2009 - JAMB Mathematics Past Questions and Answers - page 7

Tn = \(\frac{1}{2}\)n(2a + (n - 1)d)

= \(\frac{1}{2}\)n(2 x 5 + (n - 1) 6

= \(\frac{1}{2}\)n(10 + 6n - 6)

= n\(\frac{1}{2}\)(6n + 4)

= n(3n + 2)

3x - 7 \(\leq\) 0 ; x + 5 > 0

3x \(\leq\) 7 ; x > -5

= x \(\leq\) \(\frac{7}{3}\)

-5 < x \(\leq\) \(\frac{7}{3}\)

If m x n = n

= n - (m + 2)

3 \(\ast\) (-5) = -5 - (3 + 2)

= -5 - 5

= -10

If Q = \(\begin{pmatrix} 9 & -2 \ -7 & 4 \end{pmatrix}\), then |Q| is

= 9 x 4 - (-2) x (-7)

= 36 - 14

= 22

If p = \(\begin{pmatrix} x + 3 & x + 2 \ x + 1 & x - 1 \end{pmatrix}\) evaluate x if |p| = -10

|P| = (x + 3)(x - 1) - (x + 2)(x + 1)

x² + 2x - 3 - (x² + 3x + 2)

x² + 2x - 3 - x² - 3x - 2

-x - 5 = -10

-x = -10 + 5

x = 5

x \(\leq\) 90^o (acute angle)

x² = 3x

3x = 90^o

x = \(\frac{90^o}{3}\) = 30^o

x + 150^o = 180^o (sum of angle on straight line)

x = 180^o - 150^o , x = 30^o

number of sides (n) = \(\frac{360}{3}\)

= 12

sin45^o = \(\frac{y}{2}\)

y = 2 sin45^o

y = 2 (\(\frac{1}{\sqrt{2}}\))

y = \(\frac{2}{\sqrt{2}}\) x \(\frac{\sqrt{2}}{\sqrt{2}}\)

y = \(\frac{2\sqrt{2}}{2}\)

y = \(\sqrt{2}\)

Since it is an isosceles triangle

x = \(\sqrt{2}\)

Area of \(\Delta\) = \(\frac{1}{2}\)bh

= \(\frac{1}{2}\) x \(\sqrt{2}\) x \(\sqrt{2}\)

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

= 1 cm²