NECO Senior School Certificate Examination · General Mathematics

Geometry, Trigonometry, Statistics and Probability

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. An arc of a circle subtends an angle of 140° at the center of the circle. What angle does this same arc subtend at any point on the remaining part of the circumference?
  2. In a cyclic quadrilateral ABCD, the interior angle ∠A measures (3x - 10)° and the opposite interior angle ∠C measures (2x + 40)°. What is the numerical value of x?
  3. A tangent line PT touches a circle at point T, and a chord TA is drawn such that ∠PTA = 55°. If point B lies on the major arc such that triangle TAB is formed, what is the size of angle ∠TBA?
  4. If each interior angle of a regular polygon measures 144°, how many sides does the polygon possess?
  5. Calculate the straight-line distance between the Cartesian points P(1, -2) and Q(7, 6).
  6. Find the coordinates of the midpoint of the line segment joining the points A(-4, 7) and B(2, -3).
  7. Determine the gradient (slope) of a straight line that is perpendicular to the line with equation 2x + 5y - 10 = 0.
  8. Find the equation of the straight line passing through the point (3, -1) with a gradient of -2.
  9. From the top of a vertical telecommunication mast 50 m high, the angle of depression of a motorcycle on the horizontal ground is 30°. How far is the motorcycle from the base of the mast? (Take √3 ≈ 1.…
  10. A security patrol vessel sails 12 km due East and then 5 km due South. What is the three-figure bearing of the vessel from its starting port? (Take tan 22.6° ≈ 0.417)
  11. In triangle ABC, side b = 8 cm, side c = 6 cm, and angle ∠A = 60°. Calculate the length of side a. (Take cos 60° = 0.5)
  12. Calculate the area of triangle PQR where side p = 12 cm, side q = 10 cm, and the included angle ∠R = 30°.
  13. If cos θ = -3/5 and θ lies in the second quadrant (90° < θ < 180°), find the exact value of tan θ.
  14. Evaluate the exact numerical value of: sin² 45° + cos² 60°.
  15. Given 2D vectors u = 3i - 4j and v = -2i + 7j, find the magnitude of the resultant vector w = u + v.
  16. Find the value of the scalar constant m such that the vectors a = 4i + 3j and b = mi - 8j are perpendicular to each other.
  17. The point P(3, -5) is reflected in the x-axis to obtain image point P'. What are the coordinates of P'?
  18. The mean of the five numbers 8, 12, x, 15, and 21 is 14. Find the value of x.
  19. Find the median of the following ungrouped examination score distribution: 14, 8, 22, 19, 11, 17, 25, 9.
  20. Calculate the variance of the numbers: 3, 5, 7, 9, 11.
  21. In a pie chart displaying the annual federal budget allocation, education receives ₦180 billion out of a total national budget of ₦720 billion. What angle of sector represents education in the chart?
  22. Two fair six-sided dice are rolled simultaneously. What is the probability that the sum of the two uppermost faces equals 7?
  23. A bag contains 6 red pens, 4 blue pens, and 5 black pens. If one pen is drawn at random, what is the probability that it is NOT blue?
  24. Events A and B are independent events such that P(A) = 0.50 and P(B) = 0.30. Calculate the probability of the union P(A ∪ B).
  25. A container contains 5 ripe mangoes and 4 unripe mangoes. Two mangoes are picked successively at random without replacement. What is the probability that both mangoes are ripe?
  26. In a right-angled triangle, the two shorter sides measure 5 cm and 12 cm. What is the exact value of the sine of the smallest angle?
  27. Simplify the trigonometric expression: (1 - sin² θ) sec θ.
  28. A surveyor measures side a = 10 cm, side b = 15 cm, and angle ∠A = 30° in triangle ABC. What is the value of sin B?
  29. The angle of elevation of the top of a palm tree from a point on the ground 20 m from its base is 45°. Calculate the height of the palm tree.
  30. In a frequency distribution of test scores with total frequency N = 40, the cumulative frequency preceding the median class is 16, the frequency of the median class is 10, and the class width is 5. If…
  31. A chord of a circle of radius 10 cm subtends an angle of 90° at the center. What is the area of the minor segment bounded by this chord? (Take π = 3.142)
  32. What is the sum of the interior angles of a convex octagon (8-sided polygon)?
  33. If the interquartile range (IQR) of a dataset is 18 and the lower quartile Q1 is 42, find the upper quartile Q3.
  34. A card is drawn at random from a standard deck of 52 playing cards. What is the probability of drawing a King or a Heart?
  35. Point A has coordinates (2, 3). It undergoes a translation by vector T = (-4, 5) followed by an enlargement by scale factor 2 with center at origin. What are the final coordinates of the image point?

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