Secure your guaranteed 16 marks in the public exam with this targeted 10th Maths Geometry & Graph Question Paper compilation. Practical Geometry and Graph problems form the final, high-scoring section of the SSLC mathematics paper, making them crucial for both passing students and centum-aimers. This specialized test paper focuses entirely on key exam models, including constructing tangents, similar triangles, and cyclic quadrilaterals, alongside quadratic and variation graphs. Practice these blueprint-aligned questions to perfect your construction steps, draw highly accurate curves, and manage your time efficiently during the board exam!
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GEOMETRY & GRAPH
Ramanathan Chettiar Municipal High School, KARAIKUDI, SVG Dist. Mobile: 9942904874
1. Construct a triangle similar to a given triangle PQR with its sides equal to 3/5 of the corresponding sides of the triangle PQR (scale factor 3/5 < 1).
2. Construct a triangle similar to a given triangle PQR with its sides equal to 2/3 of the corresponding sides of the triangle PQR (scale factor 2/3 < 1).
3. Construct a triangle similar to a given triangle LMN with its sides equal to 4/5 of the corresponding sides of the triangle LMN (scale factor 4/5 < 1).
4. Construct a triangle similar to a given triangle PQR with its sides equal to 7/4 of the corresponding sides of the triangle PQR (scale factor 7/4 > 1).
5. Construct a triangle similar to a given triangle ABC with its sides equal to 6/5 of the corresponding sides of the triangle ABC (scale factor 6/5 > 1). PTA 1 / SEP_20
6. Construct a triangle similar to a given triangle PQR with its sides equal to 7/3 of the corresponding sides of the triangle PQR (scale factor 7/3 > 1).
7. Construct a ΔPQR in which PQ = 8 cm, ∠R = 60° and the median RG from R to PQ is 5.8 cm. Find the length of the altitude from R to PQ. PTA 3
8. Construct a ΔPQR in which QR = 5 cm, ∠P = 40° and the median PG from P to QR is 4.4 cm. Find the length of the altitude from P to QR.
9. Construct a ΔPQR in which the base PQ = 4.5 cm, ∠R = 35° and the median from R to PQ is 6 cm.
10. Construct a triangle ΔPQR such that QR = 5 cm, ∠P = 30° and the altitude from P to QR is of length 4.2 cm. PTA 5
11. Construct a ΔPQR such that QR = 6.5 cm, ∠P = 60° and the altitude from P to QR is of length 4.5 cm.
12. Construct a triangle ΔABC such that AB = 5.5 cm, ∠C = 25° and the altitude from C to AB is 4 cm.
13. Draw a triangle ABC of base BC = 8 cm, ∠A = 60° and the bisector of ∠A meets BC at D such that BD = 6 cm. GMQ
14. Draw a triangle ABC of base BC = 5.6 cm, ∠A = 40° and the bisector of ∠A meets BC at D such that CD = 4 cm.
15. Draw ΔPQR such that PQ = 6.8 cm, vertical angle 50° and the bisector of the vertical angle meets the base at D where PD = 5.2 cm. PTA 4
16. Draw a circle of radius 3 cm. Take a point P on this circle and draw a tangent at P.
17. Draw a tangent at any point R on the circle of radius 3.4 cm and centre at P.
18. Draw a circle of radius 4 cm. At a point L on it draw a tangent to the circle using the alternate-segment theorem.
19. Draw a circle of radius 4.5 cm. Take a point on the circle. Draw the tangent at that point using the alternate segment theorem.
20. Draw a circle of diameter 6 cm from a point P, which is 8 cm away from its centre. Draw the two tangents PA and PB to the circle and measure their lengths. PTA 6
21. Draw the two tangents from a point which is 10 cm away from the centre of a circle of radius 5 cm. Also, measure the lengths of the tangents. SEP_20
22. Draw the two tangents from a point which is 5 cm away from the centre of a circle of diameter 6 cm. Also, measure the lengths of the tangents.
23. Take a point which is 11 cm away from the centre of a circle of radius 4 cm and draw the two tangents to the circle from the point. PTA 2
24. Draw a tangent to the circle from the point P having radius 3.6 cm, and centre at O. Point P is at a distance 7.2 cm from the centre. HY 19
| Diameter (x) cm | 1 | 2 | 3 | 4 | 5 |
| Circumference (y) cm | 3.1 | 6.2 | 9.3 | 12.4 | 15.5 |
2. A bus is travelling at a uniform speed of 50 km/hr. Draw the distance-time graph and hence find:
(i) the constant of variation
(ii) how far will it travel in 90 minutes
(iii) the time required to cover a distance of 300 km from the graph.
3. A garment shop announces a flat 50% discount on every purchase of items for their customers. Draw the graph for the relation between the Marked Price and the Discount. Hence find:
(i) the marked price when a customer gets a discount of Rs.3250 (from Graph)
(ii) the discount when the marked price is Rs 2500
4. Graph the following linear function y = 1/2x. Identify the constant of variation and verify it with the graph. Also,
(i) find y when x = 9
(ii) find x when y = 7.5
| Time (in hours) (x) | 4 | 8 | 12 | 24 |
| Amount Rs. (y) | 60 | 120 | 180 | 360 |
(i) find the amount to be paid when parking time is 6 hrs;
(ii) find the parking duration when the amount paid is Rs.150.
| Number of workers (x) | 40 | 50 | 60 | 75 |
| Number of days (y) | 150 | 120 | 100 | 80 |
(ii) From the graph, find the number of days required to complete the work if the company decided to opt for 120 workers?
(iii) If the work has to be completed by 200 days, how many workers are required?
7. Nishanth is the winner in a Marathon race of 12 km distance. He ran at the uniform speed of 12 km/hr and reached the destination in 1 hour. He was followed by Aradhana, Jeyanth, Sathya and Swetha with their respective speed of 6 km/hr, 4 km/hr, 3 km/hr and 2 km/hr. And, they have covered the distance in 2 hrs, 3 hrs, 4 hrs and 6 hrs respectively. Draw the speed-time graph and use it to find the time taken to Kaushik with his speed of 2.4 km/hr.
8. Draw the graph of xy = 24, x, y > 0. Using the graph find, (i) y when x = 3 and (ii) find x when y = 6.
| No. of pipes (x) | 2 | 3 | 6 | 9 |
| Time taken (in min) (y) | 45 | 30 | 15 | 10 |
(i) Find the time taken to fill the tank when five pipes are used
(ii) Find the number of pipes when the time is 9 minutes
| No. of participants (x) | 2 | 4 | 6 | 8 | 10 |
| Amount for each participant in Rs. (y) | 180 | 90 | 60 | 45 | 36 |
(ii) Graph the above data. Hence, find how much will each participant get if the number of participants are 12.
20. Draw the graph of y = 2x2 and hence solve 2x2 - x - 6 = 0. PTA_4
21. Draw the graph of y = x2 - 4 and hence solve x2 - x - 12 = 0.
22. Draw the graph of y = x2 + 4x + 3 and hence find the roots of x2 + x + 1 = 0.
23. Draw the graph of y = x2 + x - 2 and hence solve x2 + x - 2 = 0. PTA_1 / HY_19
24. Draw the graph of y = x2 - 4x + 3 and use it to solve x2 - 6x + 9 = 0.
25. Draw the graph of y = x2 + x and hence solve x2 + 1 = 0.
26. Draw the graph of y = x2 + 3x + 2 and use it to solve x2 + 2x + 1 = 0. PTA_5
27. Draw the graph of y = x2 + 3x - 4 and hence use it to solve x2 + 3x - 4 = 0. GMQ
28. Draw the graph of y = x2 - 5x - 6 and hence solve x2 - 5x - 14 = 0. PTA_2 / PTA_6
29. Draw the graph of y = 2x2 - 3x - 5 and hence use it to solve 2x2 - 4x - 6 = 0. PTA_3 / SEP_20
30. Draw the graph of y = (x - 1)(x + 3) and hence use it to solve x2 - x - 6 = 0.
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