The figure below shows the net of a right cone. The radius of the circular base is 10.5 cm.

Calculate the slant height of the cone.                           (2 mks)

The points M and N have coordinates (2, -1) and (-4, 3) respectively. A point R divides line MN externally in the ratio 3:2. Find the of modulus of OR, correct to four significant figures.          (4 mks)

Fifteen men working for eight hours a day can complete a certain job in exactly 24 days. For how many hours a day must sixteen men work in order to complete the same job in exactly 20 days?   (3 mks)

A measuring cylinder of base diameter of 10 cm contains water whose level reads 5 cm high. A spherical solid marble is immersed in the water and the new level reads 9 cm. Calculate the radius of the marble      (3 mks)

An irregular polygon has n sides. Its interior angles are such that two of them are right angles while the exterior of each of the remaining angles is 30⁰. Find the value of n and hence the sum of the interior angles of the polygon.               (3 mks)

A train moving at 120 km/h approaches a bridge 50 m long which is 120 m away. If the train takes 9 seconds to completely cross the bridge, determine the length of the train in metres.            (3 mks)

Sarah, a saleslady earns a basic salary of Ksh. 25,000 and a commission of 7.5% for the sales in excess of Ksh. 100,000. In May 2023 she earned a total of Ksh. 48,700 in salaries and commissions. Determine the amount of sales that she made in that month.      (3 mks)

The figure below shows part of a circle that touches the side LM externally and tangentially at a point T.

(a) Using a ruler and a pair of compasses only, locate the point T on LM.             (2 mks)

(b) Measure the radius of the circle.                        (1 mk)

Simplify the expression                       (3 mks)

Ruth paid rent which was ¹/₁₀ of her net salary. She used ¹/₃ of the remaining amount to make a down payment for a plot. She gave mother Ksh. 2,500 and did shopping worth Ksh. 7,500 herself. She saved the remainder which was Ksh. 12,500. How much was the down payment that she made?              (3 mks)