(a) Without using mathematical table or calculator, evaluate : \(\sqrt{\frac{0.18 \times 12.5}{0.05 \times 0.2}}\).

(b) Simplify : \(\frac{8 - 4\sqrt{18}}{\sqrt{50}}\).

(c) x, y and z are related such that x varies directly as the cube of y and inversely as the square of z. If x = 108 when y = 3 and z = 4, find z when x = 4000 and y = 10.

(a) A regular polygon of n sides is such that each interior angle is 120° greater than the exterior angle. Find :

(i) the value of n ; (ii) the sum of all the interior angles.

(b) A boy walks 6km from a point P to a point Q on a bearing of 065°. He then walks to a point R, a distance of 13km, on a bearing of 146°. 

(i) Sketch the diagram of his movement. (ii) Calculate, correct to the nearest kilometre, the distance PR.

(a) A plane flies due East from A(lat. 53°N, long. 25°E) to a point B(lat. 53°N, long. 85°E) at an average speed of 400 km/h. The plane then flies South from B to a point C 2000km away. Calculate, correct to the nearest whole number : 

(a) the distance between A and B.

(b) the time the plane takes to reach point B ;

(c) the latitude of C. 

[Take radius of the earth = 6400km; \(\pi = \frac{22}{7}\)].

(a) Find the smallest integer that satisfies the inequality \(x + 8 < 4x - 15\).

(b) A sales girl is paid a monthly salary of N2,500 in addition to a commission of 5 kobo in the naira on all sales made by her during the month. If her sales for a month amounts to N200,000.00, calculate her income for that month.

(c)  The diagram shows a window consisting of a rectangular and semi- circular parts. The radius of the semi- circular part is 35 cm and the height of the rectangular part is 50 cm. Find the area of the window. [Take \(\pi = \frac{22}{7}\)].

The sketch shows a plot of land . 

(a) Using a scale of 1 cm to 10m, draw an accurate diagram of the plot ;

(b) Construct : (i) The locus \(l_{1}\) of points equidistant from AC and BC ; (ii) the locus \(l_{2}\) of points 60m from A.

(c) A tree T inside the plot is on both \(l_{1}\) and \(l_{2}\). Locate T and find |TC| in metres.

(d) A flagpole, P is to be placed such that it it is nearer AC than BC and more than 60m from A. Shade the regions where P can be located.