´Ï´Ù. |
|
|
|
|
|
|