ICSE Class 10 Maths Sample Paper 2025 - 5 | Mathematics Class 10 ICSE PDF Download

 Page 1


Time Allowed: 2 hours and 30 minutes Maximum Marks: 80 
General Instructions:
Answers to this Paper must be written on the paper provided separately.
You will not be allowed to write during the first 15 minutes.
This time is to be spent reading the question paper.
The time given at the head of this Paper is the time allowed for writing the answers.
Attempt all questions from Section A and any four questions from Section B.
All work, including rough work, must be clearly shown and must be done on the same sheet as the rest of the
answers.
Omission of essential work will result in a loss of marks.
The intended marks for questions or parts of questions are given in brackets [ ]
Mathematical tables are provided.
Section A
1. Question 1 Choose the correct answers to the questions from the given options: [15]
a) ?1848 b) ?1830
c) ?1650 d) ?1800
A retailer purchases a fan for ?1500 from a wholesaler and sells it to a consumer at 10% profit. If the
sales are intra-state and the rate of GST is 12%, the cost of the fan to the consumer inclusive of tax is:
[1] (a)
a) 60 b) 80
c) 110 d) 100
A trader bought a number of articles for ?1200. Ten were damaged and he sold each of the rest at ?2
more than what he paid for it, thus cleaning a profit of ?60 on the whole transaction. If x denotes the
number of articles he bought, then the value of x is
[1] (b)
a) 0 b) -1
c) 2 d) 1
When x
3
 - 3x
2
 + 5x - 7 is divided by x - 2, then the remainder is
[1] (c)
a) b)
If  and  are the roots of the equation x
2
 + x - 6 = 0 such that , then the product of the
matrices  and is
[1] (d)
a ß ß > a [ ] 0 a a ß [ ] ß + 1 - ß 0 a Mathematics
Page 2


Time Allowed: 2 hours and 30 minutes Maximum Marks: 80 
General Instructions:
Answers to this Paper must be written on the paper provided separately.
You will not be allowed to write during the first 15 minutes.
This time is to be spent reading the question paper.
The time given at the head of this Paper is the time allowed for writing the answers.
Attempt all questions from Section A and any four questions from Section B.
All work, including rough work, must be clearly shown and must be done on the same sheet as the rest of the
answers.
Omission of essential work will result in a loss of marks.
The intended marks for questions or parts of questions are given in brackets [ ]
Mathematical tables are provided.
Section A
1. Question 1 Choose the correct answers to the questions from the given options: [15]
a) ?1848 b) ?1830
c) ?1650 d) ?1800
A retailer purchases a fan for ?1500 from a wholesaler and sells it to a consumer at 10% profit. If the
sales are intra-state and the rate of GST is 12%, the cost of the fan to the consumer inclusive of tax is:
[1] (a)
a) 60 b) 80
c) 110 d) 100
A trader bought a number of articles for ?1200. Ten were damaged and he sold each of the rest at ?2
more than what he paid for it, thus cleaning a profit of ?60 on the whole transaction. If x denotes the
number of articles he bought, then the value of x is
[1] (b)
a) 0 b) -1
c) 2 d) 1
When x
3
 - 3x
2
 + 5x - 7 is divided by x - 2, then the remainder is
[1] (c)
a) b)
If  and  are the roots of the equation x
2
 + x - 6 = 0 such that , then the product of the
matrices  and is
[1] (d)
a ß ß > a [ ] 0 a a ß [ ] ß + 1 - ß 0 a Mathematics
c) d)
[ ] - 5 - 9 4 - 2 [ ] 6 - 1 3 9 - 6 [ ] 5 9 4 2 [ ] 6 9 1 3 6 a) 3 b) 6
c) 5 d) 2
An AP starts with a positive fraction and every alternate term is an integer. If the sum of the first 11
terms is 33, then the fourth term is
[1] (e)
a) (-3, -2) b) (3, 2)
c) (-3, 0) d) (3, -2)
If the image of the point P under the reflection in the X-axis is (-3, 2), then the coordinates of the
point P are
[1] (f)
a) OP = OQ b) OP = OQ
c) OQ = 2OP d) OP = 2OQ
O is the point of intersection of the diagonals AC and BD of a trapezium ABCD with AB || DC.
Through O, a line segment PQ is drawn parallel to AB meeting AD in P and BC in Q, then OP is
equal to
[1] (g)
1 3 a) b)
a
3
c) d)
5 a
3
A sphere of radius a units is immersed completely in water contained in a right circular cone of semi-
vertical angle 30° and water is drained off from the cone till its surface touches the sphere. Then, the
volume of water remaining in the cone will be
[1] (h)
p 5 3 a 2 5 p 3 p a 3 3 p a) 23 b) 20
c) 26 d) 17
The maximum value of 23 - |2x + 3| is [1] (i)
a) 4/7 b) 2/7
c) 1/7 d) 3/7
The probability that a non leap year selected at random will have 53 Sundays is: [1] (j)
a) A and B are square matrices of same
order
b) A and B are square matrices of different
order
c) A and B are rectangular matrices of
same order
d) A and B are rectangular matrices of
different order
If both A + B and AB are defined, then which one of the following is true? [1] (k)
a) (2, 4); 2.94 sq units b) (4, 2); 4.92 sq units
c) (2, 4); 9.42 sq units d) (4, 2); 9.42 sq units
Join two points P(2, 2) and 0(4, 2) in the point P and rotate the line PQ in anti-clockwise direction at
an angle of 270°. Then, the new coordinates of point Q and the area formed by this figure will be
[1] (l)
Page 3


Time Allowed: 2 hours and 30 minutes Maximum Marks: 80 
General Instructions:
Answers to this Paper must be written on the paper provided separately.
You will not be allowed to write during the first 15 minutes.
This time is to be spent reading the question paper.
The time given at the head of this Paper is the time allowed for writing the answers.
Attempt all questions from Section A and any four questions from Section B.
All work, including rough work, must be clearly shown and must be done on the same sheet as the rest of the
answers.
Omission of essential work will result in a loss of marks.
The intended marks for questions or parts of questions are given in brackets [ ]
Mathematical tables are provided.
Section A
1. Question 1 Choose the correct answers to the questions from the given options: [15]
a) ?1848 b) ?1830
c) ?1650 d) ?1800
A retailer purchases a fan for ?1500 from a wholesaler and sells it to a consumer at 10% profit. If the
sales are intra-state and the rate of GST is 12%, the cost of the fan to the consumer inclusive of tax is:
[1] (a)
a) 60 b) 80
c) 110 d) 100
A trader bought a number of articles for ?1200. Ten were damaged and he sold each of the rest at ?2
more than what he paid for it, thus cleaning a profit of ?60 on the whole transaction. If x denotes the
number of articles he bought, then the value of x is
[1] (b)
a) 0 b) -1
c) 2 d) 1
When x
3
 - 3x
2
 + 5x - 7 is divided by x - 2, then the remainder is
[1] (c)
a) b)
If  and  are the roots of the equation x
2
 + x - 6 = 0 such that , then the product of the
matrices  and is
[1] (d)
a ß ß > a [ ] 0 a a ß [ ] ß + 1 - ß 0 a Mathematics
c) d)
[ ] - 5 - 9 4 - 2 [ ] 6 - 1 3 9 - 6 [ ] 5 9 4 2 [ ] 6 9 1 3 6 a) 3 b) 6
c) 5 d) 2
An AP starts with a positive fraction and every alternate term is an integer. If the sum of the first 11
terms is 33, then the fourth term is
[1] (e)
a) (-3, -2) b) (3, 2)
c) (-3, 0) d) (3, -2)
If the image of the point P under the reflection in the X-axis is (-3, 2), then the coordinates of the
point P are
[1] (f)
a) OP = OQ b) OP = OQ
c) OQ = 2OP d) OP = 2OQ
O is the point of intersection of the diagonals AC and BD of a trapezium ABCD with AB || DC.
Through O, a line segment PQ is drawn parallel to AB meeting AD in P and BC in Q, then OP is
equal to
[1] (g)
1 3 a) b)
a
3
c) d)
5 a
3
A sphere of radius a units is immersed completely in water contained in a right circular cone of semi-
vertical angle 30° and water is drained off from the cone till its surface touches the sphere. Then, the
volume of water remaining in the cone will be
[1] (h)
p 5 3 a 2 5 p 3 p a 3 3 p a) 23 b) 20
c) 26 d) 17
The maximum value of 23 - |2x + 3| is [1] (i)
a) 4/7 b) 2/7
c) 1/7 d) 3/7
The probability that a non leap year selected at random will have 53 Sundays is: [1] (j)
a) A and B are square matrices of same
order
b) A and B are square matrices of different
order
c) A and B are rectangular matrices of
same order
d) A and B are rectangular matrices of
different order
If both A + B and AB are defined, then which one of the following is true? [1] (k)
a) (2, 4); 2.94 sq units b) (4, 2); 4.92 sq units
c) (2, 4); 9.42 sq units d) (4, 2); 9.42 sq units
Join two points P(2, 2) and 0(4, 2) in the point P and rotate the line PQ in anti-clockwise direction at
an angle of 270°. Then, the new coordinates of point Q and the area formed by this figure will be
[1] (l)
Section B
Attempt any 4 questions
a) (2, 3) b) (0, –1)
c) (2, 2) d) (3, 3)
The coordinates of the vertices of ?ABC are respectively (–4, –2), (6, 2) and (4, 6). The centroid G of
?ABC is:
[1] (m)
a) 25.2 b) 25.5
c) 25 d) 25.1
If x < y < 2x, then the median and mean of x, y and 2x are 27 and 33, respectively. The mean of x and
y is
[1] (n)
a) Both A and R are true and R is the
correct explanation of A.
b) Both A and R are true but R is not the
correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
Assertion (A): Three consecutive terms 2k + 1, 3k + 3 and 5k - 1 form an AP than k is equal to 6. 
Reason (R): In an AP a, a + d, a + 2d, ...the sum of n terms of the AP be S
n
 =  
[1] (o)
( 2 a + ( n - 1 ) d ) n 2 2. Question 2 [12]
Sanya has a Recurring Deposit Account in a bank of ?2000 per month at the rate of 10% per annum.
If she gets ?83100 at the time of maturity, then find the total time for which the account was held.
[4] (a)
Find the fourth proportional of the following.
i. 3a
2
b
2
, a
3
, b
3
ii. a
2
 - 5a + 6, a
2
 + a - 6, a
2
 - 9
[4] (b)
If sin  + cos  = p and sec  + cosec  = q, then prove that q(p
2
 - 1) = 2p.
[4] (c)
? ? ? ? 3. Question 3 [13]
A solid cylinder of radius 7 cm and height 14 cm is melted and recast into solid spheres each of radius
3.5 cm. Find the number of spheres formed.
[4] (a)
Three vertices of a parallelogram ABCD taken in order are A(3, 6), B(5, 10) and C(3, 2) find:
i. the coordinates of the fourth vertex D.
ii. length of diagonal BD.
iii. equation of side AB of the parallelogram ABCD.
[4] (b)
Use graph paper to answer this question.
i. Plot the points A(4, 6) and B(1, 2).
ii. A' is the image of A, when reflected in X-axis
iii. B' is the image of B, when B is reflected in X = 4.
iv. Give the geometrical name for the figure ABA'B'.
[5] (c)
4. Question 4 [10]
Mr. Verma goes to a shop and buy a Jacket having cost ? 1180 (list price). The rate of GST 18%. He
tells the shopkeeper to reduce the price such an extent that he has to pay ? 1180 inclusive of GST.
Find the reduction needed in the price of the jacket.
[3] (a)
Solve the following quadratic equation and give the answer correct to two significant figures. [3] (b)
Page 4


Time Allowed: 2 hours and 30 minutes Maximum Marks: 80 
General Instructions:
Answers to this Paper must be written on the paper provided separately.
You will not be allowed to write during the first 15 minutes.
This time is to be spent reading the question paper.
The time given at the head of this Paper is the time allowed for writing the answers.
Attempt all questions from Section A and any four questions from Section B.
All work, including rough work, must be clearly shown and must be done on the same sheet as the rest of the
answers.
Omission of essential work will result in a loss of marks.
The intended marks for questions or parts of questions are given in brackets [ ]
Mathematical tables are provided.
Section A
1. Question 1 Choose the correct answers to the questions from the given options: [15]
a) ?1848 b) ?1830
c) ?1650 d) ?1800
A retailer purchases a fan for ?1500 from a wholesaler and sells it to a consumer at 10% profit. If the
sales are intra-state and the rate of GST is 12%, the cost of the fan to the consumer inclusive of tax is:
[1] (a)
a) 60 b) 80
c) 110 d) 100
A trader bought a number of articles for ?1200. Ten were damaged and he sold each of the rest at ?2
more than what he paid for it, thus cleaning a profit of ?60 on the whole transaction. If x denotes the
number of articles he bought, then the value of x is
[1] (b)
a) 0 b) -1
c) 2 d) 1
When x
3
 - 3x
2
 + 5x - 7 is divided by x - 2, then the remainder is
[1] (c)
a) b)
If  and  are the roots of the equation x
2
 + x - 6 = 0 such that , then the product of the
matrices  and is
[1] (d)
a ß ß > a [ ] 0 a a ß [ ] ß + 1 - ß 0 a Mathematics
c) d)
[ ] - 5 - 9 4 - 2 [ ] 6 - 1 3 9 - 6 [ ] 5 9 4 2 [ ] 6 9 1 3 6 a) 3 b) 6
c) 5 d) 2
An AP starts with a positive fraction and every alternate term is an integer. If the sum of the first 11
terms is 33, then the fourth term is
[1] (e)
a) (-3, -2) b) (3, 2)
c) (-3, 0) d) (3, -2)
If the image of the point P under the reflection in the X-axis is (-3, 2), then the coordinates of the
point P are
[1] (f)
a) OP = OQ b) OP = OQ
c) OQ = 2OP d) OP = 2OQ
O is the point of intersection of the diagonals AC and BD of a trapezium ABCD with AB || DC.
Through O, a line segment PQ is drawn parallel to AB meeting AD in P and BC in Q, then OP is
equal to
[1] (g)
1 3 a) b)
a
3
c) d)
5 a
3
A sphere of radius a units is immersed completely in water contained in a right circular cone of semi-
vertical angle 30° and water is drained off from the cone till its surface touches the sphere. Then, the
volume of water remaining in the cone will be
[1] (h)
p 5 3 a 2 5 p 3 p a 3 3 p a) 23 b) 20
c) 26 d) 17
The maximum value of 23 - |2x + 3| is [1] (i)
a) 4/7 b) 2/7
c) 1/7 d) 3/7
The probability that a non leap year selected at random will have 53 Sundays is: [1] (j)
a) A and B are square matrices of same
order
b) A and B are square matrices of different
order
c) A and B are rectangular matrices of
same order
d) A and B are rectangular matrices of
different order
If both A + B and AB are defined, then which one of the following is true? [1] (k)
a) (2, 4); 2.94 sq units b) (4, 2); 4.92 sq units
c) (2, 4); 9.42 sq units d) (4, 2); 9.42 sq units
Join two points P(2, 2) and 0(4, 2) in the point P and rotate the line PQ in anti-clockwise direction at
an angle of 270°. Then, the new coordinates of point Q and the area formed by this figure will be
[1] (l)
Section B
Attempt any 4 questions
a) (2, 3) b) (0, –1)
c) (2, 2) d) (3, 3)
The coordinates of the vertices of ?ABC are respectively (–4, –2), (6, 2) and (4, 6). The centroid G of
?ABC is:
[1] (m)
a) 25.2 b) 25.5
c) 25 d) 25.1
If x < y < 2x, then the median and mean of x, y and 2x are 27 and 33, respectively. The mean of x and
y is
[1] (n)
a) Both A and R are true and R is the
correct explanation of A.
b) Both A and R are true but R is not the
correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
Assertion (A): Three consecutive terms 2k + 1, 3k + 3 and 5k - 1 form an AP than k is equal to 6. 
Reason (R): In an AP a, a + d, a + 2d, ...the sum of n terms of the AP be S
n
 =  
[1] (o)
( 2 a + ( n - 1 ) d ) n 2 2. Question 2 [12]
Sanya has a Recurring Deposit Account in a bank of ?2000 per month at the rate of 10% per annum.
If she gets ?83100 at the time of maturity, then find the total time for which the account was held.
[4] (a)
Find the fourth proportional of the following.
i. 3a
2
b
2
, a
3
, b
3
ii. a
2
 - 5a + 6, a
2
 + a - 6, a
2
 - 9
[4] (b)
If sin  + cos  = p and sec  + cosec  = q, then prove that q(p
2
 - 1) = 2p.
[4] (c)
? ? ? ? 3. Question 3 [13]
A solid cylinder of radius 7 cm and height 14 cm is melted and recast into solid spheres each of radius
3.5 cm. Find the number of spheres formed.
[4] (a)
Three vertices of a parallelogram ABCD taken in order are A(3, 6), B(5, 10) and C(3, 2) find:
i. the coordinates of the fourth vertex D.
ii. length of diagonal BD.
iii. equation of side AB of the parallelogram ABCD.
[4] (b)
Use graph paper to answer this question.
i. Plot the points A(4, 6) and B(1, 2).
ii. A' is the image of A, when reflected in X-axis
iii. B' is the image of B, when B is reflected in X = 4.
iv. Give the geometrical name for the figure ABA'B'.
[5] (c)
4. Question 4 [10]
Mr. Verma goes to a shop and buy a Jacket having cost ? 1180 (list price). The rate of GST 18%. He
tells the shopkeeper to reduce the price such an extent that he has to pay ? 1180 inclusive of GST.
Find the reduction needed in the price of the jacket.
[3] (a)
Solve the following quadratic equation and give the answer correct to two significant figures. [3] (b)
4x
2
 - 7x + 2 = 0
In a class of 40 students, marks obtained by the students in a class test (out of 10) are given below:
Marks 1 2 3 4 5 6 7 8 9 10
Number of students 1 2 3 3 6 10 5 4 3 3
Calculate the following for the given distribution:
i. Median
ii. Mode
[4] (c)
5. Question 5 [10]
If , then find the following.
i. 3A
ii. (-2)A
[3] (a)
A = [ ] 2 0 - 1 3 In the given figure, two circles intersect at S and T. STP, BSC and BAP are straight lines. Prove that
PATD is a cyclic quadrilateral. 
[3] (b)
Show that (x - 5) is a factor of 2x
2
 - 9x - 5. Hence, factorise 2x
2
 - 9x - 5.
[4] (c)
6. Question 6 [10]
The mid-point of the line joining (3a, 4) and (- 2, 2b) is (2, 2a + 2). Find the values of a and b. [3] (a)
Prove the following identities.
i. (sec A - sin A) (cosec A + cos A) = sin
2
 A tan A + cot A
ii. (1 + cot A + tan A) (sin A - cos A) = 
[3] (b)
- s e c A A c o s e c 2 c o s e c A A s e c 2 Find the sum of all two-digit odd positive numbers. [4] (c)
7. Question 7 [10]
A trader buys x articles for a total cost of ? 600.
i. Write down the cost of one article in terms of x. If the cost per article were ? 5 more, the number
of articles that can be bought for ? 600, would be four less.
ii. Write down the equation in x for the above situation and solve it to find x.
[5] (a)
The following distribution represents the height of 160 students of a school.
Height (in cm) Number of Students
140 - 145 12
145 - 150 20
150 - 155 30
155 - 160 38
160 - 165 24
[5] (b)
Page 5


Time Allowed: 2 hours and 30 minutes Maximum Marks: 80 
General Instructions:
Answers to this Paper must be written on the paper provided separately.
You will not be allowed to write during the first 15 minutes.
This time is to be spent reading the question paper.
The time given at the head of this Paper is the time allowed for writing the answers.
Attempt all questions from Section A and any four questions from Section B.
All work, including rough work, must be clearly shown and must be done on the same sheet as the rest of the
answers.
Omission of essential work will result in a loss of marks.
The intended marks for questions or parts of questions are given in brackets [ ]
Mathematical tables are provided.
Section A
1. Question 1 Choose the correct answers to the questions from the given options: [15]
a) ?1848 b) ?1830
c) ?1650 d) ?1800
A retailer purchases a fan for ?1500 from a wholesaler and sells it to a consumer at 10% profit. If the
sales are intra-state and the rate of GST is 12%, the cost of the fan to the consumer inclusive of tax is:
[1] (a)
a) 60 b) 80
c) 110 d) 100
A trader bought a number of articles for ?1200. Ten were damaged and he sold each of the rest at ?2
more than what he paid for it, thus cleaning a profit of ?60 on the whole transaction. If x denotes the
number of articles he bought, then the value of x is
[1] (b)
a) 0 b) -1
c) 2 d) 1
When x
3
 - 3x
2
 + 5x - 7 is divided by x - 2, then the remainder is
[1] (c)
a) b)
If  and  are the roots of the equation x
2
 + x - 6 = 0 such that , then the product of the
matrices  and is
[1] (d)
a ß ß > a [ ] 0 a a ß [ ] ß + 1 - ß 0 a Mathematics
c) d)
[ ] - 5 - 9 4 - 2 [ ] 6 - 1 3 9 - 6 [ ] 5 9 4 2 [ ] 6 9 1 3 6 a) 3 b) 6
c) 5 d) 2
An AP starts with a positive fraction and every alternate term is an integer. If the sum of the first 11
terms is 33, then the fourth term is
[1] (e)
a) (-3, -2) b) (3, 2)
c) (-3, 0) d) (3, -2)
If the image of the point P under the reflection in the X-axis is (-3, 2), then the coordinates of the
point P are
[1] (f)
a) OP = OQ b) OP = OQ
c) OQ = 2OP d) OP = 2OQ
O is the point of intersection of the diagonals AC and BD of a trapezium ABCD with AB || DC.
Through O, a line segment PQ is drawn parallel to AB meeting AD in P and BC in Q, then OP is
equal to
[1] (g)
1 3 a) b)
a
3
c) d)
5 a
3
A sphere of radius a units is immersed completely in water contained in a right circular cone of semi-
vertical angle 30° and water is drained off from the cone till its surface touches the sphere. Then, the
volume of water remaining in the cone will be
[1] (h)
p 5 3 a 2 5 p 3 p a 3 3 p a) 23 b) 20
c) 26 d) 17
The maximum value of 23 - |2x + 3| is [1] (i)
a) 4/7 b) 2/7
c) 1/7 d) 3/7
The probability that a non leap year selected at random will have 53 Sundays is: [1] (j)
a) A and B are square matrices of same
order
b) A and B are square matrices of different
order
c) A and B are rectangular matrices of
same order
d) A and B are rectangular matrices of
different order
If both A + B and AB are defined, then which one of the following is true? [1] (k)
a) (2, 4); 2.94 sq units b) (4, 2); 4.92 sq units
c) (2, 4); 9.42 sq units d) (4, 2); 9.42 sq units
Join two points P(2, 2) and 0(4, 2) in the point P and rotate the line PQ in anti-clockwise direction at
an angle of 270°. Then, the new coordinates of point Q and the area formed by this figure will be
[1] (l)
Section B
Attempt any 4 questions
a) (2, 3) b) (0, –1)
c) (2, 2) d) (3, 3)
The coordinates of the vertices of ?ABC are respectively (–4, –2), (6, 2) and (4, 6). The centroid G of
?ABC is:
[1] (m)
a) 25.2 b) 25.5
c) 25 d) 25.1
If x < y < 2x, then the median and mean of x, y and 2x are 27 and 33, respectively. The mean of x and
y is
[1] (n)
a) Both A and R are true and R is the
correct explanation of A.
b) Both A and R are true but R is not the
correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
Assertion (A): Three consecutive terms 2k + 1, 3k + 3 and 5k - 1 form an AP than k is equal to 6. 
Reason (R): In an AP a, a + d, a + 2d, ...the sum of n terms of the AP be S
n
 =  
[1] (o)
( 2 a + ( n - 1 ) d ) n 2 2. Question 2 [12]
Sanya has a Recurring Deposit Account in a bank of ?2000 per month at the rate of 10% per annum.
If she gets ?83100 at the time of maturity, then find the total time for which the account was held.
[4] (a)
Find the fourth proportional of the following.
i. 3a
2
b
2
, a
3
, b
3
ii. a
2
 - 5a + 6, a
2
 + a - 6, a
2
 - 9
[4] (b)
If sin  + cos  = p and sec  + cosec  = q, then prove that q(p
2
 - 1) = 2p.
[4] (c)
? ? ? ? 3. Question 3 [13]
A solid cylinder of radius 7 cm and height 14 cm is melted and recast into solid spheres each of radius
3.5 cm. Find the number of spheres formed.
[4] (a)
Three vertices of a parallelogram ABCD taken in order are A(3, 6), B(5, 10) and C(3, 2) find:
i. the coordinates of the fourth vertex D.
ii. length of diagonal BD.
iii. equation of side AB of the parallelogram ABCD.
[4] (b)
Use graph paper to answer this question.
i. Plot the points A(4, 6) and B(1, 2).
ii. A' is the image of A, when reflected in X-axis
iii. B' is the image of B, when B is reflected in X = 4.
iv. Give the geometrical name for the figure ABA'B'.
[5] (c)
4. Question 4 [10]
Mr. Verma goes to a shop and buy a Jacket having cost ? 1180 (list price). The rate of GST 18%. He
tells the shopkeeper to reduce the price such an extent that he has to pay ? 1180 inclusive of GST.
Find the reduction needed in the price of the jacket.
[3] (a)
Solve the following quadratic equation and give the answer correct to two significant figures. [3] (b)
4x
2
 - 7x + 2 = 0
In a class of 40 students, marks obtained by the students in a class test (out of 10) are given below:
Marks 1 2 3 4 5 6 7 8 9 10
Number of students 1 2 3 3 6 10 5 4 3 3
Calculate the following for the given distribution:
i. Median
ii. Mode
[4] (c)
5. Question 5 [10]
If , then find the following.
i. 3A
ii. (-2)A
[3] (a)
A = [ ] 2 0 - 1 3 In the given figure, two circles intersect at S and T. STP, BSC and BAP are straight lines. Prove that
PATD is a cyclic quadrilateral. 
[3] (b)
Show that (x - 5) is a factor of 2x
2
 - 9x - 5. Hence, factorise 2x
2
 - 9x - 5.
[4] (c)
6. Question 6 [10]
The mid-point of the line joining (3a, 4) and (- 2, 2b) is (2, 2a + 2). Find the values of a and b. [3] (a)
Prove the following identities.
i. (sec A - sin A) (cosec A + cos A) = sin
2
 A tan A + cot A
ii. (1 + cot A + tan A) (sin A - cos A) = 
[3] (b)
- s e c A A c o s e c 2 c o s e c A A s e c 2 Find the sum of all two-digit odd positive numbers. [4] (c)
7. Question 7 [10]
A trader buys x articles for a total cost of ? 600.
i. Write down the cost of one article in terms of x. If the cost per article were ? 5 more, the number
of articles that can be bought for ? 600, would be four less.
ii. Write down the equation in x for the above situation and solve it to find x.
[5] (a)
The following distribution represents the height of 160 students of a school.
Height (in cm) Number of Students
140 - 145 12
145 - 150 20
150 - 155 30
155 - 160 38
160 - 165 24
[5] (b)
165 - 170 16
170 - 175 12
175 - 180 8
Draw an ogive for the given distribution taking 2 cm = 5 cm of height on one axis and 2 cm = 20
students on the other axis. Using the graph, determine:
i. the median height
ii. the inter quartile range
iii. the number of students, whose height is above 172 cm.
8. Question 8 [10]
A child has a die whose six faces shows the letters as given below 
The die is thrown once. What is the probability of getting
i. A
ii. D
[3] (a)
The total surface area of a sphere is 616 cm
2
. Find the radius and volume of the sphere. [Take  = ]
[3] (b)
p 2 2 7 In the figure given below, CD is the diameter of the circle which meets the chord AB at P such that
AP = BP = 12 cm. If DP = 8 cm, find the radius of the circle. 
[4] (c)
9. Question 9 [10]
An integer is such that one-third of the next integer is atleast 2 more than one-fourth of the previous
integer. Find the smallest value of the integer.
[3] (a)
The mean of the following data is 14. Find the value of k.
x 5 10 15 20 25
f 7 k 8 4 5
[3] (b)
In ABC, D and E are points on the sides AB and AC respectively, such that DE || BC. If AD = 4x -
3, AE = 8x - 7, BD = 3x - 1 and CE = 5x - 3, then find the value of x.
[4] (c) ? 10. Question 10 [10]
If x : y :: y : z, prove that x : z :: x
2
 : y
2
.
[3] (a)
Construct a triangle ABC in which base BC = 6 cm, AB = 5.5 cm and ABC = 120
o
.
a. Construct circle circumscribing the triangle ABC.
b. Draw a cyclic quadrilateral ABCD so that D is equidistant from B and C.
[3] (b)
? The shadow of a vertical tower on a level ground increases by 10 m, when the altitude of the sun
changes from 45
o
 to 30
o
. Find the height of the tower correct to two decimal places.
[4] (c)