NECO Senior School Certificate Examination · General Mathematics

Algebraic Processes, Equations and Graphs

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. Solve for x in the linear algebraic equation: 3(2x - 4) - 2(x + 5) = 16.
  2. Solve the simultaneous linear equations for x and y: 2x + 3y = 13 and 3x - y = 3.
  3. Find the roots of the quadratic equation by factorization: 2x² + 5x - 3 = 0.
  4. Determine the nature of the roots of the quadratic equation: 3x² - 4x + 2 = 0.
  5. If α and β are the roots of the quadratic equation 2x² - 7x + 4 = 0, find the numerical value of α + β + αβ.
  6. Solve the quadratic inequality: x² - 5x + 6 < 0.
  7. Solve the linear inequality: (2x - 1) / 3 ≤ (x + 4) / 2.
  8. Solve the simultaneous system of linear and quadratic equations: y = x + 1 and x² + y² = 13 for positive x and y.
  9. Simplify the algebraic fraction completely: (x² - 16) / (2x² + 7x - 4).
  10. For what real values of x is the algebraic fraction (3x + 2) / (x² - 4x - 12) mathematically undefined?
  11. Make L the subject of the formula: T = 2π √(L / g).
  12. Find the remainder when the polynomial P(x) = 2x³ - 3x² + 4x - 5 is divided by (x - 2).
  13. If (x - 3) is an exact algebraic factor of the polynomial P(x) = x³ - 4x² + kx - 6, find the numerical value of the constant k.
  14. The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number formed exceeds the original number by 27. Find the original number.
  15. A quantity P varies jointly as the square of Q and the cube root of R. If P = 48 when Q = 2 and R = 27, find P when Q = 3 and R = 64.
  16. The total production cost C of an artisan bakery is partially constant and partially varies directly with the number of bread loaves n baked daily. If the cost is ₦22,000 for 100 loaves and ₦34,000 fo…
  17. Find the gradient (slope) of the straight line with linear equation: 4x - 6y + 15 = 0.
  18. Determine the equation of the line of symmetry for the parabolic curve: y = 2x² - 8x + 5.
  19. Find the coordinates of the turning point (vertex) of the quadratic graph: y = x² - 6x + 11.
  20. Factor the algebraic expression completely by grouping terms: ax + 2bx - 3ay - 6by.
  21. Factor completely: 16x² - 49y².
  22. Expand and simplify the algebraic binomial: (3x - 2y)².
  23. Solve for x in the exponential equation: 3^(2x - 1) = 27.
  24. Solve for real values of x in the equation: 2^(2x) - 5(2^x) + 4 = 0.
  25. Solve for x in the equation: log₂ x + log₄ x = 6.
  26. If α and β are the roots of the quadratic equation x² - 4x + 2 = 0, find the numerical value of α² + β².
  27. Evaluate the determinant of the 2 × 2 matrix: M = [[5, 2], [3, 4]].
  28. Find the inverse of the 2 × 2 matrix: A = [[3, 1], [5, 2]].
  29. Find the value of k for which the matrix [[2, k], [4, 6]] is singular (non-invertible).
  30. The product of two consecutive positive odd integers is 143. What is the smaller of the two integers?
  31. Solve for x in the radical equation: √(2x + 5) = x + 1.
  32. Find the coefficient of x³ in the binomial expansion of (x + 2)⁵.
  33. Solve for x in the equation: (x + 2)/3 - (x - 1)/4 = 1.
  34. Factor completely: 2x³ - 8x.
  35. If 2^(x + 3) = 8^(x - 1), find the value of x.

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