SOF IMO 2022 previous year paper practice · PYQ-pattern set

SOF IMO 2022 PYQ-pattern questions

Showing 10 of the 16 PYQ-pattern questions in this set — freshly worded in that year's pattern, not the original questions. Answers and solutions open under each question.

1. Q1 · Number and Alphabet Series

   Find the missing letter: A, C, F, J, O, ?

   • A. T
   • B. U
   • C. V
   • D. S
   Answer and solution

   Answer: B

   The differences are +2, +3, +4, +5. So, the next difference is +6. O + 6 = U.

2. Q2 · Blood Relations

   A is the brother of B. B is the sister of C. C is the father of D. How is D related to A?

   • A. Nephew or Niece
   • B. Son
   • C. Daughter
   • D. Brother
   Answer and solution

   Answer: A

   C is D's father. B is C's sister, so B is D's aunt. A is B's brother, making A also D's uncle. Therefore, D is A's nephew or niece.

3. Q3 · Cubes and Dice

   Count the total number of cubes in the given 3D figure formed by stacking unit cubes in a specific stepped pattern (with 3 layers: bottom layer has 12 cubes, middle layer has 6 cubes, top layer has 2 cubes).

   • A. 18
   • B. 20
   • C. 22
   • D. 24
   Answer and solution

   Answer: B

   Total cubes = 12 (bottom) + 6 (middle) + 2 (top) = 20 cubes.

4. Q4 · Coordinate Geometry

   In which quadrant does the point (-5, 3) lie?

   • A. First quadrant
   • B. Second quadrant
   • C. Third quadrant
   • D. Fourth quadrant
   Answer and solution

   Answer: B

   The second quadrant contains points with negative x-coordinates and positive y-coordinates. Point (-5, 3) has x < 0 and y > 0, so it lies in the second quadrant.

5. Q5 · Constructions

   To construct a triangle ABC where BC = 6 cm, ∠B = 60°, and AB + AC = 9 cm, which construction step is essential?

   • A. Draw a line segment of length AB + AC from B at angle 60°
   • B. Construct the perpendicular bisector of BC
   • C. Draw an arc of radius 9 cm from B
   • D. Bisect the angle at vertex B
   Answer and solution

   Answer: A

   To construct a triangle with given base, one angle, and sum of other two sides, we first draw a line segment of length AB + AC from the given angle, then use angle bisector to locate the third vertex.

6. Q6 · Triangles

   In triangle PQR, PQ = PR. A point S on QR is such that PS is perpendicular to QR. If QR = 12 cm and PS = 8 cm, what is the length of PQ?

   • A. 10 cm
   • B. 12 cm
   • C. 14 cm
   • D. 16 cm
   Answer and solution

   Answer: A

   Since triangle PQR is isosceles with PQ = PR and PS ⊥ QR, S is the midpoint of QR. So QS = 6 cm. Using Pythagoras theorem in triangle PQS: PQ² = PS² + QS² = 8² + 6² = 64 + 36 = 100, so PQ = 10 cm.

7. Q7 · Linear Equations in Two Variables

   For what value of k will the system of equations 3x + 4y = 7 and 6x + ky = 14 have infinitely many solutions?

   • A. k = 6
   • B. k = 7
   • C. k = 8
   • D. k = 12
   Answer and solution

   Answer: C

   For infinitely many solutions, the ratios a₁/a₂ = b₁/b₂ = c₁/c₂ must be equal. Here 3/6 = 4/k = 7/14, which gives 1/2 = 4/k, so k = 8.

8. Q8 · Probability

   A bag contains 5 red, 4 blue and 3 green balls. If one ball is drawn at random, what is the probability that it is NOT green?

   • A. 3/4
   • B. 1/4
   • C. 2/3
   • D. 5/12
   Answer and solution

   Answer: A

   Total balls = 5+4+3 = 12. Non-green balls = 5+4 = 9. Probability (not green) = 9/12 = 3/4.

9. Q9 · Heron's Formula

   A triangle has sides in the ratio 3:4:5 and its perimeter is 84 cm. What is the area of the triangle?

   • A. 294 cm²
   • B. 336 cm²
   • C. 378 cm²
   • D. 420 cm²
   Answer and solution

   Answer: A

   Sides = 3k+4k+5k=12k=84, so k=7. Sides are 21, 28, 35. This is a right triangle (3:4:5), so area = (1/2)(21)(28) = 294 cm².

10. Q10 · Quadratic Equations (Class 10)

    The sum of the roots of the equation 2x² - 5x + 3 = 0 is α and the product is β. What is α + β?

    • A. 4
    • B. 7/2
    • C. 11/2
    • D. 5
    Answer and solution

    Answer: A

    Sum of roots α = 5/2, product β = 3/2. So α + β = 5/2 + 3/2 = 8/2 = 4.