2008 - JAMB Mathematics Past Questions and Answers - page 7

4x - 7 \(\leq\) 3x

4x - 3x \(\leq\) 7

x \(\leq\) 7

ii. 3x - 4 \(\leq\) 4x

3x - 4x \(\leq\) 4

-x \(\leq\) -4

-4 \(\leq\) x \(\leq\) 7

x² - 5x + 6 \(\geq\) 0

x² - 2x - 3x + 6 \(\geq\) 0

x(x - 2) - 3(x - 2) \(\geq\) 0

(x - 2) (x - 3) \(\geq\) 0

x \(\geq\) 2 or \(\geq\) 3

x \(\leq\) 2 \(\geq\)

In = a + (n - 1)d

24 = a + (5 - 1)d

24 = a + 4d.......(i)

96 = a + (11 - 1)d

96 = a + 10d.......(ii)

a = 24 - 4d.......(iii)

96 = 24 - 4d + 10d

96 = 24 + 6d

96 - 24 = 6d

72 = 6d

d = \(\frac{72}{6}\)

d = 12

a = 24 - 4d

a = 24 - 4 x 12

a = 24 - 48

a = -24

a \(\ast\) b = b \(\ast\) a

x \(\ast\) y = y \(\ast\) x

2x - 3y + 2 \(\neq\) 2y - 3y - 3x + 2

2 \(\ast\) 3 = 2(2) -3(3) + 2

= 4 - 9 + 2

= -3

1 \(\ast\) 2 = 2(1) - 3(2) + 2

= 2 - 6 + 2

= 2 - 6 + 2

= -2

m \(\Delta\) n = m + n + mn

m \(\Delta\) e = e \(\Delta\) m = m

m \(\Delta\) e = m

m + e + me = m

e + me = m - m

e + me = 0

e(1 + m) = 0

e = \(\frac{0}{1 + m}\) = 0

\(\begin{pmatrix} 1 & 0 \ -1 & -1\ 2 & 2 \end{pmatrix}\) + \(\begin{pmatrix} x & 1 \ -1 & 0\ y & -2 \end{pmatrix}\) = \(\begin{pmatrix} -2 & 1 \ -2 & -1\ -30 & 0 \end{pmatrix}\)

therefore, (x, y) = (-3, -5) respectively

-2p + r = 1.......(i)

2p + 3r = 0.......(ii)

r - 1 + 2p ........(iii)

2p + 3(1 + 2p) = 0

2p + 3(1 + 2p) = 0

2p + 3 + 6p = 0

3 - 8p = 0 \(\to\) 8p = 3

p = \(\frac{3}{8}\)

6 = 1 - 2 \(\frac{3}{8}\)

= 1 - \(\frac{6}{8}\)

\(\frac{8 - 6}{8}\) = \(\frac{2}{8}\)

= \(\frac{1}{4}\)

Equilateral are equal in sides and angle

180^o = 60^o + 60^o + 60^o

\(\theta\) = 60^o

r = 1

h = 14

\(\pi\) = \(\frac{22}{7}\)

A = \(\pi\)r²h

A = \(\frac{22}{7}\) x 1² x 14

A = 44m²

A = 44 x 10 litres

A = 440 litres

let (6, 2) be represented as (x₁, y₁) and (4, 2) be (x₂, y₂)

p(6, 2) R(4, 2)

m.p = (\(\frac{x_1 + x_2}{2}\)) (\(\frac{y_1 + y_2}{2}\))

= (\(\frac{6 + 4}{2}\) , \(\frac{2 + 2}{2}\))

= (\(\frac{10}{2}\),\(\frac{4}{2}\))

= (5, 2)