JAMB Mathematics Past Questions & Answers - Page 270

Number of students scoring at least 50 marks = Number of students scoring 50 and above From the table 53, 70, 84, 59, 90, 60, 81, 73, 50, 37, 67, 68, 64, 52. Hence, 14 students scored at least 50 marks

Angle corresponding to 7 in a pie chart will be \(\frac{7 \times 360}{\text{sum of items}}\)

= \(\frac{7 }{18}\) x 360

= 140^o

Let each of the unknown side be x.

\(10^{2} = x^{2} + x^{2} - 2(x)(x) \cos 120\)

\(100 = 2x^{2} - 2x^{2} \cos 120\)

\(100 = 2x^{2} + x^{2} = 3x^{2}\)

x = \(\sqrt{\frac{100}{3}}\)

= \(\frac{10}{\sqrt{3}}\) x \(\frac{\sqrt{3}}{\sqrt{3}}\)

x = \(\frac{10\sqrt{3}}{3}\)cm

sin \(\theta\) = cos \(\theta\) 0 \(\leq\) \(\theta\) \(\leq\) 360°

The acute angle where sin \(\theta\) = cos \(\theta\) = 45°

But at the third Quadrant Cos \(\theta\) = -ve; sin \(\theta\) = -ve.

at the 3rd quadrant, value with respect to Q is

(180 + Q) where Q = acute angle

(180 + 45) = 225°

The two solution are 45°, 225°

The angle between 2 latitudes one in northern hemisphere and the other in southern hemisphere and the other in southern hemisphere is the sum of their latitudes.

∴ Total angle difference = (30 + 13) = 43^o