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N(A)-Level Mathematics Coordinate Geometry and Vectors quiz (SEAB 4045) quiz

13questions. Pick an answer and you'll see why right away.

  1. Find the gradient of the line through (1,2)(1, 2) and (4,11)(4, 11).

  2. Find the gradient of the line through (−2,5)(-2, 5) and (2,−3)(2, -3).

  3. A line has gradient 44 and passes through (0,−2)(0, -2). What is its equation?

  4. Find the equation of the line through (1,5)(1, 5) with gradient 33.

  5. Find the length of the segment joining (0,0)(0, 0) and (3,4)(3, 4).

  6. Find the length of the segment joining (1,2)(1, 2) and (6,14)(6, 14).

  7. Find the midpoint of the segment joining (2,4)(2, 4) and (8,10)(8, 10).

  8. Find the midpoint of the segment joining (−4,2)(-4, 2) and (2,−6)(2, -6).

  9. Given a=(23)\mathbf{a} = \begin{pmatrix} 2 \\ 3 \end{pmatrix} and b=(5−1)\mathbf{b} = \begin{pmatrix} 5 \\ -1 \end{pmatrix}, find a+b\mathbf{a} + \mathbf{b}.

  10. Given a=(64)\mathbf{a} = \begin{pmatrix} 6 \\ 4 \end{pmatrix} and b=(27)\mathbf{b} = \begin{pmatrix} 2 \\ 7 \end{pmatrix}, find a−b\mathbf{a} - \mathbf{b}.

  11. Given a=(3−2)\mathbf{a} = \begin{pmatrix} 3 \\ -2 \end{pmatrix}, find 2a2\mathbf{a}.

  12. Find the magnitude of the vector (68)\begin{pmatrix} 6 \\ 8 \end{pmatrix}.

  13. Find the magnitude of the vector (−512)\begin{pmatrix} -5 \\ 12 \end{pmatrix}.