radius. Rewriting the equation with one variable would result in a polynomial equation that you could solve to find the radius. 3. Rewrite the formula using the variable x for the radius. Substitute the value of the volume found in step 2 for V and express the height of the object in terms of x plus or minus a constant. For example‚ if the height measurement is 4 inches longer than the radius‚ then the expression for the height will be (x + 4). 4. Simplify the equation and write it in standard
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and Balancing" that was written in 830 AD. It dealt with "what is easiest and most useful". Considered as an elementary textbook of practical mathematics‚ the Al-jabr wa’l-muqabala began with a discussion of the algebra of first and second degree equations and moved on in its final two parts to the business of practical applications to questions on mensuration and legacies. This was the most important book al-Khwarizmi was known for. Other Works of al-Khwarizmi: Al-Khwarizmi is also responsible
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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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Heavenly Hash 4 cups cooked rice 1 can diced chicken ½ cup celery 1 onion 1 can cream of mushroom soup 1 cup mayo 1 can of water chestnuts 1 package frozen peas Stir in bowl. Pour into 9x13 pan. Cook at 350 degrees for 30-40 minutes (until hot). Heavenly Hash 4 cups cooked rice 1 can diced chicken ½ cup celery 1 onion 1 can cream of mushroom soup 1 cup mayo 1 can of water chestnuts 1 package frozen peas Stir in bowl. Pour into 9x13 pan. Cook at 350 degrees for 30-40 minutes
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4 5 −3 +8 12) Multiply 2 − 4 5 + 3 13) Multiply 3 − 4 3 + 4 14) Multiply 5 + 7 C. Linear Equations in One Variable: 15) 6 − 7 − 3 = −1 16) 8 2 − 3 = 6 2 + 6 17) 5 + 2 4 − 4 = 3 2 − 1 18) 19) − = = + D. Factoring Completely 20) 12 + 36 − 30 21) +5 + +5 22) 3 + 3 + 5 + 5 23) + 3 + 4 + 12 24) 2 − 8 25) 2 − 8 26) 4 − 9 27) 4 − 36 28) + 9 + 14 29) + 5 − 14 30) 3 + 9 − 30 1 E. Solving Quadratic Equations by Factoring 31) 5 + 5 = 0 32) + 8 = −12 33) = 2 + 35 F. Rational Expressions Factor and Simplify:
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Maximum Marks : 100 Note : Question no. one is compulsory. Attempt any three questions from four. 1. (a) For what value of ’k’ the points ( - k + 1‚ 2 k)‚ (k‚ 2 - 2 k) and ( - 4 - k‚ 6 - 2 k) are collinear. (b) Solve the following system of equations by using Matrix Inverse Method. 3x+ 4y+ 7z= 14 2x-y+ 3z= 4 2x + 2y - 3z = 0 (c) Use principle of Mathematical Induction to prove that : 1 ± 1 ± 1x2 2x3 (d) 1 n (n+1) n+1 5 5 5 5 -‚ How many terms of G.P ‚[3 3‚ 3 /3 Add upto 39 + 13 BCS-012
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MATHEMATICS CURRICULUM FOR SECONDARY COURSE RATIONALE Mathematics is an important discipline of learning at the secondary stage. It helps the learners in acquiring decision- making ability through its applications to real life both in familiar and unfamiliar situations. It predominately contributes to the development of precision‚ rational and analytical thinking‚ reasoning and scientific temper. One of the basic aims of teaching Mathematics at the Secondary stage is to inculcate the skill
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Differential Equations Second Order Differential Equations Introduction In the previous chapter we looked at first order differential equations. In this chapter we will move on to second order differential equations. Just as we did in the last chapter we will look at some special cases of second order differential equations that we can solve. Unlike the previous chapter however‚ we are going to have to be even more restrictive as to the kinds of differential equations that we’ll look at
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y2 − 6y − 7 = 0 d. y 2 + 8 y = −25 7. Solve by using the quadratic formula. Simplify any radicals: a. x 2 + 2x + 3 = 0 2 x 2 + 10 x − 5 = 0 b. x 2 + 3x − 1 = 0 x 2 + 5 x = −6 c. d. e. x 2 + 6 x − 12 = 0 f. 2 x 2 + 2 x − 27 = 0 __________________________________________________________________ 8. Find the vertex and the equation of the axis of symmetry. Make a table of values and graph the equation on graph paper. a. y = x 2 + 2 x − 4 b. y = −x 2 + 4x − 5 c. y =
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DIFFERENTIAL EQUATIONS 2.1 Separable Variables 2.2 Exact Equations 2.2.1 Equations Reducible to Exact Form. 2.3 Linear Equations 4. Solutions by Substitutions 2.4.1 Homogenous Equations 2.4.2 Bernoulli’s Equation 2.5 Exercises In this chapter we describe procedures for solving 4 types of differential equations of first order‚ namely‚ the class of differential equations of first order where variables x and y can be separated‚ the class of exact equations (equation
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