Aga Khan University Examination Board Mathematics (SSC IX-X) Flashcards

24 sample cards from the Mathematics (SSC IX-X) deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. Using the inverse-matrix method, how is AX = B solved?

   By computing X = A⁻¹B, provided A is non-singular (det A ≠ 0).

2. In Cramer's rule for two equations, how is x found?

   x = Dx / D, where D is the determinant of the coefficient matrix and Dx is D with the x-column replaced by the constants column.

3. What does it mean if the determinant of the coefficient matrix is zero?

   The system has no unique solution (it is either inconsistent with no solution or has infinitely many solutions).

4. What is a rational number?

   A number that can be written as p/q where p and q are integers and q ≠ 0; its decimal form terminates or recurs.

5. What is an irrational number?

   A number that cannot be written as p/q with integers p, q; its decimal form is non-terminating and non-recurring, e.g. √2 and π.

6. What numbers make up the set of real numbers?

   The real numbers consist of all rational numbers together with all irrational numbers.

7. State the closure, commutative and associative properties of real numbers under addition.

   Closure: a + b is real; Commutative: a + b = b + a; Associative: (a + b) + c = a + (b + c).

8. State the distributive property of multiplication over addition for real numbers.

   a(b + c) = ab + ac (and (b + c)a = ba + ca).

9. What are the additive and multiplicative identities of real numbers?

   The additive identity is 0 (a + 0 = a); the multiplicative identity is 1 (a x 1 = a).

10. In the radical n√a, name the parts.

    n is the index, the symbol √ is the radical sign, and a (the number under the radical) is the radicand.

11. What does it mean to rationalize the denominator?

    It means removing the radical from the denominator, usually by multiplying numerator and denominator by a suitable surd or conjugate.

12. What is the conjugate of the surd a + √b?

    Its conjugate is a − √b; multiplying them gives the rational number a² − b.

13. State the product law of exponents: aᵐ · aⁿ.

    aᵐ · aⁿ = aᵐ⁺ⁿ (add the exponents when the bases are the same).

14. State the quotient law of exponents: aᵐ ÷ aⁿ.

    aᵐ ÷ aⁿ = aᵐ⁻ⁿ (subtract the exponents, a ≠ 0).

15. State the power law of exponents: (aᵐ)ⁿ.

    (aᵐ)ⁿ = aᵐⁿ (multiply the exponents).

16. What is the value of a⁰ (a ≠ 0), and the meaning of a⁻ⁿ?

    a⁰ = 1, and a⁻ⁿ = 1/aⁿ (a negative exponent gives the reciprocal).

17. How is a fractional exponent a^(m/n) written as a radical?

    a^(m/n) = n√(aᵐ) = (n√a)ᵐ.

18. What is a complex number and its standard form?

    A complex number has the form a + bi, where a and b are real numbers and i = √(−1); a is the real part and b is the imaginary part.

19. What is the value of i² and the conjugate of a + bi?

    i² = −1; the conjugate of a + bi is a − bi.

20. How do you add and multiply the complex numbers (a + bi) and (c + di)?

    Add: (a + c) + (b + d)i. Multiply: (ac − bd) + (ad + bc)i (using i² = −1).

21. What is the standard form of scientific notation?

    A number written as a x 10ⁿ, where 1 ≤ a < 10 and n is an integer.

22. What is a logarithm? If aˣ = y, express x as a logarithm.

    A logarithm is the exponent to which a base must be raised to give a number; aˣ = y means x = logₐ y.

23. What are common and natural logarithms?

    A common logarithm has base 10 (log₁₀, written log); a natural logarithm has base e ≈ 2.718 (written ln).

24. State the product, quotient and power laws of logarithms.

    log(mn) = log m + log n; log(m/n) = log m − log n; log(mⁿ) = n log m.

What this deck covers

Mathematics (SSC IX-X) flashcards FAQ