Mathematics
Governing: MCA General Engineering Science I written examination syllabus, items 1.1 to 1.3. Builds on: school mathematics.
Where GES sits
MSN 1904 lists GES I and II among the modules for the SV Chief Engineer <3000 GT/<9000 kW CoC, and GES passes have no expiry. Engineering graduates may be exempt (MSN 1904 section 8.6; MIN 642 section 4). If you are not exempt, this course follows the published GES I and GES II syllabuses item by item.
Fractions, decimals and percentages
| Task | Working | Answer |
|---|---|---|
| 3/8 as a decimal | 3 / 8 | 0.375 |
| 5/16 as a percentage | 5 / 16 x 100 | 31.25% |
| 3/4 + 5/6 | 9/12 + 10/12 | 19/12 = 1 7/12 |
| 2/3 x 9/10 | 18/30 | 3/5 |
| 5/8 / 15/16 | 5/8 x 16/15 | 2/3 |
Ratio, proportion and percentage
Share 1,200 litres of fuel between two tanks in the ratio 5:3: 8 parts of 150 L, so 750 L and 450 L.
Consumption falls from 540 to 486 kg/h after a turbocharger wash: (540 - 486) / 540 x 100 = 10.0% saving. Always divide the change by the original value.
Signs and indices
- Multiplying or dividing two numbers with the same sign gives a positive; opposite signs give a negative: (-3) x (-4) = 12; (-12) / 4 = -3.
- 2^3 x 2^4 = 2^7 = 128
- 8^(2/3) = (cube root of 8)^2 = 4
- 16^(-1/2) = 1 / sqrt 16 = 0.25
- 27^(-2/3) = 1 / 9 = 0.1111
Dividing a quadratic by a linear factor
Factorise, then cancel.
- (x^2 + 5x + 6) / (x + 2) = (x + 2)(x + 3) / (x + 2) = x + 3
- (2x^2 + 7x - 15) / (x + 5) = (x + 5)(2x - 3) / (x + 5) = 2x - 3
Check by multiplying back: (x + 5)(2x - 3) = 2x^2 - 3x + 10x - 15 = 2x^2 + 7x - 15.
Straight-line graphs
Plot the data, draw the best straight line, and read off y = mx + c.
Generator fuel log: 18 L/h at 50 kW, 54 L/h at 200 kW.
| Step | Working | Result |
|---|---|---|
| Gradient m | (54 - 18) / (200 - 50) | 0.24 L/h per kW |
| Intercept c | 18 - 0.24 x 50 | 6 L/h |
| Law | y = 0.24x + 6 | |
| At 150 kW | 0.24 x 150 + 6 | 42 L/h |
The intercept is the no-load consumption: fuel burned just to keep the set turning. That is why two lightly loaded generators burn more than one well-loaded one.
Transposing a formula
Most GES answers need a formula rearranged before any numbers go in. Do to both sides whatever undoes the operation you want to remove, in reverse order.
| Start | Make the subject | Result |
|---|---|---|
| P = pm L A n | pm | pm = P / (L A n) |
| v^2 = u^2 + 2as | s | s = (v^2 - u^2) / 2a |
| Q = m c dT | dT | dT = Q / (m c) |
| R = V / I | I | I = V / R |
Estimating before you calculate
Round every number to one figure and do the sum in your head first. If the 1,200 L split came out at 7,500 L, you would know at once a decimal point had wandered. A ten-second estimate catches more errors than rechecking the calculator.
TIP — Show every line Examiners award method marks. A correct method with an arithmetic slip still scores; a bare wrong answer scores nothing.