CARIBBEAN EXAMINATIONS COUNCIL Caribbean Advanced Proficiency Examination Pure Mathematics Syllabus Effective for examinations from May/June 2008 Correspondence related to the syllabus should be addressed to: The Pro-Registrar Caribbean Examinations Council Caenwood Centre 37 Arnold Road‚ Kingston 5‚ Jamaica‚ W.I. Telephone Number: (876) 920-6714 Facsimile Number: (876) 967-4972 E-mail address: cxcwzo@cxc.org Website: www.cxc.org Copyright © 2007‚ by Caribbean Examinations Council The Garrison
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and INTERCEPTS TOPIC 5 - STATISTICS TOPIC 6 - GEOMETRY OF THE CIRCLE TOPIC 7 - INDICES TOPIC 8 - SUFFICIENCY CONDITIONS for QUADRILATERALS TOPIC 9 - CO-ORDINATE GEOMETRY and REGIONS TOPIC 10 - SIMULTANEOUS EQUATIONS TOPIC 11 - SOLUTION of QUADRATIC EQUATIONS and MAX/MIN PROBLEMS TOPIC 12 - LINEAR PROGRAMMING TOPIC 13 - POLYNOMIALS TOPIC 14 - TRIGONOMETRY TOPIC 15 - PROBABILITY TOPIC 16 - FUNCTIONS‚ FUNCTION NOTATION and GRAPHS JAMES RUSE AGRICULTURAL HIGH SCHOOL MATHEMATICS PROGRAMME
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Three Passions Three passions‚ helpful‚ yet at times hurtful‚ have governed my life: family‚ friends‚ and dedication. These passions‚ like waves upon the seashore have rocked me back and forth in an indefinite course‚ over a great ocean of content‚ reaching the very verge of happiness (SP10). I have mentioned family first because they bring joy – a joy that I would sacrifice my whole life for an hour of this greatness. I have mentioned it‚ next‚ because it removes loneliness; a loneliness that
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Equations Reducible to Quadratic Equations Exercise 4.2 Solve the following equations: 1. x 4 − 6 x 2 + 8 = 0 Solution: x4 − 6 x2 + 8 = 0 Let y = x 2 and y 2 = x 4 The above equation becomes: y 2 − 6 y + 8 = 0 y2 − 6 y + 8 = 0 y2 − 4 y − 2 y + 8 = 0 y ( y − 4) − 2( y − 4) = 0 ( y − 2)( y − 4) = 0 y − 2 = 0 and y − 4 = 0 y=2 y=4 2 As‚ y = x x2 = 2 x2 = 4 x = ±2 x=± 2 solution set = { 2‚ − 2‚ 2‚ −2} 2. x −2 − 10 = 3 x−1 Solution: x −2 − 10 = 3 x −1 x −2 − 3 x −1 − 10 = 0 Let
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Descartes’ Rule of Signs‚ and the Factor Theorem. (Hint: If the numbers are large‚ graph the function first using GeoGebra to help you find one of the zeros. Use that zero to find the depressed equation which can be solved by factoring or the quadratic formula.) 6. Substitute 0 for the function notation and‚ using graphing technology‚ graph the function. 7. Answer the following questions: * What does the Fundamental Theorem of Algebra indicate with respect to this equation?
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Syllabus Course Information: Course Title: Introductory Mathematics Department Name: Department of Mathematics and Science Course Number: MAT 100 a Semester Offered: Spring 2014 Course Meeting Days: Tuesday‚ Thursday Course Meeting Time: 9:00 – 10:15 Course Meeting Places: BAC 002 Prerequisites: None Cr.3. (6 ECTS Cr.) Offered every semester. Blackboard Site: Introductory Math Forum‚ accessible under the condition that you are registered for MAT 100 a and for Blackboard at the
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substitute the minimal knowledge that is needed on a standardized test. For example‚ a seventh grade teacher will try to perfect students’ ability to use the Pythagorean Theorem in order to obtain the measurement of sides and angles of a right triangle. But on the other hand‚ real life applications and word problems of how the Pythagorean Theorem can be used to find unknown distances and heights‚ as well as angles of elevation‚ will be less of a focus because there is less of a focus on longer and
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Wallace‚ Alfred Russel. (1858). On the tendency of varieties to depart indefinitely from the original type. Zoology‚ 3‚ 61-64. The author of this article clearly states his purpose of writing within the first few paragraphs: “to show that (the assumption that varieties occurring in a state of nature are … analogous to or even identical with those of domestic animals‚ and are governed by the same laws as regards their permanence or further variation) is false‚ that there is a general principle in
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Book on Calculation by Completion and Balancing”)‚ was translated into Latin in the 12th century‚ from which the title and term Algebra derives. Algebra is a compilation of rules‚ together with demonstrations‚ for finding solutions of linear and quadratic equations based on intuitive geometric arguments‚ rather than the abstract notation now associated with the subject. Its systematic‚ demonstrative approach distinguishes it from earlier treatments of the subject. It also contains sections on calculating
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this way] The cost C(x) of the pipeline as a function of x is: C(x) = distance along north shore * pipeline cost over land + distance under the river * pipeline cost under land The distance along the north shore is 6-x The distance (by Pythagorean theorem) under the water is sqrt( 2^2 + x^2) So‚ C(x) = (6-x)*200000 + sqrt(4 + x^2) * 400000 [You should graph this] To find the value of x where C(x) is minimized‚ we set dC/dx = 0‚ [Reminder - use the chain rule to differentiate the
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