Download presentation

Presentation is loading. Please wait.

Published bySavannah Kirk Modified over 4 years ago

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

2
Question No 1(a) G.C.E. (A.L.) Examination – Combined Mathematics I - August 2000 Question No 1(a) (a) and are the roots of the equation x 2 – px + q = 0. Find the equation, whose roots are. 2

3
The equation, whose roots are and x x Expanding x 2 – x – x + x 2 – ( + )x + (1) x 2 – px + q = 0 (2) Comparing the coefficients of (1) and (2) p= ( + ) and q = (3) 3 G.C.E. (A.L.) Examination – Combined Mathematics I - August 2000 QuestionNo 1(a) (Model Solutions) Question No 1(a) (Model Solutions)

4
The equation, whose roots are and x x Expanding x 2 – x – x + x 2 – x{ + (4) 4 G.C.E. (A.L.) Examination – Combined Mathematics I - August 2000 QuestionNo 1(a)(Model Solutions) … Question No 1(a) (Model Solutions) …

5
Substituting the value of p= ( + ) in the above equation (3) and the value of q = in the above equation (4) We can obtain x 2 – p 2 x + qp 2 whose roots are. 5 G.C.E. (A.L.) Examination – Combined Mathematics I - August 2000 Question No 1(a) (Model Solutions) …

6
6 (b) In order for the function f(x,y) = 2x 2 + xy + 3y 2 - 5y - 2 to be written as a product of two linear factors, find the values of G.C.E. (A.L.) Examination – Combined Mathematics I - August 2000 QuestionNo 1(b) Question No 1(b)

7
L.S.= 2x 2 + xy + 3y 2 - 5y - 2 R.S.= (ax + by + c)(lx + my + n) Substituting x = 0 in L.S. and R.S. 3y 2 - 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. 2x 2 – 2 = (ax + c)(lx + n) 2x 2 – 2 = alx 2 +(an + cl)x + cn 7 G.C.E. (A.L.) Examination – Combined Mathematics I - August 2000 Question No 1(b) (Model Solutions)

8
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 in 2=al 2=a(2a) => and L.S. = 2x 2 + xy + 3y 2 - 5y - 2 R.S. = (ax + by + c)(lx + my + n) 8 G.C.E. (A.L.) Examination – Combined Mathematics I - August 2000 QuestionNo 1(b) (Model Solutions) … Question No 1(b) (Model Solutions) …

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

10
10 (c) Express in partial fractions. G.C.E. (A.L.) Examination – Combined Mathematics I - August 2000 Question No 1(c)

11
The fraction Since the denominator and the numerator powers of this fraction are the same we need to divide numerator by the denominator. 11 G.C.E. (A.L.) Examination – Combined Mathematics I - August 2000 QuestionNo 1(c) (Model Solutions) Question No 1(c) (Model Solutions)

12
12 G.C.E. (A.L.) Examination – Combined Mathematics I - August 2000 QuestionNo 1(c) (Model Solutions) … Question No 1(c) (Model Solutions) …

13
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 13 G.C.E. (A.L.) Examination – Combined Mathematics I - August 2000 QuestionNo 1(c) (Model Solutions) … Question No 1(c) (Model Solutions) …

14
We conduct individual classes upon request for Home Based Mathematics Tuition using the Internet We conduct individual classes upon request for International Baccalaureate (IB) GCE(O/L), GCE(A/L), AQA, EDEXCEL with Past 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/ home.video.tutor@gmail.com http://scholastictutors.webs.com/

Similar presentations

OK

Rational Expressions To add or subtract rational expressions, find the least common denominator, rewrite all terms with the LCD as the new denominator,

Rational Expressions To add or subtract rational expressions, find the least common denominator, rewrite all terms with the LCD as the new denominator,

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google

Ppt on french revolution class 9 Ppt on product specification sheets Ppt on fire extinguisher types colors Ppt on creativity and innovation management journal Ppt on articles for grade 1 Ppt on current monetary and fiscal policy Ppt on brand building strategy Ppt on classical economics wikipedia Free ppt on the road not taken Ppt on 5 star chocolate pie