2007 - JAMB Mathematics Past Questions and Answers - page 2

(3 x 5) + (4(y - 1)) + (5y) + (6 x 9) + (7 x 4) + 8 = 200

15 + 4y - 4 + 5y + 54 + 28 + 8 = 200

9y + 105 - 4 = 200

9y + 101 = 200

9y = 200 - 101

9y = 99

y = 11

mean(\(\bar{x}\)) = \(\frac{\sum x}{n}\)

= \(\frac{7 + 5 + 2 + 1 + 2 + 11}{6}\) = 10

M.D = \(\frac{7 + 5 + 2 + 1 + 2 + 11}{6}\)

= \(\frac{28}{6}\)

= 4.7

a = 2, r = \(\frac{{\frac{3}{2}}}{3}\)

= \(\frac{3}{4}\)

S\(\infty\) = \(\frac{a}{1 - r}\)

\(\frac{2}{1 - \frac{3}{4}}\)

= \(\frac{2}{\frac{1}{4}}\)

= 8

W \(\alpha\) L², \(\frac{W}{L^2}\) = k(constant)

\(\frac{6}{42}\) = k

\(\frac{W}{(\sqrt{17})^2}\)

W = \(\frac{17 \times 6}{16}\)

= \(\frac{51}{8}\)

= 6\(\frac{3}{8}\)

a \(\Delta\) b = a + b + 1

a \(\Delta\) a^-1 = e

7 \(\Delta\) 7^-1 = 7 + 7^-1

therefore 7^-1 = -1 - 8

= -9
the inverse of 7 under the operation \(\Delta\) is -9

-3 (x - 2) < -2(x + 3), -3x + 6 < -2x - 6

6 + 6 < 3x - 2x, 12 < x or x > 12

f(x) = 3x - 2, f(P) = 3p - 2I

= 3\(\begin{pmatrix} 2 & 1 \ -1 & 0 \end{pmatrix}\) - 2\(\begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix}\) = \(\begin{pmatrix} 6 & 3 \ -3 & 0 \end{pmatrix}\) - \(\begin{pmatrix} 2 & 0 \ 0 & 2 \end{pmatrix}\)

= \(\begin{pmatrix} 6 & -2 \ -3 & 0 \end{pmatrix}\)\(\begin{pmatrix} 3 & -0 \ 0 & -2 \end{pmatrix}\) = \(\begin{pmatrix} 4 & 3 \ -3 & -2 \end{pmatrix}\)

2t² + t - 15 = 2t² - 5t + 6t - 15

= t(2t - 5) + 3(2t - 5) = (t + 3)(2t - 5)

x \(\oplus\) y = xy + x + y

(-\(\frac{3}{4}\)) \(\oplus\) 6 = -\(\frac{3}{4.6}\) - \(\frac{3}{4}\) + 6

= -\(\frac{9}{2}\) - \(\frac{3}{4}\) + 6

= -\(\frac{3}{4}\)

(x² + x - 12) \(\geq\) 0 , (x - 3)(x + 4) \(\geq\) 0

For the condition to hold, each of (x - 3) and (x + 4) must be of the same sign

.i.e. x - 3 \(\geq\) 0 and x + 4 \(\geq\) 0

or x - 3\(\leq\) 0 and x + 4 \(\leq\) 0

when x \(\geq\) 3, the condition is satisfied

when x \(\geq\) -4, the condition is not satisfied.

when x \(\leq\) 3, the condition is not satisfied

when x \(\leq\) -4 , the condition is not satisfied. Thus, the solution of the inequality is x \(\geq\) 3 or x \(\leq\) -4 ,