Hard SAT Practice Questions

83 free hard-difficulty SAT questions, drawn live from KomFi's calibrated bank. These are the items that separate top scorers — every one carries a full explanation and trap analysis once you sign in.

  1. If the system has no solution, what is the value of a?
  2. What is the value of k?
  3. Which of the following is the best interpretation of the number 2.4 in this model?
  4. If the system has no solution, what is the value of k?
  5. begincases y = x^2 - 4x + 7 y = 2x - 2 endcases How many points of intersection do the graphs of the equations
  6. What is the value of r?
  7. What is the value of m?
  8. The function f is defined by f(x)=x^2-3x. Which of the following is equivalent to f(x+2)-f(x) ?
  9. What is the value of f(4)?
  10. What is the maximum height, in feet, that the ball reaches?
  11. At how many distinct values of x does the graph of y=p(x) cross through the x-axis?
  12. What is the solution set for the equation (x)/(x-4) = (4)/(x-4) + 3?
  13. What is the solution set of the equation √(2x + 1) = x - 1?
  14. In the system of equations below, c is a constant. y = 2x^2 - 8x + c y = -10 If the graphs of these equations
  15. What is the solution set of the equation √(3x + 1) = x - 3?
  16. What is the value of p?
  17. What is the value of cos A-sin A?
  18. What is the radius of the circle?
  19. What is the value of x + y?
  20. If (1)/(2)x + (1)/(3)y = 7, what is the value of 3x + 2y?
  21. If the population at the start of 2024 was P, what was the population at the end of 2025 in terms of P?
  22. If |x - 5| = |x + 3|, what is the value of x?
  23. What is the value of cos θ?
  24. If the equation has exactly one real solution, what is the value of k?
  25. What is the radius of the circle?
  26. What is the sum of the solutions to the equation |3x - 7| = 5?
  27. The equation 2x^2-7x+3=0 has two real solutions. What is the sum of the two solutions?
  28. What is the value of c?
  29. What value of x satisfies the equation dfracx^2x - 3 = dfrac9x - 3 + 2?
  30. If f(2) = 17, what is the value of f(5)?

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