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PN Cadet Mathematics Flashcards
51 question-and-answer cards covering Mathematics as it is examined in PN Cadet. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Mathematics deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
What is the value of a⁰ (a ≠ 0), and what does a⁻ⁿ equal?
a⁰ = 1, and a⁻ⁿ = 1/aⁿ.
Express a fractional index a^(m/n) as a radical.
a^(m/n) = ⁿ√(aᵐ) = (ⁿ√a)ᵐ.
State the product law of logarithms.
logₐ(xy) = logₐx + logₐy.
State the quotient law of logarithms.
logₐ(x/y) = logₐx − logₐy.
State the power law of logarithms.
logₐ(xⁿ) = n·logₐx.
What is logₐ1 and what is logₐa?
logₐ1 = 0 and logₐa = 1.
State the change of base formula for logarithms.
logₐx = (log_b x)/(log_b a) for any valid base b.
What is a common logarithm, and how is it written?
A logarithm with base 10, written log x (i.e., log₁₀x).
What is a natural logarithm, its base, and its notation?
A logarithm to base e (e ≈ 2.718), written ln x (i.e., logₑx).
Convert the logarithmic statement logₐN = x into exponential form.
aˣ = N.
What is the value of ln e and ln 1?
ln e = 1 and ln 1 = 0.
To solve a logarithmic equation like logₐx = b, what step removes the log?
Rewrite in exponential form: x = aᵇ.
When solving logarithmic equations, why must solutions be checked?
Because the logarithm's argument must be positive; any value making an argument ≤ 0 is rejected (extraneous).
Define the three primary trigonometric ratios sin θ, cos θ, tan θ in a right triangle.
sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent.
Name the reciprocal trigonometric ratios of sin, cos, and tan.
cosec θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ.
Give the exact values of sin, cos, and tan of 30°.
sin 30° = 1/2, cos 30° = √3/2, tan 30° = 1/√3.
Give the exact values of sin, cos, and tan of 45°.
sin 45° = 1/√2, cos 45° = 1/√2, tan 45° = 1.
Give the exact values of sin, cos, and tan of 60°.
sin 60° = √3/2, cos 60° = 1/2, tan 60° = √3.
State the fundamental Pythagorean trigonometric identity.
sin²θ + cos²θ = 1.
State the two Pythagorean identities derived from sin²θ + cos²θ = 1.
1 + tan²θ = sec²θ and 1 + cot²θ = cosec²θ.
Express tan θ in terms of sin θ and cos θ.
tan θ = sin θ / cos θ.
In heights and distances, define the angle of elevation and angle of depression.
Angle of elevation is measured upward from the horizontal to an object above; angle of depression is measured downward from the horizontal to an object below.
How do you convert degrees to radians and what is the radian measure of a full circle?
Multiply degrees by π/180; a full circle is 2π radians (360° = 2π rad).
State the formula for the arc length s of a circle of radius r subtending angle θ (in radians).
s = rθ.
What this deck covers
The Mathematics deck follows the PN Cadet Mathematics syllabus — 6 chapters and 22 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 8.5 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 45 characters, which is long enough to carry the reasoning and short enough to say out loud.
A deck like this earns its keep on the second and third pass. Read the syllabus first so you know the shape of the subject, then use the cards to find the specific facts that have not stuck.
Mathematics flashcards FAQ
How many Mathematics flashcards are in this PN Cadet deck?
51 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these PN Cadet flashcards free?
Yes. The preview here is free to read with no signup, and the full 51-card deck is free inside the Examius app.
What do the Mathematics cards cover?
They follow the PN Cadet Mathematics syllabus — 6 chapters and 22 topics — so the questions track what is actually examinable.
How should I use these flashcards?
Read the syllabus first so you know the shape of the subject, then drill the deck. Examius schedules each card with spaced repetition, so cards you keep missing come back sooner and ones you know drift further apart.