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 Page 1


?????? ???
? – I 
SUMMATIVE ASSESSMENT – I
???? / MATHEMATICS
?
? - IX / CLASS: IX
?????? ???: 3 ?? ?????? ??? : 90
Time Allowed : 3 hours  Maximum Marks : 90 
???? ????:
1.???  ?????? ? |
2.??  ?
 ? 31  ?, ?? ??? ??? ?, ?, ? ??? ? ? ????? ??? ?? | ?-
? ? 4  ? ???? ?? 1 ??? ?? ??; ?-? ? 6  ?? ???? ?? ?? 2 ???
?; ?-? ? 10  ? ???? ?? ?? 3 ??? ?; ??? ?-? ? 11  ? ???? ??? ?? 4 ??? ? |
3.??  ?
 ? ??? ???  ???? ?? |
4.????????? ?? ??? ???$? ?? |
General Instructions: 
1. All questions are compulsory.
2. The question paper consists of 31 questions divided into four sections A, B, C and D. Section-
A comprises of 4 questions of 1 mark each; Section-B comprises of 6 questions of 2 marks
each; Section-C comprises of 10 questions of 3 marks each and Section-D comprises of 11
questions of 4 marks each.
3. There is no overall choice in this question paper.
4. Use of calculator is not permitted.
?-? / SECTION-A
 ??%? 1 ?? 4 ? ?? ?? 1 ??? ?? |
Question numbers 1 to 4 carry one mark each. 
1. ??? ?????: 
2/3 1/5
3 .3
Simplify: 
2/3 1/5
3 .3
2. 
3 3
8 125 y x - ?? ???????? ????? |
Factorise:
3 3
8 125 . y x - 3. ?? ???$? ???? l ?? ?????? m ?? n ?? ?? ??? ??.?? ???? ?? ?? ???/?
???? ????? ?? ?? ??1 ????? ?? | ??, ?? ?????? m ?? n ?? ???? ? 3? ??
???? ??
Page 2


?????? ???
? – I 
SUMMATIVE ASSESSMENT – I
???? / MATHEMATICS
?
? - IX / CLASS: IX
?????? ???: 3 ?? ?????? ??? : 90
Time Allowed : 3 hours  Maximum Marks : 90 
???? ????:
1.???  ?????? ? |
2.??  ?
 ? 31  ?, ?? ??? ??? ?, ?, ? ??? ? ? ????? ??? ?? | ?-
? ? 4  ? ???? ?? 1 ??? ?? ??; ?-? ? 6  ?? ???? ?? ?? 2 ???
?; ?-? ? 10  ? ???? ?? ?? 3 ??? ?; ??? ?-? ? 11  ? ???? ??? ?? 4 ??? ? |
3.??  ?
 ? ??? ???  ???? ?? |
4.????????? ?? ??? ???$? ?? |
General Instructions: 
1. All questions are compulsory.
2. The question paper consists of 31 questions divided into four sections A, B, C and D. Section-
A comprises of 4 questions of 1 mark each; Section-B comprises of 6 questions of 2 marks
each; Section-C comprises of 10 questions of 3 marks each and Section-D comprises of 11
questions of 4 marks each.
3. There is no overall choice in this question paper.
4. Use of calculator is not permitted.
?-? / SECTION-A
 ??%? 1 ?? 4 ? ?? ?? 1 ??? ?? |
Question numbers 1 to 4 carry one mark each. 
1. ??? ?????: 
2/3 1/5
3 .3
Simplify: 
2/3 1/5
3 .3
2. 
3 3
8 125 y x - ?? ???????? ????? |
Factorise:
3 3
8 125 . y x - 3. ?? ???$? ???? l ?? ?????? m ?? n ?? ?? ??? ??.?? ???? ?? ?? ???/?
???? ????? ?? ?? ??1 ????? ?? | ??, ?? ?????? m ?? n ?? ???? ? 3? ??
???? ??
A transversal l intersects two line m and n such that a pair of alternate interior angles is 
equal. Then, what can you say about the lines m and n? 
4. ????? P(a, b), IV ??????? ? 67?? ?? | a ?? b ? ?? ???? ??? ?????
The point P(a, b) lies in the IV Quadrant. Find which of a or b greater?
? – ? / SECTION – B
 ??%? 5 ?? 10 ?? ?? 2 ??? ? |
Question numbers 5 to 10 carry two marks each. 
5. 18.48 ?? p/q ?? 9? ? :; ?????, ???? p ?? q ????>? ? ???, 0 q ?
Express 18.48 in the form of p/q, where p and q are integers, 0 q ?
6. ??? y = 2 ?? y = 0, ????
3 2
( ) 2 5 f y y y ay b = - + + ?? ??@? ?? ?? a ?? b ??
??? A?? ????? |
If y = 2 and y = 0 are the zeroes of the polynomial
3 2
( ) 2 5 , f y y y ay b = - + + find the values
of a and b.
7. ??
 ?, ???
1 1
,
2 2
OX XY PX XZ = = ?? OX = PX ??, ?? ??6B? ?? ?? ???????? D??
??E ????? ?? XY = XZ ?? |
In the figure, if 
1 1
,
2 2
OX XY PX XZ = = and OX = PX, then using an Euclid’s axiom show that
XY = XZ. 
Page 3


?????? ???
? – I 
SUMMATIVE ASSESSMENT – I
???? / MATHEMATICS
?
? - IX / CLASS: IX
?????? ???: 3 ?? ?????? ??? : 90
Time Allowed : 3 hours  Maximum Marks : 90 
???? ????:
1.???  ?????? ? |
2.??  ?
 ? 31  ?, ?? ??? ??? ?, ?, ? ??? ? ? ????? ??? ?? | ?-
? ? 4  ? ???? ?? 1 ??? ?? ??; ?-? ? 6  ?? ???? ?? ?? 2 ???
?; ?-? ? 10  ? ???? ?? ?? 3 ??? ?; ??? ?-? ? 11  ? ???? ??? ?? 4 ??? ? |
3.??  ?
 ? ??? ???  ???? ?? |
4.????????? ?? ??? ???$? ?? |
General Instructions: 
1. All questions are compulsory.
2. The question paper consists of 31 questions divided into four sections A, B, C and D. Section-
A comprises of 4 questions of 1 mark each; Section-B comprises of 6 questions of 2 marks
each; Section-C comprises of 10 questions of 3 marks each and Section-D comprises of 11
questions of 4 marks each.
3. There is no overall choice in this question paper.
4. Use of calculator is not permitted.
?-? / SECTION-A
 ??%? 1 ?? 4 ? ?? ?? 1 ??? ?? |
Question numbers 1 to 4 carry one mark each. 
1. ??? ?????: 
2/3 1/5
3 .3
Simplify: 
2/3 1/5
3 .3
2. 
3 3
8 125 y x - ?? ???????? ????? |
Factorise:
3 3
8 125 . y x - 3. ?? ???$? ???? l ?? ?????? m ?? n ?? ?? ??? ??.?? ???? ?? ?? ???/?
???? ????? ?? ?? ??1 ????? ?? | ??, ?? ?????? m ?? n ?? ???? ? 3? ??
???? ??
A transversal l intersects two line m and n such that a pair of alternate interior angles is 
equal. Then, what can you say about the lines m and n? 
4. ????? P(a, b), IV ??????? ? 67?? ?? | a ?? b ? ?? ???? ??? ?????
The point P(a, b) lies in the IV Quadrant. Find which of a or b greater?
? – ? / SECTION – B
 ??%? 5 ?? 10 ?? ?? 2 ??? ? |
Question numbers 5 to 10 carry two marks each. 
5. 18.48 ?? p/q ?? 9? ? :; ?????, ???? p ?? q ????>? ? ???, 0 q ?
Express 18.48 in the form of p/q, where p and q are integers, 0 q ?
6. ??? y = 2 ?? y = 0, ????
3 2
( ) 2 5 f y y y ay b = - + + ?? ??@? ?? ?? a ?? b ??
??? A?? ????? |
If y = 2 and y = 0 are the zeroes of the polynomial
3 2
( ) 2 5 , f y y y ay b = - + + find the values
of a and b.
7. ??
 ?, ???
1 1
,
2 2
OX XY PX XZ = = ?? OX = PX ??, ?? ??6B? ?? ?? ???????? D??
??E ????? ?? XY = XZ ?? |
In the figure, if 
1 1
,
2 2
OX XY PX XZ = = and OX = PX, then using an Euclid’s axiom show that
XY = XZ. 
8. ??
 ?, AB||CD ?? | x ?? ?? A?? ????? |
In the figure, AB||CD. Find x. 
9. ?? ????? x-?F ?? y-?F ?? 5 ???? ?? ???? ?? ?? | ???? ???G???? A?? ????? |
????? ?? ???G???? 3? ?????, ??? ?? y-?F ?? ?? ??? x-?F ?? 5 ???? ?? ???? ??
??
A point lies on x-axis at a distance of 5 units from y-axis. What are its co-ordinates? What
will be its co-ordinates, if it lies on y-axis at a distance of 5 units from x-axis?
10. ???? ?
??? ?? ?????? 15 cm, 25cm ?? 20cm ? | ???? F?
?? A?? ????? |
The sides of a triangle are 15 cm, 25 cm and 20 cm. Find its area.
? – ? / SECTION – C
 ??%? 11 ?? 20 ? ?? ?? 3 ??? ? |
Question numbers 11 to 20 carry three marks each. 
11. ??? ?????: 
5 1
3 45 4 3
2 3
- +
Simplify: 
5 1
3 45 4 3
2 3
- +
12. a ?? b, ?? ??? A?? ?????, ???
3 2
2
3 2
a b
+
= +
- ?? |
Find the value of a and b, if 
3 2
2.
3 2
a b
+
= +
- 
Page 4


?????? ???
? – I 
SUMMATIVE ASSESSMENT – I
???? / MATHEMATICS
?
? - IX / CLASS: IX
?????? ???: 3 ?? ?????? ??? : 90
Time Allowed : 3 hours  Maximum Marks : 90 
???? ????:
1.???  ?????? ? |
2.??  ?
 ? 31  ?, ?? ??? ??? ?, ?, ? ??? ? ? ????? ??? ?? | ?-
? ? 4  ? ???? ?? 1 ??? ?? ??; ?-? ? 6  ?? ???? ?? ?? 2 ???
?; ?-? ? 10  ? ???? ?? ?? 3 ??? ?; ??? ?-? ? 11  ? ???? ??? ?? 4 ??? ? |
3.??  ?
 ? ??? ???  ???? ?? |
4.????????? ?? ??? ???$? ?? |
General Instructions: 
1. All questions are compulsory.
2. The question paper consists of 31 questions divided into four sections A, B, C and D. Section-
A comprises of 4 questions of 1 mark each; Section-B comprises of 6 questions of 2 marks
each; Section-C comprises of 10 questions of 3 marks each and Section-D comprises of 11
questions of 4 marks each.
3. There is no overall choice in this question paper.
4. Use of calculator is not permitted.
?-? / SECTION-A
 ??%? 1 ?? 4 ? ?? ?? 1 ??? ?? |
Question numbers 1 to 4 carry one mark each. 
1. ??? ?????: 
2/3 1/5
3 .3
Simplify: 
2/3 1/5
3 .3
2. 
3 3
8 125 y x - ?? ???????? ????? |
Factorise:
3 3
8 125 . y x - 3. ?? ???$? ???? l ?? ?????? m ?? n ?? ?? ??? ??.?? ???? ?? ?? ???/?
???? ????? ?? ?? ??1 ????? ?? | ??, ?? ?????? m ?? n ?? ???? ? 3? ??
???? ??
A transversal l intersects two line m and n such that a pair of alternate interior angles is 
equal. Then, what can you say about the lines m and n? 
4. ????? P(a, b), IV ??????? ? 67?? ?? | a ?? b ? ?? ???? ??? ?????
The point P(a, b) lies in the IV Quadrant. Find which of a or b greater?
? – ? / SECTION – B
 ??%? 5 ?? 10 ?? ?? 2 ??? ? |
Question numbers 5 to 10 carry two marks each. 
5. 18.48 ?? p/q ?? 9? ? :; ?????, ???? p ?? q ????>? ? ???, 0 q ?
Express 18.48 in the form of p/q, where p and q are integers, 0 q ?
6. ??? y = 2 ?? y = 0, ????
3 2
( ) 2 5 f y y y ay b = - + + ?? ??@? ?? ?? a ?? b ??
??? A?? ????? |
If y = 2 and y = 0 are the zeroes of the polynomial
3 2
( ) 2 5 , f y y y ay b = - + + find the values
of a and b.
7. ??
 ?, ???
1 1
,
2 2
OX XY PX XZ = = ?? OX = PX ??, ?? ??6B? ?? ?? ???????? D??
??E ????? ?? XY = XZ ?? |
In the figure, if 
1 1
,
2 2
OX XY PX XZ = = and OX = PX, then using an Euclid’s axiom show that
XY = XZ. 
8. ??
 ?, AB||CD ?? | x ?? ?? A?? ????? |
In the figure, AB||CD. Find x. 
9. ?? ????? x-?F ?? y-?F ?? 5 ???? ?? ???? ?? ?? | ???? ???G???? A?? ????? |
????? ?? ???G???? 3? ?????, ??? ?? y-?F ?? ?? ??? x-?F ?? 5 ???? ?? ???? ??
??
A point lies on x-axis at a distance of 5 units from y-axis. What are its co-ordinates? What
will be its co-ordinates, if it lies on y-axis at a distance of 5 units from x-axis?
10. ???? ?
??? ?? ?????? 15 cm, 25cm ?? 20cm ? | ???? F?
?? A?? ????? |
The sides of a triangle are 15 cm, 25 cm and 20 cm. Find its area.
? – ? / SECTION – C
 ??%? 11 ?? 20 ? ?? ?? 3 ??? ? |
Question numbers 11 to 20 carry three marks each. 
11. ??? ?????: 
5 1
3 45 4 3
2 3
- +
Simplify: 
5 1
3 45 4 3
2 3
- +
12. a ?? b, ?? ??? A?? ?????, ???
3 2
2
3 2
a b
+
= +
- ?? |
Find the value of a and b, if 
3 2
2.
3 2
a b
+
= +
- 
13. ???
2
2
1
34 z
z
+ = ??, ??
1
z
z
+ ?? ???? ???J? ??? ?? ??? ???? ??,
3
3
1
z
z
+ ??
??? A?? ????? |
If 
2
2
1
34, z
z
+ = find the value of 
3
3
1
, z
z
+ using only the positive value of 
1
. z
z
+ 
14. ???
2
2 ax x b + + ?? (x + 2) ?? (2x + 1) ????? ??????? ?, ?? ??E ????? ?? a –
b=0 ?? |
If both (x + 2) and (2x + 1) are factors of 
2
2 , ax x b + + prove that a – b = 0.
15. ????? ?, ?? ??? ?????? PQ ?? PS ??K? ????? O?? ??.?? ???? ? | ???
75 POT ? = °??, ?? a, b ?? c ?? ??? A?? ????? |
In the figure, two straight lines PQ and PS intersect each other at O. If 
0
75 , POT ? = find the
value of a, b and c. 
16. ??? l||m ??, n ?? ???$? ???? ?? (??6?? ?????) ??? 1: 2 7:5 ? ? = ??, ?? ???
??? A?? ????? |
If l||m, n is a transversal (see figure) and 1: 2 7:5, ? ? = then find all the angles.
Page 5


?????? ???
? – I 
SUMMATIVE ASSESSMENT – I
???? / MATHEMATICS
?
? - IX / CLASS: IX
?????? ???: 3 ?? ?????? ??? : 90
Time Allowed : 3 hours  Maximum Marks : 90 
???? ????:
1.???  ?????? ? |
2.??  ?
 ? 31  ?, ?? ??? ??? ?, ?, ? ??? ? ? ????? ??? ?? | ?-
? ? 4  ? ???? ?? 1 ??? ?? ??; ?-? ? 6  ?? ???? ?? ?? 2 ???
?; ?-? ? 10  ? ???? ?? ?? 3 ??? ?; ??? ?-? ? 11  ? ???? ??? ?? 4 ??? ? |
3.??  ?
 ? ??? ???  ???? ?? |
4.????????? ?? ??? ???$? ?? |
General Instructions: 
1. All questions are compulsory.
2. The question paper consists of 31 questions divided into four sections A, B, C and D. Section-
A comprises of 4 questions of 1 mark each; Section-B comprises of 6 questions of 2 marks
each; Section-C comprises of 10 questions of 3 marks each and Section-D comprises of 11
questions of 4 marks each.
3. There is no overall choice in this question paper.
4. Use of calculator is not permitted.
?-? / SECTION-A
 ??%? 1 ?? 4 ? ?? ?? 1 ??? ?? |
Question numbers 1 to 4 carry one mark each. 
1. ??? ?????: 
2/3 1/5
3 .3
Simplify: 
2/3 1/5
3 .3
2. 
3 3
8 125 y x - ?? ???????? ????? |
Factorise:
3 3
8 125 . y x - 3. ?? ???$? ???? l ?? ?????? m ?? n ?? ?? ??? ??.?? ???? ?? ?? ???/?
???? ????? ?? ?? ??1 ????? ?? | ??, ?? ?????? m ?? n ?? ???? ? 3? ??
???? ??
A transversal l intersects two line m and n such that a pair of alternate interior angles is 
equal. Then, what can you say about the lines m and n? 
4. ????? P(a, b), IV ??????? ? 67?? ?? | a ?? b ? ?? ???? ??? ?????
The point P(a, b) lies in the IV Quadrant. Find which of a or b greater?
? – ? / SECTION – B
 ??%? 5 ?? 10 ?? ?? 2 ??? ? |
Question numbers 5 to 10 carry two marks each. 
5. 18.48 ?? p/q ?? 9? ? :; ?????, ???? p ?? q ????>? ? ???, 0 q ?
Express 18.48 in the form of p/q, where p and q are integers, 0 q ?
6. ??? y = 2 ?? y = 0, ????
3 2
( ) 2 5 f y y y ay b = - + + ?? ??@? ?? ?? a ?? b ??
??? A?? ????? |
If y = 2 and y = 0 are the zeroes of the polynomial
3 2
( ) 2 5 , f y y y ay b = - + + find the values
of a and b.
7. ??
 ?, ???
1 1
,
2 2
OX XY PX XZ = = ?? OX = PX ??, ?? ??6B? ?? ?? ???????? D??
??E ????? ?? XY = XZ ?? |
In the figure, if 
1 1
,
2 2
OX XY PX XZ = = and OX = PX, then using an Euclid’s axiom show that
XY = XZ. 
8. ??
 ?, AB||CD ?? | x ?? ?? A?? ????? |
In the figure, AB||CD. Find x. 
9. ?? ????? x-?F ?? y-?F ?? 5 ???? ?? ???? ?? ?? | ???? ???G???? A?? ????? |
????? ?? ???G???? 3? ?????, ??? ?? y-?F ?? ?? ??? x-?F ?? 5 ???? ?? ???? ??
??
A point lies on x-axis at a distance of 5 units from y-axis. What are its co-ordinates? What
will be its co-ordinates, if it lies on y-axis at a distance of 5 units from x-axis?
10. ???? ?
??? ?? ?????? 15 cm, 25cm ?? 20cm ? | ???? F?
?? A?? ????? |
The sides of a triangle are 15 cm, 25 cm and 20 cm. Find its area.
? – ? / SECTION – C
 ??%? 11 ?? 20 ? ?? ?? 3 ??? ? |
Question numbers 11 to 20 carry three marks each. 
11. ??? ?????: 
5 1
3 45 4 3
2 3
- +
Simplify: 
5 1
3 45 4 3
2 3
- +
12. a ?? b, ?? ??? A?? ?????, ???
3 2
2
3 2
a b
+
= +
- ?? |
Find the value of a and b, if 
3 2
2.
3 2
a b
+
= +
- 
13. ???
2
2
1
34 z
z
+ = ??, ??
1
z
z
+ ?? ???? ???J? ??? ?? ??? ???? ??,
3
3
1
z
z
+ ??
??? A?? ????? |
If 
2
2
1
34, z
z
+ = find the value of 
3
3
1
, z
z
+ using only the positive value of 
1
. z
z
+ 
14. ???
2
2 ax x b + + ?? (x + 2) ?? (2x + 1) ????? ??????? ?, ?? ??E ????? ?? a –
b=0 ?? |
If both (x + 2) and (2x + 1) are factors of 
2
2 , ax x b + + prove that a – b = 0.
15. ????? ?, ?? ??? ?????? PQ ?? PS ??K? ????? O?? ??.?? ???? ? | ???
75 POT ? = °??, ?? a, b ?? c ?? ??? A?? ????? |
In the figure, two straight lines PQ and PS intersect each other at O. If 
0
75 , POT ? = find the
value of a, b and c. 
16. ??? l||m ??, n ?? ???$? ???? ?? (??6?? ?????) ??? 1: 2 7:5 ? ? = ??, ?? ???
??? A?? ????? |
If l||m, n is a transversal (see figure) and 1: 2 7:5, ? ? = then find all the angles.
17. ??? ???? ????? ?
??? ? ?? @????? ????? @????? ?? ?????? ??, ?? ??E ?????
?? ??$ ???? ???? ???? ?? ?????? ???? |
In a right angled triangle, if one acute of angle is double the other, then prove that the
hypotenuse is double the smallest side.
18. ??? ?? ??
 ? ABC ? ?? ??6M?? AD ?? | B ?? C ?? ?N BM ?? CN O???
AD ?? ???? ?? AD ?? ????? ?? ? | ???$?? ?? BM = CN ?? |
In given figure AD is the median of . ABC ? BM and CN are perpendiculars drawn from B
and C to AD and AD produced respectively. Show that BM = CN.  
19. P(3, 2) ?? Q(7, 7) ?? ????? ? | P ?? Q ?? x-?F ?? ??? ????? ?? ? ?? ?? ??? O??? L ?? M ?? ????? ? |
(a) L ?? M ?? ???G???? A?? ????? |
(b) LM ?? ?N?? A?? ????? |
P(3, 2) and Q(7, 7) are two points. Perpendiculars are drawn to x-axis from P and Q meeting
the x-axis at L and M respectively.
(a) Find the co-ordinates of L and M.
(b) Find the length of LM.

FAQs on Class 9 Maths: CBSE Past Year Paper (SA-1) - 9

1. What is the marking scheme for CBSE Class 9 Maths SA-1 examination?

Ans. The marking scheme for CBSE Class 9 Maths SA-1 examination typically includes different sections, such as objective type questions, short answer questions, and long answer questions. Each section carries a specific weightage, which is mentioned in the question paper. Students are advised to carefully read the instructions provided in the question paper to understand the marking scheme.

2. How should I prepare for CBSE Class 9 Maths SA-1 examination?

Ans. To prepare for CBSE Class 9 Maths SA-1 examination, students should start by thoroughly studying the NCERT textbook. They should understand the concepts and practice solving the examples and exercises given in the book. Additionally, students can refer to previous year question papers and sample papers to get an idea of the exam pattern and practice solving different types of questions. Regular revision and practice are key to scoring well in the exam.

3. Are there any important topics that I should focus on for CBSE Class 9 Maths SA-1 examination?

Ans. Yes, there are certain important topics that you should focus on for CBSE Class 9 Maths SA-1 examination. Some of these topics include number systems, algebraic expressions, linear equations in two variables, coordinate geometry, triangles, quadrilaterals, areas of parallelograms and triangles, circles, constructions, and statistics. It is recommended to prioritize these topics and allocate sufficient time for understanding and practicing them.

4. How can I improve my problem-solving skills for CBSE Class 9 Maths SA-1 examination?

Ans. Improving problem-solving skills for CBSE Class 9 Maths SA-1 examination requires regular practice. Start by understanding the concepts and formulas related to different topics. Then, solve a variety of problems related to each concept. Gradually increase the difficulty level of the problems and challenge yourself to solve them within a given time limit. Additionally, you can join study groups or seek help from teachers to clarify any doubts and discuss different problem-solving techniques.

5. Is it important to solve past year question papers for CBSE Class 9 Maths SA-1 examination?

Ans. Yes, solving past year question papers for CBSE Class 9 Maths SA-1 examination is highly beneficial. It helps you familiarize yourself with the exam pattern, understand the types of questions asked, and practice time management. By solving these papers, you can also assess your preparation level and identify any weak areas that need more attention. Additionally, it gives you an idea of the marking scheme and helps you strategize your approach towards the exam.

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Class 9 Maths: CBSE Past Year Paper (SA-1) - 9 Notes

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