DieselShip's Online Content Library

Q1. (a) Tank A contains a fuel mixture of petrol and oil in the ratio 12:1 and tank B contains a fuel mixture of petrol and oil in the ratio 11:2.

Determine the ratio in which fuel should be drawn from A and B to give a petrol and oil mixture in the ratio 10:1. (8)

(b) The crippling load, P, for a steel rod is directly proportional to the fourth power of its diameter, D, and is inversely proportional to the square of its length, L.

Determine the approximate percentage change in P if D is increased by 1% and L is decreased by 1%. (8)

Q2. (a) Y = (7x + 17)/(2x²- 7x - 4) + 2x/(2x + 1) - 5/(x - 4)

Express Y as a single fraction in its simplest form. (8)

(b) Solve for x in the following equation: (8)

(2x + 1) (4x – 1) = 5

Q3. (a) A propulsion problem causes a reduction in a ship’s speed of 3 knots throughout a passage of 520 nautical miles, resulting in the ship arriving at its destination 3 hours behind schedule.

Calculate EACH of the following for the ship:

(i) the normal service speed; (7)

(ii) the passage time. (3)

(b) Solve for x in the following equation: (6)

7^3x-1 = 0.5

Q4. A keyway, of width 14 mm, is cut into a steel shaft, of radius 25 mm, along its entire length, as shown in Fig. Q4.

Calculate EACH of the following for the shaft:

(a) the maximum depth of the keyway; (8)

(b) the percentage of steel removed. (8)

Q5. The fuel consumption, F tonnes per day, at a speed, V knots, for a certain vessel are related by:

F = aV² + b where a and b are constants.

Table Q5 indicates recorded values of F and V.

(a) Using the values in Table Q5 draw a graph to verify the relationship between F and V: (10)

Suggested scales:      horizontal axis 2 cm = 10

vertical axis 2 cm = 2

(b) Use the drawn graph to determine approximate values of a and b. (6)

Q6. (a) A quadrilateral shaped metal plate has dimensions as shown in Fig Q6(a).

The angle ABC is 48°

Calculate EACH of the following for the plate:

(i) the distance from A to C; (4)

(ii) the size of angle DAB. (8)

(b) Solve for Ѳ in the following equation in the range 90° < Ѳ < 180°

sin 2Ѳ = - 0.95 (4)

Q7. (a) Determine the first and second differential coefficients of the expression: (6)

y = 9x^4/3 + 2ln x – 4 sin x

(b) The displacement, s metres, of a body from a fixed point is given by the equation:

s = 45t + 3t² - t³ where t is the time in seconds.

Determine EACH of the following for the body:

(i) the time when its velocity is zero; (6)

(ii) its acceleration after 3 seconds. (4)

Q8. The uniform cross-section of a 60 metres long cargo space, in a small bulk carrier, can be represented by the area enclosed by the curve y = 1/4 x² and the lines y = 1 and y = 9, as shown by the shaded part in Fig Q8.

Calculate EACH of the following for the cargo space:

(a) the area of its cross-section; (13)

(b) its capacity in cubic metres. (3)

Q9. A rectangular swimming pool is 25 metres long and 12 metres wide.

When full, the water is 1 metre deep at the shallow end and the bottom slopes uniformly along its length to the opposite end, where it is 4 metres deep.

The pool was filled by water flowing through a pipe, of internal diameter 100 millimetres, flowing at the rate of 4 metres per second, the pipe always being full.

Calculate EACH of the following for the pool:

(a) the volume of water when full; (6)

(b) the filling rate in cubic metres per hour; (7)

(c) the total filling time. (3)