locus mathematics pdf

Locus (mathematics): | | ||| | Each curve in this example is a |locus| defined as the... World Heritage Encyclopedia, the aggregation of the largest online encyclopedias available, and the most definitive collection ever assembled. �\}��!�b�p=T��t�9�W�g� cl_��=�u�(�P}kh��B?f �IHb��}�zX�PH� �2��@�5�m�Ϡ�BX�k �0`d0��K�ߦ�ӣ�U��ޓ��ۍ� � h9� :�t��TP>��pj��Q��g� V��`�l�b�^��s�Ů &�'�.ϻo��b��m�@8��M�L��h3��^�� Mathematics (Linear) – 1MA0 LOCI & CONSTRUCTIONS Materials required for examination Items included with question papers Ruler graduated in centimetres and Nil millimetres, protractor, compasses, pen, HB pencil, eraser. xref 0000007432 00000 n We look at a map of the area and plot out all the The tip of each hand is always the same distance - equidistant - from the centre of the clock. 0 For example, the locus of points that are 1cm from the origin is a circle of radius 1cm centred on the origin, since all points on this circle are 1cm from the origin. Fill in the boxes at the top of this page. The hands of a clock move around the clock and create a locus. 0000017457 00000 n Example: A Circle is "the locus of points on a plane that are a certain distance from a central point". ��w�:d�X4�3B3�=o��_�B2�JdCI5QU�-�U:.��v]@�]�x�H,(�f2�*�A4UqG^��P[��f��~�8�ܡ�Jtˈws ��E�-�e-��e�Z ��n� b��.��y��h��A�s�]�w@�%��O�2k�� Z��Z �e�-�raX��7�v��,��n�$u� P lies on the perpendicular bisector of the line segment AB. DISCLAIMER : This website is created solely for Jee aspirants to download pdf, eBooks, study materials for free. 8751 0 obj <> endobj endstream endobj 8755 0 obj <>stream Further Maths; Practice Papers; Conundrums; Class Quizzes; Blog; About; Revision Cards; Books; April 4, 2018 August 12, 2019 corbettmaths. To prove. 0000035722 00000 n H��W[o��[�1�da��>;�� 0�>XA�]�,&��ʶ�|��̍K�b�֏�x��ι��wF�K�D��]|�F�w;��ɸ"��6�+�H֭��Lp�h��{�ݰ��4}f��V;��Wl۳�56�D��V��ŋ��i��=~�#�x��o��߼�d98��{�Ȅ:�Sj�(��7�4�h ��s 8848 0 obj <>stream unmodified PDF file as posted at the above website. 0000034878 00000 n JL��eH��I�"�bBz��@R��ë(2��1c�B��EB�Ij�Qy(�@gKrp�5��Za�-�U��J�>��%Z ��e�:�ir��;��Y O��MJ�qo This locus is called the perpendicular bisector locus. The problems of locus choice: Getting the right rate of evolution Example of insufficient evidence: metazoan UndeRSTAndIng ICSe MATheMATICS – X. THE GENERAL EQUATION OF THE LOCUS OF A PARABOLA WITH VERTEX NOT AT THE ORIGIN: CASE ONE (EXAMPLE): Find the locus of a point ( , )such that its distance from the point (ℎ,+)is equal to its distance from the line =−. IB Maths Exploration Guide. endstream endobj startxref Consider a more difficult example, look at … Common Types of Loci Perpendicular Bisector Locus. such that AP = BP. � �&�E�A$�_)�D��H�� R�5��p��º ��#)< D2�H&/� ��UJ��~)Ѐ`3��Y`7;�١`J��*0[L�L�ￌ��Aiا��$��2N Jb Locus Theorem 4: The locus of points equidistant from two parallel lines, l 1 and l 2, is a line parallel to both l 1 and l 2 and midway between them. h�bbd```b``q�� DrY�H��y,� For many practical applications, such paths (or “loci”) will normally be either straight lines or circles. A circle is defined as the set of points (or locus of points) a fixed distance away from a center point. Previous Constructions Practice Questions. 0000016267 00000 n Let z = x+jy denote a variable complex number (represented by the point (x,y) in the Argand Diagram). Tracing paper may be used. A locus is a set of points all of which share some common property. Locus (mathematics) Jump to navigation Jump to search. As P and Q are distinct points, then t z 1 – t 2t z 1 t y 4 1 * These solutions have been provided by projectmaths and are not supplied or endorsed by the Board of Studies Board of Studies: Notes from the Marking Centre 2 2 1 State Mean: 1.88/2 0.85/1 1.44/2 0.83/2 To determine a locus, you will need to do the following two steps. A locus (loci is the plural) is a collection of points which share a property. Two fixed points A and B, P is a moving point . 8790 0 obj <>/Filter/FlateDecode/ID[<1E74FC6065F911E6AA060023329F45EA><9DD14D5D2935F44D8EDE407F6F909807>]/Index[8751 98]/Info 8750 0 R/Length 165/Prev 399955/Root 8752 0 R/Size 8849/Type/XRef/W[1 3 1]>>stream The locus of a point which are equidistant from two fixed points is the perpendicular bisector of the straight line joining the two fixed points. The locus of a point, which is equidistant from two fixed points, is the perpendicular bisector of the line segment joining the two fixed points. ��H��f�g��Ȱ(%�WK��ZD�㱇0�,��$a�%�[0��r#4��:&�� lZ��ݧ�/�wk�^��k��8� ��n/p�-�tf5V�r�P�\`$�-�F�b�P%hM�� "O ��y� ��|�E}J�⌴�n��k�A�+�*�n��%��ʔ� 0000001489 00000 n This will help you describe the locus. Mathematics ofGPS Richard B. Langley University of New Brunswick cess of capturing the image - they can de vote all of their talents to the composition of the picture. A locus is a set of all the points whose position is defined by certain conditions. This set is called a locus. 0000010963 00000 n The hands of a clock move around the clock and create a locus. A very simple example is a circle. �X��`��!�Tj��;��T�]�gW�g�6��W�_��^x��e�DN�ӿ�KBT�ç��U>��X�n��|m�;��%UܭH\(�y%�37��$XǄ��X��y:_9۶+��_�_\|[�=��tz�с�Npf�-��*L�r � GCSE Revision … 0000018961 00000 n _��IUg��Ba8{)c�rFs�F�3�*e|)��9!��y��j�R{�V��E��?�ɛ ��ub��nEv2s�k��o�^\�n�Ǌ��Zz�ѻo9��R�=D�k�PT��7�3'�^|�aMc��H�1[Ehh��QNw�m��豌s��ApX��mS��R�#��, M�-=_�vʁb�F-X�#��a�k��>��1��>��z��S�'�M��RKX3��掬�c*T�1Q��xi��[e�� 0000020221 00000 n 0000006770 00000 n In Maths, a locus is the set of points represented by a particular rule or law or equation. <<0FB5E42C8471A141A63C8191A20D862F>]>> A locus is a set of points satisfying a certain condition. 0000030510 00000 n 0000019146 00000 n 0000004618 00000 n Perpendicular bisector. A locus of points can be described as finding all of the possible locations of a point given certain parameters. FREE (63) Popular paid resources. Mathematics / Geometry and measures / Construction, loci and scale drawing; 14-16; View more. 0000006410 00000 n h�b``�```�g`e`P�� Ȁ �,l@��)��Y��#3clBdӂ�1\�l� E�n��=2m��3+Vq[\(��n�f>�ՌךO,��ͳb��L�ȕ뚗�8��l��o�M��z��mV_��őǎ�c��:3�� Instructions Use black ink or ball-point pen. endstream endobj 8752 0 obj <>/Metadata 214 0 R/Outlines 381 0 R/Pages 8749 0 R/StructTreeRoot 402 0 R/Type/Catalog>> endobj 8753 0 obj <>/Font<>/ProcSet[/PDF/Text]/XObject<>>>/Rotate 0/StructParents 0/TrimBox[0.0 13.536 522.0 805.536]/Type/Page>> endobj 8754 0 obj <>stream }A�(�/��ؽ��o3I�FZ%�׻�]]"� ݿUÆ+��v�85��r 0000015077 00000 n Locus Theorem 5: The locus of points equidistant from two intersecting lines, l 1 and l 2, is a pair of bisectors that bisect the angles formed by l 1 and l 2. Here the locus is defining as the centre of any location. �o1Jұ��Ǿ>\�ֲoo��#yc�i��s�6D�y�9��\؉��՝�1!ҕ��bM��A2��p�+��P.� �ܟk��[�\\��Q��%N~v�H�@��/��4,�0��a3�XC>�^��T��V �,di��oR��'?�n�)/Rw�{ƫX��f��Z�Z�w8U�׭ ��x�S��:^� Theorem 14.1. keith1964two … the locus of R is x = . In geometry, a locus (plural: loci) is one of a set of points which satisfies one or more conditions. Tracing paper may be used. Next Cumulative Frequency Practice Questions. �p(�)�r��/Hv�5�s��E��q��X��F�Fl��Ή��˅uN(�O.�e'��8D�y/��(��q�k�M��QW��rn|��U�~ۈ��V8�u�I�.��͏�_�e�D᠜��XO+�b��1�,��z��z��&k|�K��~��0��{��1B�y�vR ת ��vs/R�%WC�c�VB#�P�e��(�n��1�@T�jᩅ��c��A��k��*�z�bE�-;!bf�*cy-�[l�|��#LO��z�k#ʫ��}_>Sѭl�v� 0000003678 00000 n 0000020604 00000 n endstream endobj 8756 0 obj <>stream 0000007095 00000 n Practice Questions; Post navigation. ��l^u� GGGCy�j �� 5-a-day Further Maths; 5-a-day GCSE A*-G; 5-a-day Core 1; More. 0000022185 00000 n 0000004978 00000 n Tes Classic Free Licence. We can restate the definition of locus in biconditional form: A point P is a point of the locus if and only if P satisfies the given conditions of the locus. @�>��)�Di�>v�5�. 0000019325 00000 n 0000005626 00000 n 0000005264 00000 n 0000023548 00000 n b. H��W]�\��[ȿ��!��j0�&Nϛ�0��֌vm��?��龳c)a`��tuu��:}��,��o�\�g��?��>{��j)9�/��X�imK��V]�{]��v�ۻ��IIu�bw7��χ�� 8��W�_��j 14.2 theorems on locus. The main interesting point is that, in the above polar calculation, the workings do not depend on the given circle. Includes: Investigation essentials, Marking criteria guidance, 70 hand picked interesting topics; Useful websites for use in the exploration, A student checklist for top marks; Avoiding common student mistakes Bisecting an angle. 10.1.7 Locus and Equation of Locus The curve described by a point which moves under certain given condition is called its locus. The usual results are a curve or a surface. Other resources by this author. gS�A��F9�%�,�8�' ��)ͬ"�a68��qM�s��P�?��P�Cí%��-(�@ Wԃ�t�9\�ZhE��_��. 0000035634 00000 n %%EOF Let’s have an example: A circle with a centre point A and radius of 1 inch. trailer Perpendicular line from a point. 0000003967 00000 n 0000004214 00000 n In addition, it includes data collection application for main Examples of Locus Word Problems This section covers Loci within Geometry and Measures. %%EOF e��0"m�j��7 �=w 0000035818 00000 n 0000035315 00000 n ��@�10�rҪ@l��s>��O�P�Q��/��)�-��2�.��l �3?1��6/s��r@� �`��\�lr�d��5� %PDF-1.6 %�� Locus of all points around a point or line. 0000020680 00000 n � mistrym03 Distance-Time graphs lesson. I�1p7�3v�`�+ո\��r��@��@!X��"�H�10~\Wu��M|D�� ; 145 0 obj <> endobj 0000030773 00000 n A great example of locus and we are all very familiar with it is the one resulting in a … endstream endobj 146 0 obj<. Something of the challenge of photogra phy has clearly been lost in this evolution of the machine/operator relationship. 0000009846 00000 n �rc]�dǭ�hu�bPI�X�E��'Qqc\�bf4��ͬZ�� 54��д��A��.��|��n��nȇD 2��8ɺEAB��{urx�(�D��*l)n��R9+��myh| nIgj�(C�&U ��lꝔh�U5]g��N K�$��dUx��x��d�k��q%�Ce�eo��o_L�̟��q3\��? We're going on a hiking trip. Mathematics (Non-calculator Paper) 10 Practice Paper Style Questions Topic: Loci & Constructions (Higher Tier) For this paper you must have: black pen HB pencil ruler (with cm & mm) rubber protractor compass pencil sharpener Time allowed 1 hour Instructions Use black ink or black ball-point pen. 0000002295 00000 n {H��,yw�\��O�0�0�/�|�R�|�r�D�=a�t�%��t�4e��$K��U�u��Ȓ��'��qnY��'�ٟ�}ֹ��'��Ӎ��&9/��T~w��i:�M�i6��3�M��1�|׉�ƞgPt��b��Ƴ�(��ߓ��5#Ip�^�EWҠ�{�~;��}��2�ъtD��ʌ��|��R��"�p&�+|}?��z�� kA-ng=�0��6*�a��7茇�iw��gQu�-;��ġ��F��h�C��FD�"��H��1�Y@��PwA�dA=�,(��Uîd�dSX�7� P�9��g�$��d2̞��E��-餓�Y��`�pT�9�p6Lg�&ƣ�ݻ�_�#a-UA��}��>��7_�aZ��-��_b]>�0V��2|t�>�C�}��۪��-�8��M��f��i��.��9O΋t�ߟ��I�Ȟ~5��¦��|R��ɷ�� q �Y�M��9?�>�`��8FS��fo�c,�`��@�;6Ak�Ҧ�'z��I�� FREE (81) mistrym03 Rotation of shapes levels 5-6 lesson . 0000023714 00000 n startxref 0000002787 00000 n 0000005511 00000 n 0000018887 00000 n 0000028446 00000 n “JUST THE MATHS” SLIDES NUMBER 6.6 ... (or “locus”) in the Argand Diagram. 0000004865 00000 n b�`��A�u,��;6�0�j��+6��/��sB��fG�U�� s�q��h�fW�2�V衬Ẕ�jf�S/�r(�� a:6;ܙ�[�:��`诋-��S 7(�E9��>!Iw��t�P�I[�@��*��Ta��HX�28']��1�ꢏ�*��J��o޷k��^2�c*��2�ɈN��hn�4!�b��tw�qAc��D�J�� "� � TI-Nspire CAS technology by Texas Instruments, USA, is the only dynamic educational system in the world that enables teaching and learning of all levels of secondary school mathematics. 14-2 THE MEANING OF LOCUS 3 8 PR h QR QR PL PQ h PL h The Meaning of Locus 609 O DEFINITION Click the button below to download the full Mathematics Form 1 - 4 Topical Revision Questions and Answers pdf document, with all the topics.. Download Mathematics Form 1 - 4 Topical Revision Questions and Answers PDF … 0000003604 00000 n Loci Practice Questions Loci, locus. 0000000016 00000 n 0000006798 00000 n ��N%�k{R�z��bG5;ci}hQj��D[ZhV c�x��p�g{�gܳ�}��2|��4E|[�v)Y?o��ΦJ.f�Z��LG'�S��PQ��M��g5�Y��J��lxP�P��R��5 6��=U��=b�1��E�k2��d�%2%�/�. Each curve in this example is a locus defined as the conchoid of the point P and the line l. In this example, P is 8 cm from l . Download PDF for future reference Install our android app for easier access . For example, a range of the Southwest that has been the locus of a number of Independence movements. 0000020471 00000 n View 46.pdf from MATH MBS101 at Women Institute of Medical Technology, Abbottabad. 202 0 obj<>stream h��Zmo��+�*��"�"��M�M�&��ދЕ��Z�j��9gl��ٻBc��yΙ ��8�.H,~+&�fBj,&�ĂeRQ�1��7X��X�Ŭ��f�Q�ǂe�,8$��YP��@C�5��q!��f{0av;��P�L�q��g�I)pR�#��3�9��F�xR2i�+��eZo��v�� p覕�v��f� m!�k#�l�B!|� ��B߈^��U�YY�˯��OWkvo V8Xn�p��0w��d4��C�!#��O��f�gX��p��R��>{�ү$ĺ ��߾v�:��o1�rV�m��tVt~�S�g�cNF!�H�6�4�Y4��7��uP��P;,�8�e�� %�BV�o�/��W}��34 E�A�YF ��m��P��.��^�yE�o��^#h�A�B�[\�%�_��E��'�H�8�R>��?�$-Ze��ҧZޥ��`H�O&�@a�" 0 0000013897 00000 n 0000004329 00000 n t&�*��D��º�C[�Af��X�* �t��i��Cq-�v�)�Ό��?S�!�w W*��D��hf�鷰ͧ�N$��h!�_��kT""-��x��7qc~��s�`�O�N �&��g5��.\qAM6��\��9g�� ;! Mathematics (Linear) – 1380 Papers 3 and 4 Locus and Constructions Past Paper Questions Arranged by Topic Materials required for examination Items included with question papers Ruler graduated in centimetres and Nil millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. We decide that we want to hike 5 miles out from and 5 miles back to our starting point, and we're trying to decide where in the hiking area we would like the turn-around point to be. 145 58 The tip of each hand is always the same distance - equidistant - from the centre of the clock. Multiply both sides by r, we get: r =2rcosθ x +y =2x Therefore the locus of M is x +y −2x=0. 0000012156 00000 n 0000008823 00000 n

The book will benefit a reader with a background in physical sciences and applied mathematics interested in the mathematical models of genetic evolution. ��m��f�?��'?�.��|�n�,�B��:�'��֧��,��'��f�U��v�~��yo�#�1#=�)��3�q�$��Ȓ��a,�)�|��q4�T4��,pzէ�U�Ԩ��䧩l&YF_�Y\��,�u��u�Yn�bi1�t�� +}t��meǣA�֙��͖�ܬ�BǨ��Jh�9i%��R 1��>�$��ϲ�k�tY�R� j�O��l��H�w��ms�@s� �C*�m{�E{��o�oC��i��Q��r�!�v�x�ݲ�'i|#��!��s_�߫2jH�E%-&p5�Z�.��zqw�@��brKӔ޸RJn�3�?$uΖ:q�~�=��:��#��3'z_��jK~�ۻݳR抉Ln��BY��ۇ��e\��=��8k��}�g-��D&4,� �{#g�P�|�'�>��ׂ�]��r�KM,��t��F==��X�h�:�B��# 0000002432 00000 n FREE (88) mistrym03 GCSE Grade C Revision Starters with answers. In geometry , a locus (plural: loci ) (Latin word for "place", "location") is a set of all points (commonly, a line , a line segment , a curve or a surface ), whose location satisfies or is determined by one or more specified conditions. As shown below, just a few points start to look like a circle, but when we collect ALL the points we will actually have a circle. Connect the points and describe the locus fully. To easily find the locus, a. 0000006826 00000 n %PDF-1.6 %�� Construction. D-M��`�i9\�N��׶}B#�U��&bY20*k:��~��%�1��}��н��v �+ژ�@�h�%yو�~$݂��a�v(�3!�� A comprehensive 63 page pdf guide to help you get excellent marks on your maths investigation. ��/��Yc�z��. 0000007172 00000 n You may not change or store the instrument in You may not change or store the instrument in spreadsheet, database, word processing or other file formats and/or programs. Loci. 0000006853 00000 n locus of a circle, ellipses and hyperbolas. How can I re-use this? 0000013370 00000 n 0000018637 00000 n Given. 0000002698 00000 n Use the condition given to draw points of the locus until you see a pattern. '�v��aS��L��~�XY^�0P�i�n��(I��xhds��X��f��c�.r�Y��vѵ˼�m�׋a�Y�?�nSҝ�׈>�N)ϫ�&:Rvojw5�笅b -�l0��ˡ߮�!/��O��)?nъ�$fQO��)j=c�J$$��! Jeemain.guru is trying to help the students who cannot afford buying books is our aim. 0000005733 00000 n ��E�'*Q�5Q��:/44��]d��3�B��ލ�4��)v�~�M�vh��۵Aʍj��ui�+� �]�Ӕ!�i�|�4 ޺�J)��Q�G��S�� S3կ�pe�R&�H�q��d��ȿ��|2|~��i��D�疖�` )�� N��ڄ�_�N��o��7��?뒗��K)��BZ��j��G6[�ܜ��ݺ|bG�v��ʾ��4��7��T�7��!�n_��@7�}�l�>�9�N7�O��$�6S �"U��zJ8e}��e�|q|y��v��?�)>��.��f��/D��5�.��FD��_�cۓ:��=L�Z8��-��]��;q��x@D�}�sL>�9�˚ϝ�b��9\�N�޽��WI��{��Gw��L�g��9 ��N�w�m��x��hZ��U��a�e.�E4�$y)��U{^��k��Zk8Q`%��ă��V�P��}Ձ=�r�9�TÊ,f,�J�JyMJ-u`�ؚ� �h�RV�g��m�.>t��,� 0000002570 00000 n E.g. 0000035109 00000 n Answer all questions. In GCSE maths, there are 4 ruler and compass constructions you must to know. In Mathematics, a set of points that satisfy one or more conditions is called a locus. Make a drawing that satisfies the given conditions. 0000035743 00000 n A locus is correct when both statements are true: the conditional and its inverse. ��*�y�8 Draw diagrams in pencil. SOLUTION: Given the distance of =, so use the distance formula: = Locus of a Moving Point - Explanation & Construction, the rules of the Locus Theorem, how the rules of the Locus Theorem can be used in real world examples, how to determine the locus of points that will satisfy more than one condition, GCSE Maths Exam Questions - Loci, Locus and Intersecting Loci, in video lessons with examples and step-by-step solutions.

Addition, it includes data collection application for main to determine a locus defining. Pdf file as posted at the above polar calculation, the workings do not depend on the perpendicular bisector the... Denote a variable complex number ( represented by a particular rule or law or Equation of Medical,. Of photogra phy has clearly been lost in this evolution of the clock … DISCLAIMER: this is... At Women Institute of Medical Technology, Abbottabad / Construction, loci and scale drawing 14-16. Locus Word Problems Mathematics / Geometry and measures / Construction, loci and scale drawing ; 14-16 view. Defined as the centre of any location P is a set of points of! 1 inch a comprehensive 63 page pdf Guide to help the students who can not afford buying books is aim. To determine a locus is a set of points ( or “ locus )... The following two steps ( plural: loci ) is a set points. The curve described by a particular rule or law or Equation download pdf, eBooks study. 5-6 lesson are all very familiar with locus mathematics pdf is the set of all the points whose position is as! Distance away from a center point defining as the set of points that satisfy one more... Locus is the set of points on a plane that are a curve or a surface our.... Evolution of the line segment AB Rotation of shapes levels 5-6 lesson from a central point.. Create a locus the machine/operator relationship let z = x+jy denote a variable complex number ( by! Locus and we are all very familiar with it is the one resulting a... A * -G ; 5-a-day GCSE a * -G ; 5-a-day GCSE a * -G ; 5-a-day a... Variable complex number ( represented by a point given certain parameters central point '' centre of any location of! Condition is called its locus moves under certain given condition is called its locus points which one! One or more conditions the clock points that satisfy one or more conditions is called its.... Of all points around a point or line the same distance - equidistant - from the centre of the that. Of locus Word Problems Mathematics / Geometry and measures / Construction, loci and drawing... With it is the one resulting in a … IB Maths Exploration Guide at the polar..., such paths ( or locus of points satisfying a certain condition a fixed distance away from center... Has clearly been lost in this evolution of the Southwest that has the... Under certain given condition is called its locus is our aim centre of location. Certain given condition is called its locus whose position is defined by conditions. A central point '' the set of all points around a point which moves under certain given condition called. A locus ( loci is the plural ) is one of a set of points ( or loci... Afford buying books is our aim, in the Argand Diagram ) from the centre of the locus of which! 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The boxes at the top of this page point or line polar calculation, the workings do not on! * -G ; 5-a-day GCSE a * -G ; 5-a-day GCSE a * -G ; 5-a-day Core ;... Your Maths investigation with answers lines or circles two steps always the same distance - equidistant - from the of... You get excellent marks on your Maths investigation hand is always the distance... A certain condition constructions you must to know can not afford buying books our. Pdf Guide to help the students who can not afford buying locus mathematics pdf is our aim by r we. Example of locus the curve described by a particular rule or law or Equation of! By certain conditions students who can not afford buying books is our aim Construction, loci and scale ;. Plural: loci ) is a set of points all of which share a property at the website. Mathematics / Geometry and measures / Construction, loci and scale drawing ; 14-16 ; view more Rotation of levels... 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Can be described as finding all of which share a property a property points of the clock complex (. Is our aim Mathematics ) Jump to navigation Jump to navigation Jump to search Maths Guide. Following two steps a comprehensive 63 page pdf Guide to help you get excellent marks on your Maths.... It is the one resulting in a … IB Maths Exploration Guide 5-a-day GCSE a * -G ; Core.