2009 - JAMB Mathematics Past Questions and Answers - page 3

m⊗n = m + n + mn
for inverse -5^-1 x -5 = e
-5^-1 + -5 + (-5^-1)(-5) = 0
-5 + (-5^-1(-5)) = 5
-5^-1.(1 + -5) = 5
-5^-1(-4) = 5
-5^-1 = -⁵/₄

Q = \( \left[ \begin{array}{ccc}
9 & -2 \\ -7 & 4 \\ \end{array} \right]\)
|Q| = 9x4 - (-2x7)
= 36 - 14
= 22

\(P=\left[\begin{array}{cc}x+3 & x+2\\ x+1 & x-1\end{array}\right]\) evaluate x if |P| = -10
(x+3)(x-1) - {(x+1)(x+2)} = -10
x² - x + 3x - 3 - {x² + 2x + x + 2} = -10
x² + 2x - 3 - {x² + 3x + 2} = -10
-x - 5 = -10
-5 + 10 = x
5 = x
∴x = 5

y = x, Gradient (m₁) = 1
y = √3x gradient (m₂) = √3
\(tan\theta = \frac{m_2 - m_1}{1+m_2 m_1}\\ tan\theta = \frac{\sqrt{3}-1}{1+\sqrt{3}\times 1}\\ =\frac{1.73 -1 }{1+1.73}=
\frac{0.73}{2.73}=0.268\)
θ = Tan^-1 (0.268)
= 15^o

Sum of interior angles of a polygon = each interior ∠ x n
(n-2)180 = 150 x n
180n - 360 = 150n
180n-150n = 360
30n = 360
n = 360/30
n = 12 sides

In Δ TYX
XY = TY ∴y =47^o base ∠s of ISCΔ
But y+x+34+47 = 180 interior
opposite ∠s are supplementary
47 + x + 34 + 47 = 180
x + 128= 180
x = 180- 128
x = 52^o

X² + x² = 2²
2x² = 4
x² = ⁴/₂
x² = 2
x = +/-√2
Area of Δ = ¹/₂bh
= ¹/₂ x √2 x √2
= ²/₂
= 1 cm²

x² + 5² = 13²
x² + 25 = 169
x² = 144

x = √ 144 

= 12
Length of the chord AB = 2x
2*12= 24cm

154 = 4 x	22	x r2
7

154x7	= r2
4x22

Locus of a particle which moves in the first quadrant so that it is equidistant from the lines
X = 0 and Y = 0 and x = 0 and y = 0 are the x and y axes is the lines bisecting the angle between x and y axes