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- 1 - 
 
 
 MATHEMATICS 
ICSE Board Class X Exam (2024) 
Answers & Solutions
GENERAL INSTRUCTIONS  
Read the following instructions very carefully and follow them: 
(i) You will not be allowed to write during first 15 minutes. 
(ii) Attempt all questions from Section A and any four questions from Section B. 
(iii) Omission of essential working will result in loss of marks. 
(iv) The intended marks for questions or parts of questions are given in brackets [ ]. 
(v) Mathematical tables and graph papers are provided. 
  
 
Time: 2½ Hrs. Max. Marks: 80 
 
  
Page 2


- 1 - 
 
 
 MATHEMATICS 
ICSE Board Class X Exam (2024) 
Answers & Solutions
GENERAL INSTRUCTIONS  
Read the following instructions very carefully and follow them: 
(i) You will not be allowed to write during first 15 minutes. 
(ii) Attempt all questions from Section A and any four questions from Section B. 
(iii) Omission of essential working will result in loss of marks. 
(iv) The intended marks for questions or parts of questions are given in brackets [ ]. 
(v) Mathematical tables and graph papers are provided. 
  
 
Time: 2½ Hrs. Max. Marks: 80 
 
  
  Mathematics (ICSE)_Class X 
- 2 - 
SECTION-A (40 Marks) 
(Attempt all questions from this Section.) 
1. Choose the correct answers to the questions from the given options. [15] 
 (i) For an Intra-state sale, the CGST paid by a dealer to the Central government is `120. If the marked price 
of the article is `2000, the rate of GST is 
  (a) 6% (b) 10% 
  (c) 12% (d) 16.67% 
 Answer (c)  [1] 
 Sol. Rate of G.S.T. = 
2 120
100
2000
?
? 
      = 12% 
 (ii) What must be subtracted from the polynomial x
3
 + x
2
 – 2x + 1, so that the result is exactly divisible by 
(x –3)? 
  (a) –31 (b) –30 
  (c) 30 (d) 31 
 Answer (d)  [1] 
 Sol. 3
3
 + 3
2
 – 2(3) + 1 = 31 
 (iii) The roots of the quadratic equation px
2 
– qx + r = 0 are real and equal if: 
  (a) p
2
 = 4qr (b) q
2
 = 4pr 
  (c) –q
2
 = 4pr (d) p
2
 > 4qr 
 Answer (b)  [1] 
 Sol. (–q)
2
 – 4pr = 0 
  ? q
2
 = 4pr 
 (iv) If matrix 
22
02
A
??
=
??
??
 and 
2
4
,
04
x
A
??
=
??
??
 then the value of x is 
  (a) 2 (b) 4 
  (c) 8 (d) 10 
 Answer (c)  [1] 
 Sol. 
2
4 8 4
0 4 0 4
x
A
? ? ? ?
==
? ? ? ?
? ? ? ?
 
  x = 8 
 (v) The median of the following observations arranged in ascending order is 64. 
  Find the value of x: 
27, 31, 46, 52, x, x + 4, 71, 79, 85, 90 
  (a) 60 (b) 61 
  (c) 62 (d) 66 
 Answer (c)  [1] 
 Sol. 
( ) 4
64 62
2
xx
x
++
= ? = 
Page 3


- 1 - 
 
 
 MATHEMATICS 
ICSE Board Class X Exam (2024) 
Answers & Solutions
GENERAL INSTRUCTIONS  
Read the following instructions very carefully and follow them: 
(i) You will not be allowed to write during first 15 minutes. 
(ii) Attempt all questions from Section A and any four questions from Section B. 
(iii) Omission of essential working will result in loss of marks. 
(iv) The intended marks for questions or parts of questions are given in brackets [ ]. 
(v) Mathematical tables and graph papers are provided. 
  
 
Time: 2½ Hrs. Max. Marks: 80 
 
  
  Mathematics (ICSE)_Class X 
- 2 - 
SECTION-A (40 Marks) 
(Attempt all questions from this Section.) 
1. Choose the correct answers to the questions from the given options. [15] 
 (i) For an Intra-state sale, the CGST paid by a dealer to the Central government is `120. If the marked price 
of the article is `2000, the rate of GST is 
  (a) 6% (b) 10% 
  (c) 12% (d) 16.67% 
 Answer (c)  [1] 
 Sol. Rate of G.S.T. = 
2 120
100
2000
?
? 
      = 12% 
 (ii) What must be subtracted from the polynomial x
3
 + x
2
 – 2x + 1, so that the result is exactly divisible by 
(x –3)? 
  (a) –31 (b) –30 
  (c) 30 (d) 31 
 Answer (d)  [1] 
 Sol. 3
3
 + 3
2
 – 2(3) + 1 = 31 
 (iii) The roots of the quadratic equation px
2 
– qx + r = 0 are real and equal if: 
  (a) p
2
 = 4qr (b) q
2
 = 4pr 
  (c) –q
2
 = 4pr (d) p
2
 > 4qr 
 Answer (b)  [1] 
 Sol. (–q)
2
 – 4pr = 0 
  ? q
2
 = 4pr 
 (iv) If matrix 
22
02
A
??
=
??
??
 and 
2
4
,
04
x
A
??
=
??
??
 then the value of x is 
  (a) 2 (b) 4 
  (c) 8 (d) 10 
 Answer (c)  [1] 
 Sol. 
2
4 8 4
0 4 0 4
x
A
? ? ? ?
==
? ? ? ?
? ? ? ?
 
  x = 8 
 (v) The median of the following observations arranged in ascending order is 64. 
  Find the value of x: 
27, 31, 46, 52, x, x + 4, 71, 79, 85, 90 
  (a) 60 (b) 61 
  (c) 62 (d) 66 
 Answer (c)  [1] 
 Sol. 
( ) 4
64 62
2
xx
x
++
= ? = 
 
Mathematics (ICSE)_Class X 
- 3 - 
 (vi) Points A(x, y), B(3, –2) and C(4, –5) are collinear. The value of y in terms of x is 
  (a) 3x – 11 (b) 11 – 3x 
  (c) 3x – 7 (d) 7 – 3x 
 Answer (d)  [1] 
 Sol. 
3 4 3
73
2 5 2
x
yx
y
--
= ? = -
- - - +
 
 (vii) The given table shows the distance covered and the time taken by a train moving at a uniform speed along 
a straight track. 
Distance (in m) 60 90 y 
Time (in sec) 2 x 5 
  The values of x and y are: 
  (a) x = 4, y = 150 (b) x = 3, y = 100 
  (c) x = 4, y = 100 (d) x = 3, y = 150 
 Answer (d)  [1] 
 Sol. Distance and time are directly proportional 
  x = 3 seconds 
  y = 150 meters 
 (viii) The 7
th
 term of the given Arithmetic Progression (A.P.) 
  
1 1 1
, 1 , 2 ...
a a a
? ? ? ?
++
? ? ? ?
? ? ? ?
 is 
  (a) 
1
6
a
??
+
??
??
 (b) 
1
7
a
??
+
??
??
 
  (c) 
1
8
a
??
+
??
??
 (d) 
7
1
7
a
??
+
??
??
 
 Answer (a)  [1] 
 Sol. a
7
 = a + (7 – 1)d 
    = 
1
a
 + 6(1) 
    = 
1
a
 + 6 
 (ix) The sum invested to purchase 15 shares of a company of nominal value ?75 available at a discount of 
20% is 
  (a) ?60 (b) ?90 
  (c) ?1350 (d) ?900 
 Answer (d)  [1] 
 Sol. Money invested = Number of shares × Market value of 1 share 
      = 15 × (75 – 20% of 75) 
      = 15 × 60 
      = ?900 
Page 4


- 1 - 
 
 
 MATHEMATICS 
ICSE Board Class X Exam (2024) 
Answers & Solutions
GENERAL INSTRUCTIONS  
Read the following instructions very carefully and follow them: 
(i) You will not be allowed to write during first 15 minutes. 
(ii) Attempt all questions from Section A and any four questions from Section B. 
(iii) Omission of essential working will result in loss of marks. 
(iv) The intended marks for questions or parts of questions are given in brackets [ ]. 
(v) Mathematical tables and graph papers are provided. 
  
 
Time: 2½ Hrs. Max. Marks: 80 
 
  
  Mathematics (ICSE)_Class X 
- 2 - 
SECTION-A (40 Marks) 
(Attempt all questions from this Section.) 
1. Choose the correct answers to the questions from the given options. [15] 
 (i) For an Intra-state sale, the CGST paid by a dealer to the Central government is `120. If the marked price 
of the article is `2000, the rate of GST is 
  (a) 6% (b) 10% 
  (c) 12% (d) 16.67% 
 Answer (c)  [1] 
 Sol. Rate of G.S.T. = 
2 120
100
2000
?
? 
      = 12% 
 (ii) What must be subtracted from the polynomial x
3
 + x
2
 – 2x + 1, so that the result is exactly divisible by 
(x –3)? 
  (a) –31 (b) –30 
  (c) 30 (d) 31 
 Answer (d)  [1] 
 Sol. 3
3
 + 3
2
 – 2(3) + 1 = 31 
 (iii) The roots of the quadratic equation px
2 
– qx + r = 0 are real and equal if: 
  (a) p
2
 = 4qr (b) q
2
 = 4pr 
  (c) –q
2
 = 4pr (d) p
2
 > 4qr 
 Answer (b)  [1] 
 Sol. (–q)
2
 – 4pr = 0 
  ? q
2
 = 4pr 
 (iv) If matrix 
22
02
A
??
=
??
??
 and 
2
4
,
04
x
A
??
=
??
??
 then the value of x is 
  (a) 2 (b) 4 
  (c) 8 (d) 10 
 Answer (c)  [1] 
 Sol. 
2
4 8 4
0 4 0 4
x
A
? ? ? ?
==
? ? ? ?
? ? ? ?
 
  x = 8 
 (v) The median of the following observations arranged in ascending order is 64. 
  Find the value of x: 
27, 31, 46, 52, x, x + 4, 71, 79, 85, 90 
  (a) 60 (b) 61 
  (c) 62 (d) 66 
 Answer (c)  [1] 
 Sol. 
( ) 4
64 62
2
xx
x
++
= ? = 
 
Mathematics (ICSE)_Class X 
- 3 - 
 (vi) Points A(x, y), B(3, –2) and C(4, –5) are collinear. The value of y in terms of x is 
  (a) 3x – 11 (b) 11 – 3x 
  (c) 3x – 7 (d) 7 – 3x 
 Answer (d)  [1] 
 Sol. 
3 4 3
73
2 5 2
x
yx
y
--
= ? = -
- - - +
 
 (vii) The given table shows the distance covered and the time taken by a train moving at a uniform speed along 
a straight track. 
Distance (in m) 60 90 y 
Time (in sec) 2 x 5 
  The values of x and y are: 
  (a) x = 4, y = 150 (b) x = 3, y = 100 
  (c) x = 4, y = 100 (d) x = 3, y = 150 
 Answer (d)  [1] 
 Sol. Distance and time are directly proportional 
  x = 3 seconds 
  y = 150 meters 
 (viii) The 7
th
 term of the given Arithmetic Progression (A.P.) 
  
1 1 1
, 1 , 2 ...
a a a
? ? ? ?
++
? ? ? ?
? ? ? ?
 is 
  (a) 
1
6
a
??
+
??
??
 (b) 
1
7
a
??
+
??
??
 
  (c) 
1
8
a
??
+
??
??
 (d) 
7
1
7
a
??
+
??
??
 
 Answer (a)  [1] 
 Sol. a
7
 = a + (7 – 1)d 
    = 
1
a
 + 6(1) 
    = 
1
a
 + 6 
 (ix) The sum invested to purchase 15 shares of a company of nominal value ?75 available at a discount of 
20% is 
  (a) ?60 (b) ?90 
  (c) ?1350 (d) ?900 
 Answer (d)  [1] 
 Sol. Money invested = Number of shares × Market value of 1 share 
      = 15 × (75 – 20% of 75) 
      = 15 × 60 
      = ?900 
  Mathematics (ICSE)_Class X 
- 4 - 
 (x) The circumcentre of a triangle is the point which is 
  (a) at equal distance from the three sides of the triangle. 
  (b) at equal distance from the three vertices of the triangle. 
  (c) the point of intersection of the three medians. 
  (d) the point of intersection of the three altitudes of the triangle. 
 Answer (b)  [1] 
 Sol. Circumcentre of a triangle is the point which is at equal distance from the three vertices of the triangle. 
 (xi) Statement 1: sin
2 
? + cos
2 
? = 1 
  Statement 2: cosec
2 
? + cot
2 
? = 1 
  Which of the following is valid? 
  (a) Only 1 (b) Only 2 
  (c) Both 1 and 2 (d) Neither 1 nor 2 
 Answer (a)  [1] 
 Sol. We know that, sin
2
? + cos
2
? = 1 and 
  cosec
2
? – cot
2
? = 1 
  ? Only Statement 1 is valid. 
 (xii) In the given diagram, PS and PT are the tangents to the circle. SQ || PT and ?SPT = 80°. The value of 
?QST is 
 
  (a) 140° (b) 90° 
  (c) 80° (d) 50° 
 Answer (d)  [1] 
 Sol.  
  Let ?QST = ? 
  ? ?STP = ?QST = ? [Alternate interior angles] 
Page 5


- 1 - 
 
 
 MATHEMATICS 
ICSE Board Class X Exam (2024) 
Answers & Solutions
GENERAL INSTRUCTIONS  
Read the following instructions very carefully and follow them: 
(i) You will not be allowed to write during first 15 minutes. 
(ii) Attempt all questions from Section A and any four questions from Section B. 
(iii) Omission of essential working will result in loss of marks. 
(iv) The intended marks for questions or parts of questions are given in brackets [ ]. 
(v) Mathematical tables and graph papers are provided. 
  
 
Time: 2½ Hrs. Max. Marks: 80 
 
  
  Mathematics (ICSE)_Class X 
- 2 - 
SECTION-A (40 Marks) 
(Attempt all questions from this Section.) 
1. Choose the correct answers to the questions from the given options. [15] 
 (i) For an Intra-state sale, the CGST paid by a dealer to the Central government is `120. If the marked price 
of the article is `2000, the rate of GST is 
  (a) 6% (b) 10% 
  (c) 12% (d) 16.67% 
 Answer (c)  [1] 
 Sol. Rate of G.S.T. = 
2 120
100
2000
?
? 
      = 12% 
 (ii) What must be subtracted from the polynomial x
3
 + x
2
 – 2x + 1, so that the result is exactly divisible by 
(x –3)? 
  (a) –31 (b) –30 
  (c) 30 (d) 31 
 Answer (d)  [1] 
 Sol. 3
3
 + 3
2
 – 2(3) + 1 = 31 
 (iii) The roots of the quadratic equation px
2 
– qx + r = 0 are real and equal if: 
  (a) p
2
 = 4qr (b) q
2
 = 4pr 
  (c) –q
2
 = 4pr (d) p
2
 > 4qr 
 Answer (b)  [1] 
 Sol. (–q)
2
 – 4pr = 0 
  ? q
2
 = 4pr 
 (iv) If matrix 
22
02
A
??
=
??
??
 and 
2
4
,
04
x
A
??
=
??
??
 then the value of x is 
  (a) 2 (b) 4 
  (c) 8 (d) 10 
 Answer (c)  [1] 
 Sol. 
2
4 8 4
0 4 0 4
x
A
? ? ? ?
==
? ? ? ?
? ? ? ?
 
  x = 8 
 (v) The median of the following observations arranged in ascending order is 64. 
  Find the value of x: 
27, 31, 46, 52, x, x + 4, 71, 79, 85, 90 
  (a) 60 (b) 61 
  (c) 62 (d) 66 
 Answer (c)  [1] 
 Sol. 
( ) 4
64 62
2
xx
x
++
= ? = 
 
Mathematics (ICSE)_Class X 
- 3 - 
 (vi) Points A(x, y), B(3, –2) and C(4, –5) are collinear. The value of y in terms of x is 
  (a) 3x – 11 (b) 11 – 3x 
  (c) 3x – 7 (d) 7 – 3x 
 Answer (d)  [1] 
 Sol. 
3 4 3
73
2 5 2
x
yx
y
--
= ? = -
- - - +
 
 (vii) The given table shows the distance covered and the time taken by a train moving at a uniform speed along 
a straight track. 
Distance (in m) 60 90 y 
Time (in sec) 2 x 5 
  The values of x and y are: 
  (a) x = 4, y = 150 (b) x = 3, y = 100 
  (c) x = 4, y = 100 (d) x = 3, y = 150 
 Answer (d)  [1] 
 Sol. Distance and time are directly proportional 
  x = 3 seconds 
  y = 150 meters 
 (viii) The 7
th
 term of the given Arithmetic Progression (A.P.) 
  
1 1 1
, 1 , 2 ...
a a a
? ? ? ?
++
? ? ? ?
? ? ? ?
 is 
  (a) 
1
6
a
??
+
??
??
 (b) 
1
7
a
??
+
??
??
 
  (c) 
1
8
a
??
+
??
??
 (d) 
7
1
7
a
??
+
??
??
 
 Answer (a)  [1] 
 Sol. a
7
 = a + (7 – 1)d 
    = 
1
a
 + 6(1) 
    = 
1
a
 + 6 
 (ix) The sum invested to purchase 15 shares of a company of nominal value ?75 available at a discount of 
20% is 
  (a) ?60 (b) ?90 
  (c) ?1350 (d) ?900 
 Answer (d)  [1] 
 Sol. Money invested = Number of shares × Market value of 1 share 
      = 15 × (75 – 20% of 75) 
      = 15 × 60 
      = ?900 
  Mathematics (ICSE)_Class X 
- 4 - 
 (x) The circumcentre of a triangle is the point which is 
  (a) at equal distance from the three sides of the triangle. 
  (b) at equal distance from the three vertices of the triangle. 
  (c) the point of intersection of the three medians. 
  (d) the point of intersection of the three altitudes of the triangle. 
 Answer (b)  [1] 
 Sol. Circumcentre of a triangle is the point which is at equal distance from the three vertices of the triangle. 
 (xi) Statement 1: sin
2 
? + cos
2 
? = 1 
  Statement 2: cosec
2 
? + cot
2 
? = 1 
  Which of the following is valid? 
  (a) Only 1 (b) Only 2 
  (c) Both 1 and 2 (d) Neither 1 nor 2 
 Answer (a)  [1] 
 Sol. We know that, sin
2
? + cos
2
? = 1 and 
  cosec
2
? – cot
2
? = 1 
  ? Only Statement 1 is valid. 
 (xii) In the given diagram, PS and PT are the tangents to the circle. SQ || PT and ?SPT = 80°. The value of 
?QST is 
 
  (a) 140° (b) 90° 
  (c) 80° (d) 50° 
 Answer (d)  [1] 
 Sol.  
  Let ?QST = ? 
  ? ?STP = ?QST = ? [Alternate interior angles] 
 
Mathematics (ICSE)_Class X 
- 5 - 
  ? ?SQT = ?STP = ? [Alternate segment theorem] 
  ? ?PST = ?SQT = ? [Alternate segment theorem] 
  Now,  
  In ?PST, 
  ? + ? + 80° = 180° 
  ? ? = 50° 
 (xiii) Assertion (A): A die is thrown once and the probability of getting an even number is .
2
3
 
  Reason (R): The sample space for even numbers on a die is {2, 4, 6} 
  (a) A is true, R is false (b) A is false, R is true 
  (c) Both A and R are true (d) Both A and R are false 
 Answer (b)  [1] 
 Sol. A is false, R is true 
 (xiv) A rectangular sheet of paper of size 11 cm × 7 cm is first rotated about the side 11 cm and then about the 
side 7 cm to form a cylinder, as shown in the diagram. The ratio of their curved surface areas is 
 
  (a) 1 : 1 (b) 7 : 11 
  (c) 11 : 7 (d) 
11 7
:
7 11
??
 
 Answer (a)  [1] 
 Sol. 1 : 1 
 (xv) In the given diagram, ?ABC ? ?PQR. If AD and PS are bisectors of ?BAC and ?QPR respectively then 
 
  (a) ?ABC ? ?PQS 
  (b) ?ABD ? ?PQS 
  (c) ?ABD ? ?PSR 
  (d) ?ABC ? ?PSR 
 Answer (b)  [1] 
 Sol. ?ABD ? ?PQS

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FAQs on ICSE Mathematics Past Year Paper with Solutions - 2024 - Mathematics Class 10 ICSE

1. What are the key topics covered in the ICSE Class 10 Mathematics syllabus?

Ans. The ICSE Class 10 Mathematics syllabus includes various key topics such as Algebra, Geometry, Trigonometry, Statistics, and Mensuration. Students are expected to understand concepts like linear equations, quadratic equations, coordinate geometry, properties of triangles, circles, and the basics of probability.

2. How can students effectively prepare for the ICSE Mathematics exam?

Ans. Effective preparation for the ICSE Mathematics exam can be achieved through regular practice of past papers, understanding concepts thoroughly, and solving sample questions. Students should focus on time management while practicing, create a study schedule, and seek help from teachers or tutors for difficult topics.

3. What is the marking scheme for the ICSE Class 10 Mathematics exam?

Ans. The marking scheme for the ICSE Class 10 Mathematics exam typically includes a combination of long answer questions, short answer questions, and objective type questions. Students are advised to check the official syllabus for specific weightage assigned to different sections to strategize their exam preparation accordingly.

4. Why are past year papers important for ICSE Mathematics exam preparation?

Ans. Past year papers are important for ICSE Mathematics exam preparation as they give students insight into the exam pattern, types of questions asked, and the level of difficulty. Practicing these papers helps students identify their strengths and weaknesses, allowing them to focus on areas that need improvement.

5. What are some common mistakes to avoid while solving ICSE Mathematics papers?

Ans. Common mistakes to avoid while solving ICSE Mathematics papers include not reading questions carefully, skipping steps in calculations, misinterpreting graphs or charts, and not managing time effectively. Students should ensure they double-check their answers and follow the correct format for presenting solutions.

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ICSE Mathematics Past Year Paper with Solutions - 2024 Notes

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ICSE Mathematics Past Year Paper with Solutions - 2024 Class 10 Questions

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