Free PAF Aeronautical Engineering Initial Test Exam Flashcards

State the relationship in the first pair as one precise sentence, such as "an altimeter measures altitude", then read that same sentence with each option. If two options both fit, make the sentence narrower rather than guessing.

Compare letter positions first: a constant shift (+1, -2), a reversal (A becomes Z), or letters swapped in pairs. Derive the rule from one letter, confirm it on a second, and only then apply it. Decoding the whole word before finding the rule wastes the time the item is testing.

Test differences first, then second differences, then ratios, then alternating patterns, then squares and cubes plus or minus a constant. A constant ratio gives a geometric jump (2, 6, 18, 54); a gap that itself doubles usually means multiply by 2 and add a fixed number.

Find the property shared by every item except one: category, physical state, spelling pattern, or a numeric property such as being a perfect square. When two answers look defensible, choose the property that excludes exactly one item.

Only a conclusion that must be true counts. "All A are B" does not permit "all B are A", and "some A are B" never supports "all" or "none". Combine the premises exactly as written; real-world knowledge about the subject is the trap.

Track one attribute at a time across the frames: direction and size of rotation, number of elements, shading, and the position of a marked element. Most series run two attributes on independent cycles, so a single-rule guess fails on the last frame.

Check columns as well as rows. Test whether the third cell is the sum, difference, product or overlay of the first two, then confirm the same rule holds in a second line before choosing. A rule that works in only one row is a coincidence.

A 90 degree clockwise turn sends up to right, right to down, down to left, left to up; anticlockwise reverses it, and 180 degrees sends every point to the opposite corner. Rotation preserves handedness, so an option that is a mirror image is a reflection, not a rotation.

Each fold doubles the layers, so a single punch through n folds gives 2 to the power n holes when it misses every fold line. Unfold in reverse order and mirror the holes across each fold line as you go.

Opposite faces of a standard die sum to seven, and opposite faces can never both appear in one view. In a folded-net question, two squares separated by exactly one square in the same row or column end up on opposite faces.

These are memorised collocations, not rules: consist of, comply with, differ from, depend on, capable of, familiar with, responsible for, superior to, insist on, deprive of. Candidate reports name prepositions as the most frequent English item on this test.

The object becomes the subject, the verb becomes a form of "be" plus the past participle in the same tense, and the original subject follows "by" if it is kept. "The technician calibrated the instrument" becomes "The instrument was calibrated by the technician" — the tense must not drift.

Each, every, either and neither take a singular verb. With "neither ... nor" or "either ... or", the verb agrees with the nearer subject. A phrase sitting between subject and verb, such as "the set of tools", never changes the agreement.

A real condition uses the present simple in the if-clause and either the present simple or "will" in the main clause: "If the pressure drops, the valve closes." Putting "will" inside the if-clause of a real condition is the error the item is looking for.

Watch doubled letters and the -ance/-ence ending: maintenance, occurrence, accommodate, necessary, separate, recommend, definitely, equipment. Accommodate takes double c and double m; equipment takes a single p.

Test collocation and register rather than difficulty: conduct research, carry out a test, accurate representation. Read the full sentence with each option in place; the strongest distractor is usually a near-synonym that breaks the standard phrase.

In multiplication or division the answer keeps as many significant figures as the least precise factor. In addition or subtraction it keeps as many decimal places as the least precise term. Applying the multiplication rule to a sum is the standard measurement-chapter error.

First condition: the vector sum of forces is zero, so there is no linear acceleration. Second condition: the sum of torques about any point is zero, so there is no angular acceleration. A body can satisfy the first and still spin, which is why both are required.

F equals the rate of change of momentum, and this reduces to F = ma only when mass is constant. The impulse form Ft = change in momentum explains why extending the collision time lowers the peak force — the principle behind crumple zones and arrestor gear.

Net work equals the change in kinetic energy. Power is work divided by time, and for a constant force along the motion P = Fv. Doubling speed quadruples kinetic energy but only doubles the power needed at the same force.

a = v squared over r, directed toward the centre. Centripetal force is a role played by an existing force — tension, gravity, friction, or a component of lift — not an extra force added to the diagram. Centrifugal force appears only in a rotating frame.

A1v1 = A2v2: for steady incompressible flow the volume flow rate is constant, so speed rises where the duct narrows. It is mass conservation applied to a fluid and does not hold once compressibility matters.

P + half rho v squared + rho g h stays constant along a streamline for steady, non-viscous, incompressible flow, so pressure falls where speed rises. This is the intermediate-level account of the reduced pressure over a curved wing surface.

Acceleration is proportional to displacement from equilibrium and directed back toward it. A mass-spring system has period 2 pi times the square root of m/k; a simple pendulum has 2 pi times the square root of l/g — independent of the bob's mass and, for small angles, of amplitude.

v = f times lambda. Frequency is fixed by the source and does not change at a boundary, so a change in speed forces a change in wavelength. Expecting the frequency to change is the classic refraction error.

Fringe separation equals lambda times L divided by d, so fringes widen with longer wavelength or a more distant screen and narrow as the slits move apart. Bright fringes occur where the path difference is a whole number of wavelengths.

Change in internal energy = heat added minus work done by the gas. Isothermal: internal energy is unchanged, so all the heat added becomes work. Adiabatic: no heat flows, so work done by the gas comes straight out of its internal energy and it cools, while work done on it heats it.

Both the force between two point charges and the field of a single point charge follow an inverse-square law, so tripling the separation cuts the force to one ninth. Force depends on both charges; field strength depends only on the source charge and the distance.

Series resistances add, giving a total larger than any single resistor. Parallel resistances add as reciprocals, giving a total smaller than the smallest resistor — two equal resistors in parallel give exactly half their value. If your parallel answer exceeds the smallest resistor, it is wrong.

F = BIL sin(theta), where theta is the angle between conductor and field: maximum when perpendicular and zero when parallel. For a single moving charge the equivalent is F = qvB sin(theta), with direction given by the right-hand rule.

Induced EMF depends on the rate of change of flux, not on the amount of flux — a stationary magnet inside a coil induces nothing. The minus sign is Lenz's law: the induced current opposes the change that produced it, which is energy conservation rather than a separate rule.

The rms value is the peak divided by the square root of two, about 0.707 of the peak, for both voltage and current. A quoted mains figure such as 220 V is the rms value, so its peak is roughly 311 V. RMS is the DC value that would deliver the same average power.

n-type is doped with a pentavalent impurity such as arsenic, adding free electrons as majority carriers; p-type uses a trivalent impurity such as boron, creating holes. Both stay electrically neutral overall — doping changes the carriers available, not the net charge.

Maximum kinetic energy equals photon energy minus the work function. Below the threshold frequency no electrons are emitted however intense the light. Above it, greater intensity increases the number of photoelectrons while only a higher frequency increases their maximum kinetic energy.

Only when its determinant is non-zero (non-singular). For the 2x2 matrix [[a, b], [c, d]] the inverse is 1/(ad - bc) times [[d, -b], [-c, a]]. A zero determinant means the linear system has no unique solution.

For ax squared + bx + c = 0 the discriminant is b squared minus 4ac. Positive gives two distinct real roots (rational if it is a perfect square), zero gives one repeated real root, negative gives a conjugate pair of complex roots. You never have to solve the equation to answer this.

For ax squared + bx + c = 0 the roots sum to -b/a and multiply to c/a. That rebuilds the equation from its roots as x squared minus (sum)x plus (product) = 0, and answers most "find the other root" items in a few seconds.

AP: nth term = a + (n-1)d, and the sum is n/2 times [2a + (n-1)d]. GP: nth term = a times r to the power (n-1), and the sum is a(1 - r to the n)/(1 - r). An infinite GP converges to a/(1 - r) only when the common ratio has magnitude below 1.

In the expansion of (a + b) to the power n, the (r+1)th term is C(n, r) times a to the power (n-r) times b to the power r. To find the coefficient of a particular power, solve for r first — expanding the whole bracket is exactly the time sink the item is testing.

Use nPr = n!/(n-r)! when order matters (seating, ranking, forming numbers) and nCr = n!/(r!(n-r)!) when it does not (committees, teams, handshakes). Since nPr = nCr times r!, the permutation count is always the larger one.

Independent events multiply: P(A and B) = P(A) times P(B). Mutually exclusive events cannot overlap, so P(A and B) = 0 and P(A or B) = P(A) + P(B). Two events with non-zero probability cannot be both independent and mutually exclusive.

sin(A +/- B) = sinA cosB +/- cosA sinB, while cos(A +/- B) = cosA cosB -/+ sinA sinB — note the cosine formula flips the sign. Doubling gives sin2A = 2 sinA cosA and cos2A = cos squared A minus sin squared A, also written 1 - 2sin squared A or 2cos squared A - 1.

Inverse sine returns angles from -90 to 90 degrees, inverse cosine from 0 to 180 degrees, inverse tangent strictly between -90 and 90 degrees. A trigonometric equation has infinitely many solutions, so add multiples of 360 degrees (180 for tangent) unless the interval is restricted.

0/0 is indeterminate, not finished: factorise and cancel, rationalise the surd, or use a standard limit such as sin x over x approaching 1 as x approaches 0 with x in radians. A limit can exist at a point where the function itself is undefined.

(uv)' = u'v + uv'. (u/v)' = (u'v - uv')/v squared — the numerator order matters and reversing it flips the sign. Chain rule: dy/dx = dy/du times du/dx, needed for composites such as sin(3x squared), where differentiating only the outer function is the standard slip.

Solve f'(x) = 0 to locate stationary points, then check the second derivative: negative means a maximum, positive means a minimum, zero is inconclusive and needs the sign of f' either side. Applied maxima and minima problems expect exactly this two-step method.

The integral of x to the power n is x to the power (n+1) divided by (n+1), plus a constant — for every n except -1, where the integral of 1/x is ln|x| + C. Also worth holding: e to the x integrates to itself, sin x to minus cos x, cos x to sin x.

A definite integral equals F(b) - F(a) and carries no constant of integration. When you substitute u = g(x), either convert the limits to u-values as well or change back to x before substituting the original limits; mixing the two is the usual error.

One squared variable means a parabola: y squared = 4ax has focus (a, 0). Both squares added with different denominators give an ellipse; both squares subtracted give a hyperbola; equal coefficients on both squares give a circle. Classify by the signs before touching the algebra.

The dot product is a scalar, |a||b|cos(theta), and is zero when the vectors are perpendicular. The cross product is a vector, |a||b|sin(theta) along the normal, is zero when they are parallel, and is anti-commutative: a x b = -(b x a). With unit vectors, i cross j gives k.