Tawjihi (Palestinian General Secondary Examination), Scientific Stream · Mathematics

Algebra, Functions and Calculus

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

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All 21 questions

  1. Solve the equation 2x + 5 = 17.
  2. What are the roots of x² − 5x + 6 = 0?
  3. What is the vertex of the parabola y = x² − 4x + 7?
  4. Differentiate f(x) = 3x⁴ − 2x² + 5 with respect to x.
  5. Find d/dx of (x² + 1)³.
  6. Evaluate the indefinite integral ∫(6x² + 4) dx.
  7. What is log₂ 8 + log₂ 4?
  8. What is the domain of f(x) = √(x − 3) / (x − 5)?
  9. Solve |2x − 1| = 7.
  10. For which value of k does kx² + 6x + 3 = 0 have exactly one repeated root?
  11. What is the gradient of the tangent to y = x³ at x = 2?
  12. What is the maximum value of f(x) = −x² + 6x + 1?
  13. If f(x) = 3x − 2, what is f(4)?
  14. Let f(x) = 2x + 1 and g(x) = x². What is (f ∘ g)(3)?
  15. Find the inverse function of f(x) = (x − 1)/2.
  16. Solve 2^(x+1) = 32.
  17. What is the area under y = x² between x = 0 and x = 3?
  18. What is the sum of the roots of 2x² − 7x + 3 = 0?
  19. At which x does f(x) = x³ − 3x have a local minimum?
  20. Simplify (x²)³.
  21. Evaluate the limit as x → 2 of (x² − 4)/(x − 2).

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