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PN Cadet Mathematics Syllabus
The Mathematics syllabus for PN Cadet in full: 6 chapters and 22 topics, every one listed below, plus 51 Mathematics flashcards with answers.
Mathematics syllabus: all 6 chapters
Expand any chapter to see its topics and sub-topics.
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Algebra
4 topics- Algebraic Expressions and Factorization
- Quadratic Equations
- Simultaneous Linear Equations
- Surds and Indices
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Logarithms
3 topics- Laws of Logarithms
- Common and Natural Logarithms
- Logarithmic Equations
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Trigonometry
4 topics- Trigonometric Ratios
- Trigonometric Identities
- Heights and Distances
- Angles and Radian Measure
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Matrices and Determinants
3 topics- Matrix Operations
- Determinants
- Inverse of a Matrix
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Arithmetic and Number System
4 topics- Percentages, Ratio and Proportion
- Profit, Loss and Discount
- Average, Speed, Time and Distance
- HCF and LCM
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Geometry and Mensuration
4 topics- Lines, Angles and Triangles
- Circles and Polygons
- Area and Perimeter
- Surface Area and Volume
PN Cadet Mathematics flashcards — 51 questions with answers
What is the formula for the difference of two squares?
a² − b² = (a + b)(a − b).
Expand the perfect-square identity (a + b)².
(a + b)² = a² + 2ab + b².
What is the expansion of (a − b)²?
(a − b)² = a² − 2ab + b².
State the sum of cubes factorization a³ + b³.
a³ + b³ = (a + b)(a² − ab + b²).
State the difference of cubes factorization a³ − b³.
a³ − b³ = (a − b)(a² + ab + b²).
To factor a quadratic of the form x² + bx + c, what must the two numbers satisfy?
They must add up to b and multiply to c.
What is the standard (general) form of a quadratic equation?
ax² + bx + c = 0, where a ≠ 0.
State the quadratic formula for ax² + bx + c = 0.
x = [−b ± √(b² − 4ac)] / (2a).
What expression is called the discriminant of a quadratic, and what symbol is used?
The discriminant is D = b² − 4ac.
What does the discriminant tell you when D > 0, D = 0, and D < 0?
D > 0: two distinct real roots; D = 0: one repeated real root; D < 0: two complex (no real) roots.
For ax² + bx + c = 0, what is the sum of the roots?
Sum of roots = −b/a.
For ax² + bx + c = 0, what is the product of the roots?
Product of roots = c/a.
How do you form a quadratic equation when the sum (S) and product (P) of its roots are known?
x² − Sx + P = 0.
Name three methods commonly used to solve quadratic equations.
Factorization, completing the square, and the quadratic formula.
In completing the square for x² + bx, what term must be added to make a perfect square?
Add (b/2)², giving (x + b/2)².
Name two algebraic methods for solving simultaneous linear equations.
The substitution method and the elimination method.
How does the substitution method solve a pair of simultaneous linear equations?
Solve one equation for one variable, then substitute that expression into the other equation.
In the elimination method, how is one variable removed?
Multiply equations to match coefficients, then add or subtract the equations to cancel one variable.
A 2×2 linear system has a unique solution under what condition on the lines?
When the two lines intersect, i.e., they have different slopes (a₁/a₂ ≠ b₁/b₂).
When does a 2×2 linear system have no solution or infinitely many solutions?
No solution when lines are parallel (a₁/a₂ = b₁/b₂ ≠ c₁/c₂); infinitely many when the lines coincide (a₁/a₂ = b₁/b₂ = c₁/c₂).
Show the other 31 Mathematics flashcards
By Cramer's rule, what is x for a 2×2 system, in terms of determinants?
x = Dₓ/D, where D is the coefficient determinant and Dₓ replaces the x-column with the constants (D ≠ 0).
What is a surd?
A surd is an irrational root of a rational number that cannot be simplified to a rational value, e.g., √2 or √3.
How do you rationalize a denominator of the form 1/√a?
Multiply numerator and denominator by √a to get √a/a.
How do you rationalize a denominator of the form 1/(a + √b)?
Multiply by the conjugate (a − √b)/(a − √b), giving (a − √b)/(a² − b).
State the product law of indices: aᵐ × aⁿ.
aᵐ × aⁿ = aᵐ⁺ⁿ.
State the quotient law of indices: aᵐ ÷ aⁿ.
aᵐ ÷ aⁿ = aᵐ⁻ⁿ.
State the power of a power law: (aᵐ)ⁿ.
(aᵐ)ⁿ = aᵐⁿ.
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.
PN Cadet Mathematics FAQ
What is in the PN Cadet Mathematics syllabus?
PN Cadet Mathematics is split into 6 chapters: Algebra, Logarithms, Trigonometry, Matrices and Determinants, Arithmetic and Number System and Geometry and Mensuration. Together they contain 22 topics.
How many chapters are in PN Cadet Mathematics?
6 chapters, containing 22 topics. The largest chapter is Algebra, with 4 topics.
Are there flashcards for PN Cadet Mathematics?
Yes — a 51-card Mathematics deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.