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CBSE Class 10 Maths Additional Practice Paper Questions 2023-24

CBSE Class 10 Maths Additional Practice Paper Questions 2023-24 has been published on the official website of CBSE @cbse.academic.nic.in. You can download the complete question paper from the website.
authorImageYashasvi Tyagi3 Jan, 2024
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CBSE Class 10 Maths Additional Practice Paper Questions 2023-24

CBSE Class 10 Maths Additional Practice Paper Questions 2023-24: The Central Board of Secondary Education (CBSE) has released the Class 10 Maths Additional Practice Paper Questions 2023-24 along with the marking schemes on its official website @cbseacademic.nic.in. This year, CBSE will conduct a single board examination, and there won't be any terms from now on.

Students preparing for the CBSE Class 10th exam in the 2023-24 session are recommended to review these additional sample papers carefully. By using these sample papers, students can understand and get used to the actual board exam pattern. You can find out more details about the Class 10 Maths Additional Practice Paper Questions 2023-24 in the article below.

CBSE Class 10 Maths Additional Practice Paper Questions 2023-24 Overview

The recently issued Class 10 Maths Additional Practice Paper Questions 2023-24 are crafted based on the complete syllabus. The Maths Additional Practice Paper for 2023-24 is divided into five Sections: Section-A, Section-B, Section-C, Section-D, and Section-E, totaling 80 marks. Students have a time limit of 3 hours to complete the question paper. Here are some important instructions for students to be aware of before attempting the paper.
  1. Every question in the Mathematics paper is mandatory, and some questions may have internal choices.
  2. Section A includes 18 Multiple Choice Questions and 02 assertion-reason-based questions, each carrying one mark.
  3. Section B comprises 05 very short answer questions, each worth 02 marks.
  4. In Section C, there are 06 short answer questions, with each question carrying 03 marks.
  5. Section D consists of 04 long answer questions, with each question having a weightage of 05 marks.
  6. Section E presents 03 case-based integrated units of assessment, each with a value of 04 marks, and sub-parts with values of 01, 01, and 02 marks, respectively.

CBSE Class 10 Exam Pattern 2023-24

CBSE Class 10 Maths Additional Practice Paper Questions 2023-24 PDF

These extra practice questions for CBSE Class 10 Mathematics aim to give a sense of the real board exam setup. This includes details like the number of sections, the kinds of questions (objective, short answer, and long answer), and the general format of the question paper.

CBSE Class 10 Maths Additional Practice Paper Questions 2023-24 PDF

CBSE Class 10 Maths Additional Practice Paper Questions 2023-24 & Solutions

Here we have provided the CBSE Class 10 Maths Additional Practice Question Paper with answers

Section A – MCQs

Q1. Which of the following could be the graph of the polynomial? (x – 1)²(x + 2)? Answer- (c) Q 2: The lines k1, k2, and k3 represent three different equations as shown in the graph below. The solution of the equations represented by the lines k1 and k3 is x = 3 and y = 0 while the solution of the equations represented by the lines k2 and k3 is x = 4 and y = 1.

Which of these is the equation of the line k3? (a) x – y = 3 (b) x – y = -3 (c) x + y = 3 (d) x + y = 1 Answer- (a) x – y = 3 Q3: What is/are the roots of 3x² = 6x? (a) only 2 (b) only 3 (c) 0 and 6 (d) 0 and 2 Answer- (d) 0 and 2 Q4: The coordinates of the centre of the circle, O, and a point on the circle, N, are shown in the figure below. What is the radius of the circle? (a) √0.4 units (b) 2 units (c) 4 units (d) √42.4 Answer- (b) 2 units Q5: ΔPQR is shown below. ST is drawn such that ∠ PRQ = ∠ STQ. If ST divides QR in a ratio of 2:3, then what is the length of ST? (a) 10/3 cm (b) 8 cm (c) 12 cm (d) 40/3cm Answer- (b) 8 cm Q6: Two scalene triangles are given below. Anas and Rishi observed them and said the following: Anas: ΔPQR is similar to ΔCBA Rishi: ΔPQR is congruent to ΔCBA Which of them is/are correct? (a) Only Anas (b) Only Rishi (c) Both Anas and Rishi (d) Neither of them, as two scalene triangles can never be similar or congruent. Answer- (a) Only Anas

CBSE Class 10 Previous Year Question Papers

Section B – Very Short Answer Type Questions

Q7. Check whether the statement below is true or false. “The square root of every composite number is rational.” Justify your answer by proving rationality or irrationality as applicable. Answer. Take a number that is not a perfect square but is a composite number. For example, 6. Assumes √6 = 𝑎 / 𝑏 , where b ≠ 0, a, and b are co-primes. Write b√6 = a and squares on both sides to get 6b² = a². Writes that as a² is divisible by 2 and 3 which are both prime numbers, a is also divisible by both 2 and 3. Hence concludes that a is divisible by 6. Write a = 6c, where c is an integer and squares on both sides to get a² = 36c². Replaces a² with 6b² from step 2 to get 6b² = 36c² and solves it to get b² = 6c². Writes that as b² is divisible by 2 and 3 which are both prime numbers, b is also divisible by both 2 and 3. Hence concludes that b is divisible by 6. Writes that 2 and 3 divide both a and b which contradicts the assumption that a and b are co-prime and hence √6 is irrational. Concludes that the given statement is false. Q8. Kimaya and Heena started walking from point P at the same moment in opposite directions on a 800 m long circular path as shown below. Kimaya walked to the clubhouse at an average speed of 100 m/min and Heena walked to the badminton court at an average speed of 80 m/min. The length of the circular track between the clubhouse and the badminton court is 180 If Heena took 1 minute more than Kimaya to reach her destination, find the time taken by Heena to reach the badminton court. Show your work. Answer. Assumes the time taken by Kimaya and Heena to reach the club house and the badminton court as t1 and t2 respectively and frames the equation as: t2 – t1 = 1 Assumes the distance travelled by Kimaya as x m and by Heena as y m and frames the equation for the total distance travelled by Kimaya and Heena together as: x + y = 800 – 180 = 620 Uses the constant speeds of Kimaya and Heena to find the values of x and y as: x = 100t1 and y = 80t2 Replaces the values of x and y in the equation of distance travelled as: 100t1 + 80t2 = 620 Substitutes the value of t1 in the above equation as: 100(t2 -1) + 80t2 = 620 Solves the above equation to find the value of t2 as 4 minutes

Section C – Short Answer Type Questions

Q9. Prime factorization of three numbers A, B, and C is given below: A = (2r × 3p × 5q) B = (2p × 3r × 5p) C = (2p × 3q × 5p) such that, p < q < r and p, q, & r are natural numbers..
  • The largest number that divides A, B, and C without leaving a remainder is 30.
  • The smallest number that leaves a remainder of 2 when divided by each of A, B, and C are 5402. Find A, B, and C. Show your work.
Answer. Finds the HCF and LCM of A, B and C from the prime factorisation as: HCF = 2p × 3p × 5p LCM = 2r × 3r × 5q From the given information, infers that HCF of A, B and C is 30 and equates it to the HCF obtained in step 1 to get the value of p as: 2p × 3p × 5p = 30 => (2 × 3 × 5)p = (2 × 3 × 5)1 => p = 1 From the given information, the LCM of A, B and C is 5402 – 2 = 5400. Equates it to the LCM obtained in step 1 to get the values of q and r as: 2r × 3r × 5q = 5400 => (2 × 3)r × (5)q = (2 × 3)3 × (5)2 => q = 2 and r = 3 Substitutes the values of p, q, and r to find the values of A, B, and C as: A = 2³ × 3¹ × 5² = 600 B = 2¹ × 3³× 5¹= 270 C = 2² × 3² × 5¹ = 180 Q10. Riddhi throws a stone in the air such that it follows a parabolic path before it lands at P on the ground as depicted by the graph below.
  1. i) The above graph is represented by a polynomial where the sum of its zeroes is 1 and the sum of the squares of its zeroes is 25. Find the coordinates of P and Q. ii) If one unit on the graph represents 25 metres, how far from Riddhi does the stone land? Show your work.
Answer. i) Assumes the polynomial to be ax2 + bx + c and considers its zeroes to be α and β. Given: α + β = 1 α² + β² = 25 Uses the identity (α + β)² to find αβ as (-12). From the relation between coefficients and zeros of a polynomial, finds b and c in terms of a as: b = (-a) and c = (-12a) Frames the expression of a polynomial as: ax² – axe – 12a Assumes the value of a as 1 and factorises the above polynomial as: x² – x – 12 = (x – 4)(x + 3) Find the zeros as 4 and (-3). Thus, finds the coordinates of P and Q as (4, 0) and (-3, 0).
  1. ii) Writes that the distance between Riddhi and the point where the stones land (P) is (2 + 4) = 6 units.
Finds the distance between Riddhi and point P as (6 × 25) = 150 metres.
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Section D – Long Answer Type Questions

Q11. Manu and Aiza are competing in a 60 km cycling race. Aiza’s average speed is 10 km/hr greater than Manu’s average speed and she finished the race in hours less than Manu. Find the time taken by Manu to finish the race. Show your work. Answer. Assumes the time Manu took to finish the race as t hours and writes the equation for his average speed as 60/ 𝑡 km/hr. Frames the equation for Aiza using the given information as: (60/ 𝑡 + 10)(t -1/2) = 60 Simplifies the above equation into standard quadratic equation form as: 2t/2 – t – 6 = 0 Factorises the above equation as (t – 2)(t + 3/2) = 0 Finds the time taken by Manu to finish the race as 2 hours. OR Q11. Shown below is a cuboid with water in two different orientations. The length, breadth and height of the cuboid are distinct. The cuboid has 480 cm³ of water. If the height of water in orientation II is half of that in orientation I, then find the heights of water in both orientations. Show your work. Answer. Assumes the vertical length of the cuboid in orientation I as h cm and finds the height of water as (h – 4) cm. Finds the height of water in orientation II as 1/2(h – 4) cm. Writes the equation for the volume of water as: 5 × h × 1/2(h – 4) = 480 Simplifies the above equation as: h² – 4h – 192 = 0 Solves and finds the roots of the above equation as (-12) and 16. (Rejects h = (-12) as height cannot be negative.) Finds the height of water in: orientation I as 16 – 4 = 12 cm orientation II as 1/2× 12 = 6 cm (Award full marks if an alternate method is correctly used.) Q12. In the following figure, ΔABC is a right-angled triangle, such that:
  • AC = 25 cm
  • PT || AB and SR || BC
Find the area of ΔPQR. Show your work. Answer. Find PR as PC – RC. Finds RC as 50/5 = 10 cm and PC as 50³cm. Hence, finds PR as 20³cm. Writes that ΔPQR ∼ ΔPTC by basic proportionality theorem, as QR || BC. Writes that 𝑃𝑅 / 𝐶𝑅 = 𝑃𝑄 / 𝑄𝑇 . Hence, 20/10×3 = 𝑃𝑄 /8 => PQ = 16³cm. Uses Pythagoras theorem in ΔPQR to find the length of QR as: QR = (√20/3)² – (√16/3)² = 4 cm Finds the area of ΔPQR as 1/2 × 4 × 16/3 = 32/3cm². (Award full marks if a different solution method is used correctly to find the answer.) Q13. Two rectangular sheets of dimensions 45 cm × 155 cm are folded to make hollow right circular cylindrical pipes, such that there is exactly 1 cm of overlap when sticking the ends of the sheet. Sheet 1 is folded along its length, while Sheet 2 is folded along its width. That is, the top edge of the sheet is joined with its bottom edge in both the sheets, as depicted by the arrow in the figure below. Both pipes are closed on both ends to form cylinders.
  1. i) Find the difference in the curved surface areas of the two cylinders. ii) Find the ratio of the volumes of the two cylinders formed.
Show your work. (Note: Use π as 22/7. Assume that the sheets have negligible thickness.) Answer. i) Write that, in the sheet 1 cylinder, the height of the cylinder = 155 cm. Hence finds the area wasted in overlap = 155 x 1 = 155 cm². Write that, in the sheet 2 cylinder, the height of the cylinder = 45 cm. Hence finds area wasted in overlap = 45 x 1 = 45 cm². Writes that, as the sheets used are identical, the difference in curved surface area = difference between area wasted in overlap = 155 – 45 = 110 cm². (Award full marks if solved using formula).
  1. ii) Notes that the circumference of the circle in the Sheet 1 cylinder is: 45 cm – 1 cm = 44 cm
Find the radius of the sheet 1 cylinder as 7 cm. The working may look as follows: 2πr1= 44 cm => r1 = 7 cm Notes that the circumference of the circle in the Sheet 2 cylinder is: 155 cm – 1 cm = 154 cm Finds the radius of the sheet 2 cylinder as 49/2cm. The working may look as follows: 2πr2 = 154 cm => r2 = 49/2cm Finds the ratio of the volumes of the two cylinders as follows: where V1 is the volume of the cylinder made by sheet 1, and V2 is the volume of the cylinder made by sheet 2. OR Q13. Shown below is a cylindrical can placed in a cubical container.
  1. i) How many of these cans can be packed in the container such that no more cans are fitted? ii) If the capacity of one can is 539 ml, find the internal volume of the cubical container.
Show your work. (Note: Take π as 22/7.) Answer. i) Find the side of the cubical container as 2p from the figure. Calculates that 2p ÷ 𝑝 /2 = 4 cans can be packed in each of the length’s and the breadth’s directions in the container. Finds the total number of cans that can fit in the container as: 4 × 4 × 2 = 32
  1. ii) Writes the formula for the volume of the can to find the value of p as:
539 = 22/7 × p²/16 × p Solves the above equation to find the value of p as 14 cm. (Award 0.5 marks if only the formula for the volume of a cylinder is written correctly.) Find the side of the cube as 2 × 14 = 28 cm. Find the internal volume of the cubical container as (28)³ cm³ or 21952 cm³.

Section E – Case Study Questions

Q14. Answer the questions based on the given information. An interior designer, Sana, hired two painters, Manan and Bhima to make paintings for her buildings. Both painters were asked to make 50 different paintings each. The prices quoted by both the painters are given below:
  • Manan asked for Rs 6000 for the first painting, and an increment of Rs 200 for each following painting.
  • Bhima asked for Rs 4000 for the first painting, and an increment of Rs 400 for each following painting.
(i) How much money did Manan get for his 25th painting? Show your work. (ii) How much money did Bhima get in all? Show your work. (iii) If both Manan and Bhima make paintings at the same pace, find the first painting for which Bhima will get more money than Manan. Show your steps. OR (iii) Sana’s friend, Aarti hired Manan and Bhima to make paintings for her at the same rates as for Sana. Aarti had both painters make the same number of paintings and paid them the exact same amount in total. How many paintings did Aarti get each painter to make? Show your work. Answer. i) Note that the amounts Manan is paid for each painting form an AP. Takes a = 6000, d = 200 and n = 25 to find the amount as 6000 + (25 – 1)200 = Rs 10800.
  1. ii) Find the total amount earned by Bhima as follows: S50 =50/2 [2(4000) + (50 – 1)(400)]
Solves the above expression to find the total amount as Rs 6,90,000. iii) Frames equation as follows: 6000 + (n – 1)200 = 4000 + (n – 1)400 Solve the above equation to find the value of n as 11. Writes that, since they both earn the same amount for the 11th painting, as Bhima’s increment is more, Bhima gets more money than Manan for the 12th painting. OR iii) Assume that the number of paintings required is n. Frames equation as follows: Sn(Manan) = Sn(Bhima) => 𝑛 /2 [2(6000) + (n -1)200] = 𝑛 /2 [2(4000) + (n -1)400] Solve the equation from step 1 to find n as 21.

CBSE Class 10 Maths Additional Practice Paper Questions 2023-24 FAQs

Are there additional resources recommended for Class 10 Maths preparation?

The blog suggests textbooks, online resources, and video tutorials to complement your preparation.

Can these practice papers be used for revision before the final exam?

Yes, they are excellent for revision, helping you reinforce concepts and identify areas that may need additional attention.

Are there opportunities to seek clarifications on specific practice questions?

You can reach out with your questions through our contact page or engage with the online community for assistance.

Is it advisable to attempt the practice papers under exam conditions?

Yes, practising under timed conditions can help simulate exam scenarios and improve your time management skills.

How can I track my progress using these practice papers?

Regular self-assessment, tracking correct and incorrect answers, can help you gauge your progress over time.
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