1994 - JAMB Mathematics Past Questions and Answers - page 2
a2x - b2y - b2x + a2y = a2x - b2x - b2y + a2y Rearrange
= x(a2 - b2) + y(a2 - b2)
= (x + y)(a2 - b2)
= (x + y)(a + b)(a + b)
Users' Answers & CommentsSince (x - 1), is a factor, when the polynomial is divided by (x - 1), the remainder = zero
∴ (x - 1) = 0
x = 1
Substitute in the polynomial the value x = 1
= p(1)3 + q(1)2 + 11(1) - 6 = 0
p + q + 5 = 0 .....(i)
Also since x - 3 is a factor, ∴ x - 3 = 0
x = 3
Substitute p(3)3 + q(3)2 + 11(3) - 6 = 0
27p + 9q = -27 ......(2)
Combine eqns. (i) and (ii)
Multiply equation (i) by 9 to eliminate q
9p + 9q = -45
Subt. (\frac{27p + 9q = -27}{-18p = -18})
∴ p = 1
Users' Answers & Comments(\frac{a}{a - x}) = (\frac{b}{x - b})
(\frac{1}{1 - x}) = (\frac{3}{x - 3})
∴ 3(1 - x) = x - 3
3 - 3x = x - 3
Rearrange 6 = 4x; x = (\frac {6}{4})
= (\frac{3}{2})
Users' Answers & Comments(\frac{1}{r - 1}) + (\frac{2}{r + 1}) = (\frac{3}{r})
Multiply through by r(r -1) which is the LCM
= (r)(r + 1) + 2(r)(r - 1)
= 3(r - 1)(r + 1)
= r2 + r + 2r2 - 2r
3r2 - 3 = 3r2
r = 3r2 - 3
-r = -3
∴ r = 3
Users' Answers & Comments(\frac{x - 3}{(1 - x)(x + 2)}) = (\frac{p}{1 - x}) + (\frac{Q}{x + 2})
Multiply both sides by LCM i.e. (1 - x(x + 2))
∴ x - 3 = p(x + 2) + Q(1 - x)
When x = +1
(+1) - 3 = p(+1 + 2) + Q(1 - 1)
-2 = 3p + 0(Q)
3p = -2
∴ p = (\frac{-2}{3})
Users' Answers & Comments(\frac{1}{x}) > 2 = (\frac{x}{x^2}) > 2
x > 2x2
= 2x2 < x
= 2x2 - x < 0
= x(2x - 10 < 0
Case 1(+, -) = x > 0, 2x - 1 < 0
x > 0, x < (\frac{1}{2}) (solution)
Case 2(-, 4) = x < 0, 2x - 1 > 0
x < 0, x , (\frac{1}{2}) = 0
Users' Answers & CommentsIn an AP, Tn = a + (n - 1)d
T6 = a + 5d = 11
The first term = a = 1
∴ T6 = 1 + 5d = 11
5d = 11 - 1
5d = 10
∴ d = 2
Users' Answers & Commentslog10 r + log10 r2 + log10 r4 + log10 r8 + log10 r16 + log10 r32 = 63
log10r63 = 63
63 = 1063
∴ r = 10
Users' Answers & Comments(\frac{(n + 1)(n + 2)}{2})
If n = 1, the expression becomes 3
n = 2, the expression becomes 6
n = 4, the expression becomes 15
n = 5, the expression becomes 21
Users' Answers & Commentsa (\oplus) b = ab
The set of all national rules Q, is closed under the operations, additions, subtraction, multiplication and division. Since a (\oplus) b = ab; b (\oplus) a = ba = ab
The number 1 is the identity element under multiplication
Users' Answers & Comments