PN Cadet Mathematics Syllabus

Mathematics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics in PN Cadet, not a summary of it.

1. 1

   Algebra

   4 topics

   • Algebraic Expressions and Factorization
   • Quadratic Equations
   • Simultaneous Linear Equations
   • Surds and Indices
2. 2

   Logarithms

   3 topics

   • Laws of Logarithms
   • Common and Natural Logarithms
   • Logarithmic Equations
3. 3

   Trigonometry

   4 topics

   • Trigonometric Ratios
   • Trigonometric Identities
   • Heights and Distances
   • Angles and Radian Measure
4. 4

   Matrices and Determinants

   3 topics

   • Matrix Operations
   • Determinants
   • Inverse of a Matrix
5. 5

   Arithmetic and Number System

   4 topics

   • Percentages, Ratio and Proportion
   • Profit, Loss and Discount
   • Average, Speed, Time and Distance
   • HCF and LCM
6. 6

   Geometry and Mensuration

   4 topics

   • Lines, Angles and Triangles
   • Circles and Polygons
   • Area and Perimeter
   • Surface Area and Volume

Mathematics flashcards for PN Cadet

21 of 51 cards from the Mathematics deck — real questions with worked answers.

1. What is the formula for the difference of two squares?

   a² − b² = (a + b)(a − b).

2. Expand the perfect-square identity (a + b)².

   (a + b)² = a² + 2ab + b².

3. What is the expansion of (a − b)²?

   (a − b)² = a² − 2ab + b².

4. State the sum of cubes factorization a³ + b³.

   a³ + b³ = (a + b)(a² − ab + b²).

5. State the difference of cubes factorization a³ − b³.

   a³ − b³ = (a − b)(a² + ab + b²).

6. 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.

7. What is the standard (general) form of a quadratic equation?

   ax² + bx + c = 0, where a ≠ 0.

8. State the quadratic formula for ax² + bx + c = 0.

   x = [−b ± √(b² − 4ac)] / (2a).

9. What expression is called the discriminant of a quadratic, and what symbol is used?

   The discriminant is D = b² − 4ac.

10. 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.

11. For ax² + bx + c = 0, what is the sum of the roots?

    Sum of roots = −b/a.

12. For ax² + bx + c = 0, what is the product of the roots?

    Product of roots = c/a.

13. How do you form a quadratic equation when the sum (S) and product (P) of its roots are known?

    x² − Sx + P = 0.

14. Name three methods commonly used to solve quadratic equations.

    Factorization, completing the square, and the quadratic formula.

15. 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.

16. Name two algebraic methods for solving simultaneous linear equations.

    The substitution method and the elimination method.

17. 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.

18. In the elimination method, how is one variable removed?

    Multiply equations to match coefficients, then add or subtract the equations to cancel one variable.

19. 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).

20. 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).

21. 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).

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