PAF Aeronautical Engineering Initial Test cheat sheet

Subject-verb agreement: a singular subject takes a singular verb, and phrases in parentheses or between commas never change the number of the subject.

Present perfect (has/have + past participle) pairs with 'since' for a starting point in time and with 'for' for a length of time.

'Between' takes exactly two items and an object pronoun (between you and me); 'among' takes three or more.

Active to passive: the object becomes the subject, the verb becomes be + past participle, and the doer is introduced by 'by'.

Prepositions of time: 'in' for months, years and seasons; 'on' for days and dates; 'at' for clock times and night.

A semicolon may join two independent clauses; a comma alone may not join two independent clauses (comma splice).

Reported speech backshift: present becomes past, 'will' becomes 'would', 'can' becomes 'could', 'now' becomes 'then', 'here' becomes 'there'.

An introductory participial phrase must modify the noun that immediately follows the comma, otherwise the modifier is dangling.

A synonym shares the meaning of the given word; an antonym is its opposite; choose the option that fits the sentence's context.

Percentage: x% of N = (x/100) x N; percentage change = (change / original value) x 100.

Areas and volumes: triangle = 1/2 x base x height; circle = pi r^2; cylinder = pi r^2 h; sphere = (4/3) pi r^3.

Speed = distance / time; for equal distances at speeds x and y, average speed = 2xy / (x + y).

For ax^2 + bx + c = 0, x = [-b +/- sqrt(b^2 - 4ac)] / 2a; the discriminant b^2 - 4ac decides whether roots are real, equal or imaginary.

Sum of the first n natural numbers = n(n + 1)/2; arithmetic progression sum = (n/2)(first term + last term).

For two positive integers, LCM x HCF = product of the two numbers.

Simple interest = PRT/100; compound amount = P(1 + r/100)^t.

In a ratio a : b the total is a + b parts, and each share = (its parts / total parts) x total quantity.

Sum of interior angles of an n-sided polygon = (n - 2) x 180 degrees; each exterior angle of a regular n-gon = 360/n.

Uniform-acceleration equations: v = u + at; s = ut + (1/2)at^2; v^2 = u^2 + 2as (valid only when acceleration is constant).

Newton's second law: net force = mass x acceleration; weight W = mg with g approximately 9.8 m/s^2.

Work = force x displacement along the force; power = work / time, measured in watts (1 horsepower is about 746 W).

Kinetic energy = (1/2)mv^2; gravitational potential energy = mgh; mechanical energy is conserved when only gravity does work.

Ohm's law V = IR; series resistances add directly, parallel total obeys 1/R = 1/R1 + 1/R2.

Wave relation v = f x lambda; sound needs a material medium, light does not.

Mirror formula 1/f = 1/v + 1/u; the focal length of a plane mirror is infinite and its image is virtual and the same size.

Density = mass / volume (kg/m^3); pressure = force / area, measured in pascals.

SI units: force newton, work and energy joule, power watt, charge coulomb, current ampere, frequency hertz.

Analogy questions: name the exact relationship (worker : tool, cause : effect, part : whole) and keep the direction of the relation the same.

Letter series: convert letters to positions 1-26 and test constant gaps, increasing gaps, or alternating patterns.

Opposite-letter rule: letters whose positions sum to 27 are mirror pairs (A-Z, B-Y, C-X), often used in coding questions.

Odd one out: find the property (category, spelling pattern, numerical type) that all but one item share.

Blood relations: draw a family tree by generation, mark males and females explicitly, and never infer gender from a name.

Direction sense: fix north at the top; a right turn is 90 degrees clockwise, a left turn 90 degrees anticlockwise; use Pythagoras for the shortest distance.

Syllogism: 'All A are B' does not justify 'All B are A'; a conclusion must follow from every statement given.

Number series: check differences first, then ratios, then squares and cubes, then two interleaved series at odd and even positions.

Mirror image (vertical mirror placed at the side): left and right swap, top and bottom stay the same.

Water image: top and bottom swap, while left and right stay the same.

Rotation: a 90-degree clockwise turn moves the top edge to the right; 180 degrees reverses both axes; angles and side counts stay unchanged.

Paper folding: unfold in reverse order, and remember that each fold doubles the number of holes produced by one punch.

Painted cube cut into n^3 small cubes: three painted faces = 8 (corners); two painted faces = 12(n - 2); one painted face = 6(n - 2)^2; none = (n - 2)^3.

Figure series: track separately the number of sides, the number of line segments or dots, and the rotation step.

Embedded figure: locate all lines of the target inside the complex figure, allowing change of size or rotation only if the question permits it.

Odd figure out: compare symmetry, number of enclosed regions, open versus closed outlines, and straight versus curved lines.