2008 - JAMB Mathematics Past Questions and Answers - page 3

mΔn = m+n+mn
Let e be the identity element
∴mΔe = eΔm = m
m+e+me = m
e+me = m-m
e+me = 0
e(1+m) = 0
e = 0 / (1+m)
e = 0

Exterior angle = sum of two interior opposite angles
y = 50^o (vert. opp ∠s are equal)
X = y + 30
X = 50 + 30
X = 80^o

Exterior angle = 360 / n
= 360 / 12
= 30^o

a = a(base ∠s of Iss Δ)
∴ a+a+74 = 180
2a + 74 = 180
2a = 180-74
2a = 106
a = 53
∴∠OPQ = 53^o

Area of the figure = Area of rect + area of semi circle
\(=L \times h + \frac{1}{2}\pi r^2\\ 5 \times 15 + \frac{1}{2} \times \frac{22}{7} \times \left(\frac{5}{2}\right)^2\\ =75+\frac{(22\times 25)}{2\times7}\\ =75 + 9\frac{23}{28}\\ =84.8cm\)

If a length of a chord is equal to the length of a radius in the same circle, the triangle formed y the chord and the radii is an equilateral triangle
∴each angle = 60^o

V = πr²h
1m = 100cm
14cm = 1400cm
\(∴V = \frac{22}{7} \times \frac{100x100x1400}{1000}\\ = 44, 000 liters\)

\(X = \frac{6+2}{2}=\frac{10}{2}=5\\ Y = \frac{2+2}{2}=\frac{4}{2}=2\\ ∴X,Y = (5,2)\)

3X + 2Y + 1 = 0
2Y = -3X - 1
\(\frac{-3}{2}X - \frac{1}{2}\)
Gradient of 3X + 2Y +1 = 0 is -³/₂
Gradient of a line perpendicular to 3X + 2Y + 1 = 0
\(=-1 \div \frac{3}{2}\\ =-1 \times \frac{-2}{3}=\frac{2}{3}\)

sinθ = ³/₅
x² = 5² - 3²