Higher Secondary Certificate Examination (Bangladesh) · Higher Mathematics

Algebra, Conic Sections, Trigonometry and Mechanics

35 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 35 questions

  1. If omega is an imaginary cube root of unity, what is the value of 1 + omega + omega^2?
  2. What is the value of omega^3 if omega is a cube root of unity?
  3. What is the modulus of the complex number z = 3 - 4i?
  4. What is the argument (in radians) of the complex number z = 1 + i?
  5. If alpha and beta are the roots of ax^2 + bx + c = 0, what is the product of roots alpha * beta?
  6. What is the discriminant of the quadratic equation 2x^2 - 5x + 3 = 0?
  7. What is the focus of the parabola y^2 = 12x?
  8. What is the length of the latus rectum of the parabola y^2 = 16x?
  9. What is the eccentricity e of a parabola?
  10. What is the eccentricity e of an ellipse?
  11. What is the eccentricity of the ellipse x^2 / 25 + y^2 / 16 = 1? (Hard)
  12. What is the equation of the directrix of the parabola y^2 = 8x?
  13. What is the value of sin(75 degrees)? (Hard)
  14. What is the principal value of arcsin(1/2)?
  15. What is the general solution of the equation sin(theta) = 0?
  16. What is the general solution of the equation cos(theta) = 0?
  17. What is the value of arcsin(x) + arccos(x) for all x in [-1, 1]?
  18. What is the value of arctan(1) + arctan(1/2) + arctan(1/3)? (Hard)
  19. What is the maximum range R_max of a projectile launched with speed u on horizontal ground?
  20. What is the maximum height H achieved by a projectile launched with speed u at angle alpha?
  21. What is the time of flight T of a projectile launched with initial velocity u at angle alpha?
  22. According to Lami's Theorem, if three coplanar concurrent forces P, Q, and R keep a body in equilibrium, what relation holds?
  23. What is the resultant R of two forces P and Q acting at right angles (90 degrees) to each other?
  24. What is the resultant of two equal forces P acting at an angle of 120 degrees to each other? (Hard)
  25. What is the conjugate of the complex number z = -5 + 7i?
  26. What is the value of i^4n where n is any integer and i = sqrt(-1)?
  27. If one root of quadratic equation with rational coefficients is 3 + root 5, what must the other root be?
  28. What is the nature of roots of ax^2 + bx + c = 0 if discriminant D = b^2 - 4ac < 0?
  29. What are the coordinates of the vertices of the hyperbola x^2 / 9 - y^2 / 16 = 1?
  30. What is the distance between the two foci of the hyperbola x^2 / 9 - y^2 / 16 = 1? (Hard)
  31. In an ellipse, what is the relation between semi-major axis a, semi-minor axis b, and eccentricity e?
  32. What is the formula for the sum of roots of cubic equation ax^3 + bx^2 + cx + d = 0?
  33. What is the value of tan(2 theta) in terms of tan(theta)?
  34. Under what condition does a quadratic equation ax^2 + bx + c = 0 have equal roots?
  35. What is the period of the function f(x) = sin(4x)?

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