ECAT Pakistan · Mathematics

Matrices, Determinants and Coordinate Geometry

28 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 28 questions

  1. Find the determinant of the 3×3 matrix with rows (0, -3, 5); (-3, -1, 0); (-3, -3, -1).
  2. Find the coordinates of the focus of the parabola y² = 16x.
  3. Find the eccentricity of the ellipse x²/169 + y²/25 = 1.
  4. Find the eccentricity of the hyperbola x²/16 − y²/9 = 1.
  5. Find a × b for a = 3i + 0j + 4k and b = 3i + 4j − 2k.
  6. Solve dy/dx = 5x with y(0) = 2. What is y(4)?
  7. Evaluate the integral of 2x(x² + 1)^4 from x = 0 to x = 1.
  8. How many permutations of 12 objects taken 3 at a time are there?
  9. What are the eigenvalues of the matrix with rows (1, -4) and (0, 4)?
  10. If and are the roots of , find .
  11. is a factor of . Find the value of .
  12. Find the term independent of in the expansion of .
  13. Find .
  14. The first term of an arithmetic progression is and the common difference is . Find the sum of the first terms.
  15. Evaluate .
  16. Find .
  17. Find the maximum value of .
  18. If , find when .
  19. The curve has two stationary points. Find the difference between their -coordinates (larger minus smaller).
  20. Evaluate .
  21. Evaluate .
  22. Find the coordinates of the centre of the circle .
  23. Find the -intercept of the line through and .
  24. Find the determinant of the matrix with rows (-4, -6) and (-5, 4).
  25. Find the determinant of the 3×3 matrix with rows (3, 3, 2); (-3, 1, 4); (1, 5, -3).
  26. If A has rows (3, 3) and (-3, 2) and B has rows (3, -3) and (-1, 1), find the entry in row 1, column 2 of AB.
  27. Find the coordinates of the focus of the parabola y² = 24x.
  28. Find the eccentricity of the ellipse x²/25 + y²/16 = 1.

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