ECAT Pakistan · Mathematics

Calculus, Algebra and Trigonometry

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 eccentricity of the hyperbola x²/25 − y²/144 = 1.
  2. Find a × b for a = 2i + 0j + 2k and b = -3i − 1j − 2k.
  3. Solve dy/dx = 6x with y(0) = 3. What is y(3)?
  4. Evaluate the integral of 2x(x² + 1)^3 from x = 0 to x = 1.
  5. How many permutations of 10 objects taken 2 at a time are there?
  6. If and are the roots of , find .
  7. Find the remainder when is divided by .
  8. Find the term independent of in the expansion of .
  9. Evaluate .
  10. The first term of an arithmetic progression is and the common difference is . Find the sum of the first terms.
  11. Solve .
  12. Find the value of .
  13. Find the local minimum value of .
  14. Evaluate .
  15. Find the determinant of the matrix with rows (-2, -1) and (9, 9).
  16. Find the determinant of the 3×3 matrix with rows (4, 4, -1); (3, -2, 3); (1, 4, 0).
  17. If A has rows (-3, 4) and (2, 3) and B has rows (-1, -3) and (-3, 4), find the entry in row 2, column 1 of AB.
  18. Find the eccentricity of the ellipse x²/100 + y²/36 = 1.
  19. Find the eccentricity of the hyperbola x²/64 − y²/225 = 1.
  20. Find a × b for a = 3i − 2j − 1k and b = 2i + 4j + 4k.
  21. How many permutations of 8 objects taken 2 at a time are there?
  22. If and are the roots of , find .
  23. Find the coefficient of in the expansion of .
  24. Evaluate .
  25. The first term of an arithmetic progression is and the common difference is . Find the sum of the first terms.
  26. Evaluate .
  27. If and , find the real part of .
  28. If and is acute, find .

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