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SQA Advanced Higher Mathematics Geometry, Proof and Systems of Equations overview quiz quiz

15questions. Pick an answer and you'll see why right away.

  1. To divide complex numbers, you multiply numerator and denominator by:

  2. The modulus of z=a+biz = a + bi is:

  3. De Moivre's theorem states [r(cos⁡θ+isin⁡θ)]n[r(\cos\theta + i\sin\theta)]^n equals:

  4. How many distinct nnth roots does a non-zero complex number have?

  5. The determinant of (abcd)\begin{pmatrix} a & b \\ c & d \end{pmatrix} is:

  6. A square matrix has no inverse when its determinant is:

  7. In Gaussian elimination, a final row reading 0 0 0∣40\ 0\ 0 \mid 4 means:

  8. A final row reading 0 0 0∣00\ 0\ 0 \mid 0 in a 3×33\times 3 system means:

  9. The scalar product a⋅b\mathbf{a} \cdot \mathbf{b} is zero when the vectors are:

  10. The vector product a×b\mathbf{a} \times \mathbf{b} produces a vector that is:

  11. A line through point a\mathbf{a} with direction d\mathbf{d} has vector equation:

  12. Proof by contrapositive proves 'if PP then QQ' by instead proving:

  13. Proof by contradiction begins by assuming:

  14. To disprove a universal claim you need:

  15. The Euclidean algorithm finds the gcd by repeated: