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Model Solutions for G.C.E. (A.L.) Combined Mathematics I - August 2000 Exam

Explore comprehensive model solutions for Question 1 from the G.C.E. (A.L.) Combined Mathematics I August 2000 examination. This document offers detailed step-by-step explanations for deriving equations and solving mathematical problems, tailored for students preparing for their G.C.E. exams. We provide individual classes upon request, focusing on past exam paper discussions for subjects like International Baccalaureate (IB), GCE (O/L), and GCE (A/L). Contact us at home.video.tutor@gmail.com for personalized tutoring services.

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Model Solutions for G.C.E. (A.L.) Combined Mathematics I - August 2000 Exam

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  1. Scholastic home.video.tutor @gmail.com G.C.E. (A.L.) Examination G.C.E. (A.L.) Examination August 2000 Combined Mathematics I‌ (Q1) Model Solutions We conduct individual classes upon request. Contact us at: home.video.tutor@gmail.com for more information

  2. Scholastic home.video.tutor @gmail.com G.C.E. (A.L.) Examination – Combined Mathematics I - August 2000Question No 1(a) (a) a andb are the roots of the equation x2 – px + q = 0. Find the equation, whose roots are a(a + b) හා b(a + b).

  3. G.C.E. (A.L.) Examination – Combined Mathematics I - August 2000 QuestionNo 1(a) (Model Solutions) Scholastic home.video.tutor @gmail.com • The equation, whose roots area andb • (x - a) (x - b) = 0 ‍ • ‍Expanding • x2 – xa– xb+ ab = 0 • x2 – (a + b)x+ ab = 0 --- (1) • x2 – px+ q = 0 --- (2) • Comparing the coefficients of (1) and (2) • p= (a + b)andq = ab --- (3)

  4. G.C.E. (A.L.) Examination – Combined Mathematics I - August 2000 QuestionNo 1(a)(Model Solutions) … Scholastic home.video.tutor @gmail.com • The equation, whose roots area(a + b) andb(a + b) • {x - a(a + b)}{(x -b(a + b))}= 0 ‍ • Expanding • x2 – xb(a + b)– xa(a + b) + ab(a + b)2} = 0 • x2 – x{(a + b) (a + b)} + ab(a + b)2 = 0 -- (4)

  5. G.C.E. (A.L.) Examination – Combined Mathematics I - August 2000 QuestionNo 1(a) (Model Solutions) … Scholastic home.video.tutor @gmail.com • Substituting the value of p= (a + b)in the above equation (3) and the value of q = ab in the above equation (4) . • We can obtain x2 – p2x+ qp2 = 0, whose roots are a(a + b) හා b(a + b).

  6. G.C.E. (A.L.) Examination – Combined Mathematics I - August 2000 QuestionNo 1(b) Scholastic home.video.tutor @gmail.com (b) In order for the function f(x,y) = 2x2 + lxy + 3y2 - 5y - 2to be written as a product of two linear factors, find the values of l.

  7. G.C.E. (A.L.) Examination – Combined Mathematics I - August 2000 Question No 1(b) (Model Solutions) Scholastic home.video.tutor @gmail.com • L.S.= 2x2 + lxy + 3y2 - 5y - 2‍ • ‍R.S.= (ax + by + c)(lx + my + n) • Substituting x = 0 in L.S. and R.S. • 3y2 - 5y - 2 = (by + c)(my + n) • (3y + 1)(y - 2) = (by + c)(my + n) • Therefore b=3, c=1, m=1, n=-2 • Substituting y = 0 in L.S. and R.S. • 2x2 – 2 = (ax + c)(lx + n) • 2x2 – 2 = alx2 +(an + cl)x + cn

  8. G.C.E. (A.L.) Examination – Combined Mathematics I - August 2000 QuestionNo 1(b) (Model Solutions) … Scholastic home.video.tutor @gmail.com • ‍Comparing above coefficients of L.S and R.S. • 2=al, 0=an+cl, and-2=cn • Substitute c=1, n = -2 in 0=an+cl • 0=an+cl = a(-2)+1(l)=>l=2a • Substitute l=2a in2=al • 2=a(2a) => and • L.S. = 2x2 + lxy + 3y2 - 5y - 2‍ • ‍R.S.= (ax + by + c)(lx + my + n)

  9. G.C.E. (A.L.) Examination – Combined Mathematics I - August 2000 Question No 1(b) (Model Solutions) … Scholastic home.video.tutor @gmail.com • Comparing the coefficients of L.S and R.S. • l=am+bl • Substituting m=1,and in above equation • Therefore

  10. G.C.E. (A.L.) Examination – Combined Mathematics I - August 2000 Question No 1(c) Scholastic home.video.tutor @gmail.com (c) Express in partial fractions.

  11. G.C.E. (A.L.) Examination – Combined Mathematics I - August 2000 QuestionNo 1(c) (Model Solutions) Scholastic home.video.tutor @gmail.com • ‌The fraction • Since the denominator and the numerator powers of this fraction are the same we need to divide numerator by the denominator.

  12. G.C.E. (A.L.) Examination – Combined Mathematics I - August 2000 QuestionNo 1(c) (Model Solutions) … Scholastic home.video.tutor @gmail.com • ‌ ‍

  13. G.C.E. (A.L.) Examination – Combined Mathematics I - August 2000 QuestionNo 1(c) (Model Solutions) … Scholastic home.video.tutor @gmail.com • ‌Comparing the coefficients of L.S and R.S. • A+B=4, -2A-B+C=-3, A=3 • B=4-A=1, C=B+2A-3=1+6-3=4 ‍ • Therefore

  14. Scholastic home.video.tutor @gmail.com ‌Home Based Mathematics Tuition using the Internet We conduct individual classes upon request forInternational Baccalaureate (IB)GCE(O/L), GCE(A/L) , AQA, EDEXCELwithPast Exam Paper Discussions.University Foundation Year Mathematics Flexible contact hours. Save time of travelling.A unique way of tutoring. For more information please contact:home.video.tutor@gmail.com http://scholastictutors.webs.com/

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