The Government of Nepal, through the Teachers Service Commission, has conducted an open competitive examination for the position of Secondary Level Teacher (Level-3rd class) for the Mathematics subject 2081. You can use this question as a guideline and modality of the questions.
Teachers Service Commission Secondary Level Third Class Teacher Position Open Competitive Examination
Mathematics Subject Examination-2081
Level: Secondary Level
Time: 3 hours
Full Marks: 100 Passing Marks: 40
Subject: Mathematics
Group A
1. a) How do you let your students differentiate between sequence and series? How do you teach the sum of the cube of the first n natural numbers by mathematical induction ? 2+3
b) Explain the procedures to teach the concept of area and volume of prism with suitable examples. 2+3
2.A theorem states "Opposite sides and angles of a parallelogram are equal." Describe four steps of problem solving approach in teaching this theorem. 10
3. Define conic sections with examples and explain their fundamental features. How would you teach conic sections diagrammatically? 2+4+4
4. What are the different types of central tendency? Illustrate them with suitable diagrams. Describe situation where they are used most appropriately. 4+6
5. Justify with examples why curriculum is necessary on top of a good textbook. Critically appraise the concepts included in the Mathematics curriculum of Grade IX. Also, mention your suggestions for the improvement of the contents included in that of above curriculum. 3+5+2
Group B
6. a) Explain why integration is the reverse process of differentiation. 4
b) Find the area of the ellipse given below by using the method of integration. 6
7. State the postulates of Euclidean and non-Euclidean geometries. Discuss the main characteristics of Hyperbolic and Elliptic geometry which differ from that of Euclidean geometry. 5+5
8. List down the problems of antiquity in the history of Mathematics. Explain them with suitable examples. 10
9. In answering an achievement test of Mathematics, following scores were obtained by 10 girls and 10 boys:
| Boys | 22 | 23 | 25 | 25 | 31 | 33 | 34 | 34 | 35 | 37 |
| Girls | 22 | 31 | 38 | 47 | 48 | 48 | 49 | 50 | 53 | 61 |
Test whether boys and girls differ significantly in their mean score. 10
10. What are the processes of 'child learning' and 'adult learning with reference to learning Mathematics? And, write your understanding about 'how children learn' with consideration to the assumptions of behaviorism and constructivism. 10
