Engineering Technician (EngTech) Mathematics and Scientific Principles for Engineering Technicians Syllabus

Mathematics and Scientific Principles for Engineering Technicians syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics and Scientific Principles for Engineering Technicians in Engineering Technician (EngTech), not a summary of it.

1. 1

   Applied Engineering Mathematics

   4 topics

   • Numeracy, Units and Estimation
     • SI base and derived units, prefixes and unit conversion
     • Significant figures, rounding and approximation
     • Order-of-magnitude estimation and sanity-checking results
     • Percentages, ratios and proportion in engineering contexts
   • Algebra and Equations
     • Rearranging and transposing formulae
     • Linear and simultaneous equations
     • Indices, powers and standard form
     • Substitution into engineering formulae
   • Trigonometry and Geometry
     • Pythagoras and right-angled triangle solutions
     • Sine, cosine and tangent ratios for measurement
     • Area, volume and surface area calculations
     • Angles, bearings and coordinate geometry on drawings
   • Graphs and Data Interpretation
     • Plotting and reading linear graphs (y = mx + c)
     • Gradient and intercept as physical quantities
     • Reading charts, tables and calibration curves
     • Basic statistics: mean, range and tolerance bands
2. 2

   Mechanical Science Fundamentals

   4 topics

   • Forces, Moments and Equilibrium
     • Scalars, vectors and force resolution
     • Moments, couples and the principle of moments
     • Free-body diagrams and static equilibrium
     • Centre of gravity and stability
   • Motion and Dynamics
     • Distance, speed, velocity and acceleration
     • Newton's laws applied to simple systems
     • Friction and its effect on machinery
   • Work, Energy and Power
     • Work done, kinetic and potential energy
     • Power, efficiency and energy losses
     • Mechanical advantage in levers, gears and pulleys
   • Pressure and Fluids
     • Pressure in fluids and hydraulics basics
     • Pascal's principle and force multiplication
     • Pneumatics and compressed-air systems
3. 3

   Electrical and Materials Science Fundamentals

   3 topics

   • Electrical Principles
     • Voltage, current, resistance and Ohm's law
     • Series and parallel circuit calculations
     • Electrical power, energy and the kilowatt-hour
     • AC vs DC fundamentals and the UK 50 Hz supply
   • Heat and Thermal Effects
     • Temperature, heat transfer and thermal expansion
     • Effects of heat on materials and tolerances
   • Properties of Engineering Materials
     • Metals, polymers, ceramics and composites
     • Strength, hardness, ductility and toughness
     • Stress, strain and Hooke's law
     • Selecting materials for purpose and cost

Mathematics and Scientific Principles for Engineering Technicians flashcards for Engineering Technician (EngTech)

23 of 51 cards from the Mathematics and Scientific Principles for Engineering Technicians deck — real questions with worked answers.

1. What are the seven SI base units and their quantities?

   Metre $m$ (length), kilogram $\text{kg}$ (mass), second $s$ (time), ampere $A$ (electric current), kelvin $K$ (temperature), mole $\text{mol}$ (amount of substance), candela $\text{cd}$ (luminous intensity).

2. List the SI prefixes from giga down to nano with their powers of ten.

   Giga $G=10^{9}$, mega $M=10^{6}$, kilo $k=10^{3}$, milli $m=10^{-3}$, micro $\mu=10^{-6}$, nano $n=10^{-9}$.

3. How do you express a number in standard form (scientific notation)?

   As $a \times 10^{n}$ where $1 \leq |a| < 10$ and $n$ is an integer. Example: $48000 = 4.8 \times 10^{4}$.

4. What is the rule for significant figures when multiplying or dividing measured quantities?

   The result is rounded to the same number of significant figures as the measurement with the fewest significant figures.

5. Define percentage error in a measurement.

   $$\text{percentage error} = \frac{|\text{measured} - \text{true}|}{\text{true}} \times 100\%$$

6. What is the derived SI unit of force and its base-unit equivalent?

   The newton, $N$. In base units $1\,N = 1\,\text{kg}\cdot\text{m}\cdot\text{s}^{-2}$.

7. State the laws of indices for $a^{m} \times a^{n}$, $a^{m} \div a^{n}$, and $(a^{m})^{n}$.

   $a^{m} \times a^{n} = a^{m+n}$, $\quad a^{m} \div a^{n} = a^{m-n}$, $\quad (a^{m})^{n} = a^{mn}$. Also $a^{0}=1$ and $a^{-n} = \frac{1}{a^{n}}$.

8. What is the quadratic formula for solving $ax^{2}+bx+c=0$?

   $$x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$$

9. What does the discriminant $b^{2}-4ac$ tell you about the roots of a quadratic?

   If $b^{2}-4ac > 0$ there are two real roots; if $=0$ one repeated real root; if $<0$ no real roots (complex roots).

10. How do you rearrange $v = u + at$ to make $a$ the subject?

    $$a = \frac{v-u}{t}$$

11. State Pythagoras' theorem for a right-angled triangle.

    $$c^{2} = a^{2} + b^{2}$$ where $c$ is the hypotenuse and $a$, $b$ are the other two sides.

12. Define $\sin\theta$, $\cos\theta$ and $\tan\theta$ in a right-angled triangle (SOHCAHTOA).

    $\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}$, $\quad \cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}$, $\quad \tan\theta = \frac{\text{opposite}}{\text{adjacent}}$.

13. State the sine rule for a triangle with sides $a,b,c$ and opposite angles $A,B,C$.

    $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$

14. State the cosine rule for a triangle.

    $$a^{2} = b^{2} + c^{2} - 2bc\cos A$$

15. What is the relationship between radians and degrees?

    $\pi$ radians $= 180^{\circ}$, so $1\,\text{rad} = \frac{180}{\pi} \approx 57.3^{\circ}$. A full circle is $2\pi$ radians.

16. Give the formulas for the circumference and area of a circle of radius $r$.

    Circumference $C = 2\pi r$; area $A = \pi r^{2}$.

17. What are the formulas for the arc length and sector area subtending angle $\theta$ (in radians) at radius $r$?

    Arc length $s = r\theta$; sector area $A = \frac{1}{2}r^{2}\theta$.

18. State the fundamental trigonometric identity relating $\sin$ and $\cos$.

    $$\sin^{2}\theta + \cos^{2}\theta = 1$$

19. What does the gradient of a straight-line graph $y = mx + c$ represent, and how is it calculated?

    $m$ is the gradient (rate of change of $y$ with $x$), $m = \frac{\Delta y}{\Delta x} = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$; $c$ is the $y$-intercept.

20. On a distance-time graph, what does the gradient represent? On a velocity-time graph?

    On a distance-time graph the gradient is velocity (speed). On a velocity-time graph the gradient is acceleration and the area under the line is distance travelled.

21. What is the difference between the mean, median and mode of a data set?

    Mean is the arithmetic average $\bar{x} = \frac{\sum x}{n}$; median is the middle value when ordered; mode is the most frequently occurring value.

22. How is the range of a data set defined?

    $$\text{range} = \text{largest value} - \text{smallest value}$$

23. Distinguish between a scalar and a vector quantity, with examples of each.

    A scalar has magnitude only (e.g. mass, speed, energy, temperature). A vector has both magnitude and direction (e.g. force, velocity, acceleration, displacement).

See more Mathematics and Scientific Principles for Engineering Technicians flashcards →

Planning Mathematics and Scientific Principles for Engineering Technicians for Engineering Technician (EngTech)

Mathematics and Scientific Principles for Engineering Technicians (Engineering Technician (EngTech)) FAQ