2005 - JAMB Mathematics Past Questions and Answers - page 2

x = -2, x = -1 and x = 3

∴x+2 = 0, x+1 = 0 and x-3 = 0

Product of the factors

(x+2)(x+1)(x-3) = 0

(x² + 3x + 2)(x-3)

x(x² + 3x + 2) -3(x² + 3x + 2) = 0

x³ + 3x² + 2x - 3x² - 9x - 6 = 0

x³ - 7x - 6 = 0

t = time taken and N = number of men

t ∝ ¹/_N

t = ^K/_N

K = Nt

K = 30 * 6

K = 180

∴t = ¹⁸⁰/_N

4 = ¹⁸⁰/_N

4N = 180

N = ¹⁸⁰/₄

45 men

(W\infty LD^2\W=KLd^2\K=\frac{W}{Ld^2}=\frac{140}{54}\times\left(4\frac{2}{3}\right)^2 =\frac{140}{54}\times\left(\frac{14}{3}\right)^2=\frac{140\times 9}{54\times 14\times 14}=\frac{5}{42}\∴W=\frac{5}{42Ld^2}\42W=5Ld^2\frac{42W}{5L}=d^2\d=\sqrt{\frac{42W}{5L}})

7x - 3 > 25 + 3x

7x - 3x > 25 + 3

4x > 28

x > ²⁸/₄

x > 7

U₇ = a + (7 - 1)d

= a + 6d

U₃ = a + (3 - 1)d

= a + 2d

But U₇ = 2(U₃)

∴a + 6d = 2(a + 2d)

a + 6d = 2a + 4d

2a - a + 4d - 6d = 0

a - 2d = 0 → eqn1

Sn = ⁿ/₂ (2a + (n - 1)d)

42 = ⁴/₂ (2a + (4 - 1)d)

42 = 2(2a + 3d)

21 = 2a + 3d → eqn2

eqn1 * eqn2 0 = 2a - 4d

21 = 7d

∴d = ²¹/₇

d = 3

8, 12, 16, .....96

a = 8, d = 4, l = 96, n = 20

S₂₀ = ⁿ/₂(a + l)

= ²⁰/₂(8 + 96)

= 10 * 104

= 1040

a * b = ab + 2(a + b + 1)

let e be the identity element

∴ a * e = e * b = a

∴ a * e

ae + 2(a + e + 1) = a

ae + 2a + 2e + 2 = a

ae + 2e = a - 2a = 2

(a + 2)e = -a - 2

e = -(a-2) / (a+2)

e = -(a+2) / (a+2)

e = -1

p + 40^o = 100^o (exterior ∠ = sum of two interior opp ∠s)

p = 100^o - 40^o

P = 60^o

But q + p = 180^o (∠s on a straight line)

q + 60^o

q = 180^o - 60^o

q = 120^o

x = q (corresponding ∠)

∴x = 120^o

∠GOK = 85^o (vertical opposite angle ∠s)

∠EOG + ∠GOK + ∠KOF = 180 (∠s on a straight line)

∠EOg + 85^o + 52^o = 180^o

∠EOG + 137^o = 180^o

∠EOG = 43^o