SOF IMO Sample Paper 2026 Class 10

CLASS 10 SAMPLE PAPER 2025-26 SOF INTERNATIONAL MATHEMATICS OLYMPIAD Total Questions : 50 Time : 1 hr. PATTERN & MARKING SCHEME Section (1) Logical (2) Mathematical (3) Everyday (4) Achievers Reasoning Reasoning Mathematics Section No. of Questions 15 20 10 5 Marks per Ques. 1 1 1 3 SYLLABUS Section – 1 : Verbal and Non-Verbal Reasoning. Section – 2 : Real Numbers, Polynomials, Pair of Linear Equations in Two Variables, Quadratic Equations, Arithmetic Progressions, Triangles, Coordinate Geometry, Introduction to Trigonometry, Some Applications of Trigonometry, Circles, Areas Related to Circles, Surface Areas and Volumes, Statistics, Probability. Section – 3 : The syllabus of this section will be based on the syllabus of Mathematical Reasoning and Quantitative Aptitude. Section – 4 : Higher Order Thinking Questions - Syllabus as per Section – 2. LOGICAL REASONING 1. A square transparent sheet with a pattern and a dotted line on it is shown here. Select a figure from the options as to how the pattern would appear when the transparent sheet is folded along the dotted line. (A) (B) (C) (D) Problem Figures 2. Select a figure from the options which will * * * * continue the same series as established by * the Problem Figures. * * (A) (B) * (C) * (D) 3. In a row of boys, Nitish is 8th from the right end and Prem is 17th from the left end. If they interchange their positions, then Nitish becomes 10th from the right end. How many boys are there in the row? (A) 25 (B) 26 (C) 27 (D) 24 MATHEMATICAL REASONING S3n 4. Let Sn denotes the sum of first n terms of an A.P. If S2n = 3Sn, then the value of Sn is equal to (A) 4 (B) 6 (C) 8 (D) 10 Sample Paper | Class-10 | 1

5. If AB is chord of a circle with centre O & PQ is a tangent to the circle at B with reflex ∠AOB = 210°, then the value of A O 210° ∠ABQ is P (A) 105° (B) 150° B (C) 210° (D) 75° Q 6. The angles of depression of two consecutive kilometre stones on the road on right and left of an aeroplane are 60° and 45°, respectively as observed from the aeroplane. Find the height of the aeroplane from the ground. (Use : 3 = 1.732) (A) 0.634 km (B) 1.682 km (C) 2.384 km (D) 0.236 km EVERYDAY MATHEMATICS 7. Two trains leave a railway station at the same time. The first train travels due West and the second train due North. The first train travels 5 km/hr faster than the second train. If after two hours, they are 50 km apart, then find the average speed of each train. (A) 20 km/hr, 15 km/hr (B) 25 km/hr, 30 km/hr (C) 40 km/hr, 30 km/hr (D) 60 km/hr, 55 km/hr 8. A design on a floor is made up of triangular tiles. The sides of each triangle being 24 cm, 32 cm and 40 cm. Find the cost of polishing all 170 tiles on the floor at the rate of ` 1.50 per cm2. (A) ` 97920 (B) ` 65280 (C) ` 99480 (D) ` 89460 ACHIEVERS SECTION 9. Solve the following questions and select the correct option. cos α cos α (i) If = m and = n, then (m2 + n2) cos a cos b cot b is equal to _______. cos β sin β 1 1− cos A (ii) If cosec A = 2, then the value of + is _______. tan A sin A (A) (i) - n3; (ii) - 2 − 1 (B) (i) - n; (ii) - 2 (C) (i) - n3; (ii) - 2 (D) (i) - n2; (ii) - 3 + 2 10. Read the given statements carefully and select the correct option. Statement-I : If the quadratic equation (4 – k)x2 + (2k + 4)x + (8k + 1) = 0 is a perfect square, then the values of k are 0 and 3. Statement-II : If a, b are the roots of the equation 25x2 +20x + 4 = 0, then the 1 1 equation whose roots are and is 4x2 + 20x + 25 = 0. α β (A) Both Statement-I and Statement-II are true. (B) Both Statement-I and Statement-II are false. (C) Statement-I is true but Statement-II is false. (D) Statement-I is false but Statement-II is true. ANSWER KEY 1. (A) 2. (C) 3. (B) 4. (B) 5. (D) 6. (A) 7. (A) 8. (A) 9. (C) 10. (A) 2 | Sample Paper | Class-10