GHS
Kalavara
SSLC
MATHS QP-05
2025
Presented By
Ganesha Shettigar
, KARNATAKA SCHOOL EXAMINATION AND ASSESSMENT BOARD
Malleshwaram, Bengaluru-560003
S.S.L.C. MODEL QUESTION PAPER-1 – 2024-25
Subject : MATHEMATICS
Medium : English
Time : 3 hours 15 minutes Subject Code : 81E
Max. Marks : 80 Model Answers No of Questions : 38
General Instructions to the Candidate :
1. This question paper consists of 38 questions.
2. Follow the instructions given against the questions.
3. Figures in the right hand margin indicate maximum marks for the questions.
4. The maximum time to answer the paper is given at the top of the question paper. It
includes 15 minutes for reading the question paper.
I. Four alternatives are given for each of the following questions/ incomplete
statements. Choose the correct alternative and write the complete answer
along with its letter of alphabet. 𝟖×𝟏= 𝟖
1. The HCF of 52 × 2 and 25 × 5 is
A) 2 × 5 B) 25 × 5 C) 52 × 26 D) 25 × 52
Ans : A) 𝟐 × 𝟓
2. The sum of first ‘𝑛’ natural numbers is
𝑛(𝑛+2) 𝑛(𝑛+1)
A) 𝑛(𝑛 + 1) B) C) D) 𝑛(𝑛 − 1)
2 2
𝒏(𝒏+𝟏)
Ans : C) 𝟐
3. In a pair of linear equations 𝑎1 𝑥 + 𝑏1 𝑦 + 𝑐1 = 0 and 𝑎2 𝑥 + 𝑏2 𝑦 + 𝑐2 = 0 , which
of the following situations cannot arise ?
𝑎 𝑏 𝑎1 𝑏1 𝑐1
A) 𝑎1 ≠ 𝑏1 B)
𝑎2
=
𝑏2
≠
𝑐2
2 2
𝑎1 𝑏1 𝑐1
C) = = D) 𝑎1 = 𝑎2 , 𝑏1 = 𝑏2 , 𝑐1 = 𝑐2
𝑎2 𝑏2 𝑐2
Ans : D) 𝒂𝟏 = 𝒂𝟐 , 𝒃𝟏 = 𝒃𝟐 , 𝒄𝟏 = 𝒄𝟐
4. The number of zeroes of the polynomial 𝑦 = 𝑃 ( 𝑥 ) in the given graph is
A) 2 B) 3 C) 4 D) 5
Ans : B) 𝟑
, 5. 𝑥 ( 𝑥 + 2 ) = 6 is a
A) linear equation B) quadratic equation
C) cubic polynomial D) quadratic polynomial
Ans : B) quadratic equation
6. In the figure, ∆ 𝑃𝑄𝑅 ~ ∆ 𝐴𝐵𝐶. The pair of corresponding sides in the following is
A) 𝑃𝑄 𝑎𝑛𝑑 𝐴𝐵 B) 𝑃𝑅 𝑎𝑛𝑑 𝐴𝐵 C) 𝑄𝑅 𝑎𝑛𝑑 𝐴𝐶 D) 𝑃𝑅 𝑎𝑛𝑑 𝐵𝐶
Ans :A) 𝑷𝑸 𝒂𝒏𝒅 𝑨𝑩
7. 𝑠𝑖𝑛2 𝐴 − 𝑐𝑜𝑠 2 𝐴 is equal to
A) 1 B) 1 − 2𝑐𝑜𝑠 2 𝐴 C) 1 + 2𝑐𝑜𝑠 2 𝐴 D) −1
Ans : B) 𝟏 − 𝟐𝒄𝒐𝒔𝟐 𝑨
𝑠𝑖𝑛2 𝐴 − 𝑐𝑜𝑠 2 𝐴 = 1 − 𝑐𝑜𝑠 2𝐴 − 𝑐𝑜𝑠 2𝐴 = 1 − 2𝑐𝑜𝑠 2 𝐴
8. The sum of the probability of all elementary events of a random experiment is
1
A) 0 B) 2 C) 1 D) −1
Ans : C) 1
II. Answer the following questions 𝟖×𝟏 =𝟖
9. Find the value of ‘𝑏’ if the pair of linear equations 2𝑥 + 𝑏𝑦 = 8 and
2 ( 2𝑥 + 3𝑦 ) = 16 has infinite solutions.
Ans : 𝟑
2𝑥 + 𝑏𝑦 = 8 ⇒ 𝑎1 = 2, 𝑏1 = 𝑏, 𝑐1 = −8
2 ( 2𝑥 + 3𝑦 ) = 16 ⇒ 4𝑥 + 6𝑦 = 16 ⇒ 𝑎2 = 4, 𝑏2 = 6, 𝑐2 = −16
2 𝑏 −8
⇒ = =
4 6 −16
2×6 12
⇒𝑏= = =3
4 4
, 10. Write the degree of the polynomial 𝑃 ( 𝑥 ) = 5𝑥 3 − 3𝑥 2 + 12𝑥 − 8
Ans : 𝟑
√3 1
11. If 𝑠𝑖𝑛 𝐴 = and 𝑐𝑜𝑠 𝐴 = , then find the value of 𝑡𝑎𝑛 𝐴.
2 2
Ans : √𝟑
√3
sin 𝐴
tan 𝐴 = = 2
1 = √3
cos 𝐴
2
12. Write the empirical relation between the three measures of central tendency
Mean, Median and Mode.
Ans : 𝟑𝑴𝒆𝒅𝒊𝒂𝒏 = 𝑴𝒐𝒅𝒆 + 𝟐𝑴𝒆𝒂𝒏
𝑥+1 3
13. Express the quadratic equation
2
= 𝑥 in the standard form.
Ans : 𝒙𝟐 +𝒙−𝟔 =𝟎
𝑥+1 3
=
2 𝑥
𝑥(𝑥 + 1) = 6
𝑥2 + 𝑥 − 6 = 0
14. Find the distance of the point ( 6, 8 ) from the origin.
Ans : 𝟏𝟎 𝒖𝒏𝒊𝒕𝒔
𝑑 = √𝑥 2 + 𝑦 2 = √62 + 82 = √36 + 64 = √100 = 10 𝑢𝑛𝑖𝑡𝑠
15. In the figure, ∆ 𝑃𝑂𝑄 ~ ∆ 𝑅𝑂𝑆 and 𝑃𝑄 || 𝑆𝑅. If 𝑃𝑄 ∶ 𝑆𝑅 = 1 ∶ 2, then find
𝑂𝑆 ∶ 𝑂𝑄.
Ans : 𝑶𝑺 ∶ 𝑶𝑸 = 𝟐: 𝟏
∆ 𝑃𝑂𝑄 ~ ∆ 𝑅𝑂𝑆
𝑃𝑄 𝑂𝑄 1
∴ 𝑆𝑅
= 𝑂𝑆
=2
∴ 𝑂𝑆 ∶ 𝑂𝑄 = 2: 1
16. The circumference of the circular base of a cylinder is 44 𝑐𝑚 and its height is
10 𝑐𝑚. Find the curved surface area of the cylinder.
Ans : 𝟒𝟒𝟎 𝒄𝒎𝟐
𝐴 = 2𝜋𝑟ℎ = 44 × 10 = 440 𝑐𝑚2 ∵ circumference = 2𝜋𝑟
Kalavara
SSLC
MATHS QP-05
2025
Presented By
Ganesha Shettigar
, KARNATAKA SCHOOL EXAMINATION AND ASSESSMENT BOARD
Malleshwaram, Bengaluru-560003
S.S.L.C. MODEL QUESTION PAPER-1 – 2024-25
Subject : MATHEMATICS
Medium : English
Time : 3 hours 15 minutes Subject Code : 81E
Max. Marks : 80 Model Answers No of Questions : 38
General Instructions to the Candidate :
1. This question paper consists of 38 questions.
2. Follow the instructions given against the questions.
3. Figures in the right hand margin indicate maximum marks for the questions.
4. The maximum time to answer the paper is given at the top of the question paper. It
includes 15 minutes for reading the question paper.
I. Four alternatives are given for each of the following questions/ incomplete
statements. Choose the correct alternative and write the complete answer
along with its letter of alphabet. 𝟖×𝟏= 𝟖
1. The HCF of 52 × 2 and 25 × 5 is
A) 2 × 5 B) 25 × 5 C) 52 × 26 D) 25 × 52
Ans : A) 𝟐 × 𝟓
2. The sum of first ‘𝑛’ natural numbers is
𝑛(𝑛+2) 𝑛(𝑛+1)
A) 𝑛(𝑛 + 1) B) C) D) 𝑛(𝑛 − 1)
2 2
𝒏(𝒏+𝟏)
Ans : C) 𝟐
3. In a pair of linear equations 𝑎1 𝑥 + 𝑏1 𝑦 + 𝑐1 = 0 and 𝑎2 𝑥 + 𝑏2 𝑦 + 𝑐2 = 0 , which
of the following situations cannot arise ?
𝑎 𝑏 𝑎1 𝑏1 𝑐1
A) 𝑎1 ≠ 𝑏1 B)
𝑎2
=
𝑏2
≠
𝑐2
2 2
𝑎1 𝑏1 𝑐1
C) = = D) 𝑎1 = 𝑎2 , 𝑏1 = 𝑏2 , 𝑐1 = 𝑐2
𝑎2 𝑏2 𝑐2
Ans : D) 𝒂𝟏 = 𝒂𝟐 , 𝒃𝟏 = 𝒃𝟐 , 𝒄𝟏 = 𝒄𝟐
4. The number of zeroes of the polynomial 𝑦 = 𝑃 ( 𝑥 ) in the given graph is
A) 2 B) 3 C) 4 D) 5
Ans : B) 𝟑
, 5. 𝑥 ( 𝑥 + 2 ) = 6 is a
A) linear equation B) quadratic equation
C) cubic polynomial D) quadratic polynomial
Ans : B) quadratic equation
6. In the figure, ∆ 𝑃𝑄𝑅 ~ ∆ 𝐴𝐵𝐶. The pair of corresponding sides in the following is
A) 𝑃𝑄 𝑎𝑛𝑑 𝐴𝐵 B) 𝑃𝑅 𝑎𝑛𝑑 𝐴𝐵 C) 𝑄𝑅 𝑎𝑛𝑑 𝐴𝐶 D) 𝑃𝑅 𝑎𝑛𝑑 𝐵𝐶
Ans :A) 𝑷𝑸 𝒂𝒏𝒅 𝑨𝑩
7. 𝑠𝑖𝑛2 𝐴 − 𝑐𝑜𝑠 2 𝐴 is equal to
A) 1 B) 1 − 2𝑐𝑜𝑠 2 𝐴 C) 1 + 2𝑐𝑜𝑠 2 𝐴 D) −1
Ans : B) 𝟏 − 𝟐𝒄𝒐𝒔𝟐 𝑨
𝑠𝑖𝑛2 𝐴 − 𝑐𝑜𝑠 2 𝐴 = 1 − 𝑐𝑜𝑠 2𝐴 − 𝑐𝑜𝑠 2𝐴 = 1 − 2𝑐𝑜𝑠 2 𝐴
8. The sum of the probability of all elementary events of a random experiment is
1
A) 0 B) 2 C) 1 D) −1
Ans : C) 1
II. Answer the following questions 𝟖×𝟏 =𝟖
9. Find the value of ‘𝑏’ if the pair of linear equations 2𝑥 + 𝑏𝑦 = 8 and
2 ( 2𝑥 + 3𝑦 ) = 16 has infinite solutions.
Ans : 𝟑
2𝑥 + 𝑏𝑦 = 8 ⇒ 𝑎1 = 2, 𝑏1 = 𝑏, 𝑐1 = −8
2 ( 2𝑥 + 3𝑦 ) = 16 ⇒ 4𝑥 + 6𝑦 = 16 ⇒ 𝑎2 = 4, 𝑏2 = 6, 𝑐2 = −16
2 𝑏 −8
⇒ = =
4 6 −16
2×6 12
⇒𝑏= = =3
4 4
, 10. Write the degree of the polynomial 𝑃 ( 𝑥 ) = 5𝑥 3 − 3𝑥 2 + 12𝑥 − 8
Ans : 𝟑
√3 1
11. If 𝑠𝑖𝑛 𝐴 = and 𝑐𝑜𝑠 𝐴 = , then find the value of 𝑡𝑎𝑛 𝐴.
2 2
Ans : √𝟑
√3
sin 𝐴
tan 𝐴 = = 2
1 = √3
cos 𝐴
2
12. Write the empirical relation between the three measures of central tendency
Mean, Median and Mode.
Ans : 𝟑𝑴𝒆𝒅𝒊𝒂𝒏 = 𝑴𝒐𝒅𝒆 + 𝟐𝑴𝒆𝒂𝒏
𝑥+1 3
13. Express the quadratic equation
2
= 𝑥 in the standard form.
Ans : 𝒙𝟐 +𝒙−𝟔 =𝟎
𝑥+1 3
=
2 𝑥
𝑥(𝑥 + 1) = 6
𝑥2 + 𝑥 − 6 = 0
14. Find the distance of the point ( 6, 8 ) from the origin.
Ans : 𝟏𝟎 𝒖𝒏𝒊𝒕𝒔
𝑑 = √𝑥 2 + 𝑦 2 = √62 + 82 = √36 + 64 = √100 = 10 𝑢𝑛𝑖𝑡𝑠
15. In the figure, ∆ 𝑃𝑂𝑄 ~ ∆ 𝑅𝑂𝑆 and 𝑃𝑄 || 𝑆𝑅. If 𝑃𝑄 ∶ 𝑆𝑅 = 1 ∶ 2, then find
𝑂𝑆 ∶ 𝑂𝑄.
Ans : 𝑶𝑺 ∶ 𝑶𝑸 = 𝟐: 𝟏
∆ 𝑃𝑂𝑄 ~ ∆ 𝑅𝑂𝑆
𝑃𝑄 𝑂𝑄 1
∴ 𝑆𝑅
= 𝑂𝑆
=2
∴ 𝑂𝑆 ∶ 𝑂𝑄 = 2: 1
16. The circumference of the circular base of a cylinder is 44 𝑐𝑚 and its height is
10 𝑐𝑚. Find the curved surface area of the cylinder.
Ans : 𝟒𝟒𝟎 𝒄𝒎𝟐
𝐴 = 2𝜋𝑟ℎ = 44 × 10 = 440 𝑐𝑚2 ∵ circumference = 2𝜋𝑟
