Mathematics Sample Paper Class 10, Exams of Mathematics

Download Mathematics Sample Paper Class 10 and more Exams Mathematics in PDF only on Docsity! CBSE X | Mathematics Sample Paper 1 (Standard) (Updated 2020-2021) www.topperlearning.com 1 CBSE Board Class X Mathematics Sample Paper 1 (Standard) Time: 3 hrs Total Marks: 80 General Instructions: 1. This question paper contains two parts A and B. 2. Both Part A and Part B have internal choices. Part – A: 1. It consists two sections - I and II. 2. Section I has 16 questions of 1 mark each. Internal choice is provided in 5 questions. 3. Section II has 4 questions on case study. Each case study has 5 case-based sub- parts. An examinee is to attempt any 4 out of 5 sub-parts. Each subpart carries 1 mark. Part – B: 1. It consists three sections – III, IV and V 2. Section III: Question No 21 to 26 are Very short answer Type questions of 2 marks each. 3. Section IV: Question No 27 to 33 are Short Answer Type questions of 3 marks each. 4. Section V: Question No 34 to 36 are Long Answer Type questions of 5 marks each. 5. Internal choice is provided in 2 questions of 2 marks, 2 questions of 3 marks and 1 question of 5 marks Part A Section I Section I has 16 questions of 1 mark each. (Internal choice is provided in 5 questions) 1. What is the LCM of (23×3×5) and (24×5×7)? OR What is the largest number that divides each one of 1152 and 1664 exactly? 2. 2x y 1 x 2y If 0 and 3 then 3 2 6 2 3      CBSE X | Mathematics Sample Paper 1 (Standard) (Updated 2020-2021) www.topperlearning.com 3 If and  are the zeroes of the quadratic polynomial f(x) = x2 + 2x + 1, find the value value of 1 1    . 15. The HCF of two numbers is 27 and their LCM is 162. If one of the numbers is 81, find the other. 16. )f ∆ABC ∼ ∆DEF such that AB = DE and BC = cm, find EF. Section II (Q 17 to Q 20 carry 4 marks each) Case study based questions are compulsory. Attempt any four sub parts of each question. Each subpart carries 1 mark 17. Case Study based-1 SUN ROOM The diagrams show the plans for a sun room. It will be built onto the wall of a house. The four walls of the sunroom are square clear glass panels. The roof is made using • Four clear glass panels, trapezium in shape, all the same size • One tinted glass panel, half a regular octagon in shape (a) Refer to Front View Find the mid-point of the segment joining the points J (6, 17) and I (9, 16). (i) (33/2, 15/2) (ii) (3/2, 1/2) (iii) (15/2, 33/2) (iv) (1/2, 3/2) CBSE X | Mathematics Sample Paper 1 (Standard) (Updated 2020-2021) www.topperlearning.com 5 Hence, two shapes are Similar when one can become the other after a resize, flip, slide or turn. (a) A model of a boat is made on the scale of 1:4. The model is 120cm long. The full size of the boat has a width of 60cm. What is the width of the scale model? (i) 20cm (ii) 25cm (iii) 15cm (iv) 240cm (b) What will affect the similarity of any two polygons? (i) They are flipped horizontally (ii) They are dilated by a scale factor (iii) They are translated down (iv) They are not the mirror image of one another (c) If two similar triangles have a scale factor of a: b. Which statement regarding the two triangles is true? (i) The ratio of their perimeters is 3a: b (ii) Their altitudes have a ratio a: b (iii) Their medians have a ratio �/2: b (iv) Their angle bisectors have a ratio a2: b2 (d) The shadow of a stick 5m long is 2m. At the same time the shadow of a tree 12.5m high is CBSE X | Mathematics Sample Paper 1 (Standard) (Updated 2020-2021) www.topperlearning.com 6 (i) 3m (ii) 3.5m (iii) 4.5m (iv) 5m (e) Below you see a student's mathematical model of a farmhouse roof with measurements.The attic floor, ABCD in the model, is a square. The beams that support the roof are the edges of a rectangular prism, EFGHKLMN. E is the middle of AT, F is the middle of BT, G is the middle of CT, and H is the middle of DT. All the edges of the pyramid in the model have length of 12 m. What is the length of EF, where EF is one of the horizontal edges of the block? (i) 24m (ii) 3m (iii) 6m (iv) 10m 19. Case Study Based- 3 Applications of Parabolas-Highway Overpasses/Underpasses A highway underpass is parabolic in shape. CBSE X | Mathematics Sample Paper 1 (Standard) (Updated 2020-2021) www.topperlearning.com 7 Parabola A parabola is the graph that results from p(x)=ax2+bx+c Parabolas are symmetric about a vertical line known as the Axis of Symmetry. The Axis of Symmetry runs through the maximum or minimum point of the parabola which is called the (a) If the highway overpass is represented by x2–2x –8. Then its zeroes are (i) (2, –4) (ii) (4, –2) (iii) (–2, –2) (iv) (–4, –4) (b) The highway overpass is represented graphically. Zeroes of a polynomial can be expressed graphically. Number of zeroes of polynomial is equal to number of points where the graph of polynomial (i) Intersects x-axis (ii) Intersects y-axis (iii) Intersects y-axis or x-axis (iv) None of the above (c) Graph of a quadratic polynomial is a (i) straight line (ii) circle (iii) parabola (iv) ellipse (d) The representation of Highway Underpass whose one zero is 6 and sum of the zeroes is 0, is (i) x2 – 6x + 2 (ii) x2 – 36 (iii) x2 – 6 (iv) x2 – 3 (e) The number of zeroes that polynomial f(x) = (x – 2)2 + 4 can have is: (i)1 (ii) 2 (iii) 0 (iv) 3 CBSE X | Mathematics Sample Paper 1 (Standard) (Updated 2020-2021) www.topperlearning.com 10 28. Find the number of solid spheres, each of diameter 6 cm that could be molded to form a solid metallic cylinder of height 45 cm and diameter 4 cm. 29. 2 Prove that is irrational. 7 30. The arithmetic mean of the following frequency distribution is 25. Class 0-10 10-20 20-30 30-40 40-50 Frequency 16 p 30 32 14 Find the value of p. 31. Bridge across a river makes an angle of 45° with the river bank as shown in the figure. If the length of the bridge across the river is 150 m, what is the width of the river? 32. Find the mean of following distribution by the step deviation method. Daily Expenditure: 100-150 150-200 200-250 250-300 300-350 No. of householders: 4 5 12 2 2 33. Solve: 23x + 29y = 98, 29x + 23y = 110 OR Solve: 6x + 3y = 7xy and 3x + 9y = 11xy Section V (Q 34 to Q 36 carry 5 marks each) 34. A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank which is 10 m in diameter and 2 m deep. If the water flows through the pipe at the rate of 4 km/hr, in how much time will the tank be filled completely? 35. An electrician has to repair an electric fault on a pole of height 4 metres. He needs to reach a point 1 metre below the top of the pole to undertake the repair work. What should be the length of the ladder that he should use, which when inclined at an angle of 60° to the horizontal would enable him to reach the required position?   Take 3 1.732 CBSE X | Mathematics Sample Paper 1 (Standard) (Updated 2020-2021) www.topperlearning.com 11 OR A straight highway leads to foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30o, which is approaching the foot of the tower with a uniform speed. Six seconds later the angle of depression of the car is found to be 60o. Find the time taken by the car to reach the foot of the tower from this point. 36. A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work. Powered by TCPDF (www.tcpdf.org)