Class 9 Maths: CBSE Past Year Paper (SA-1) - 4 PDF Download

 Page 1


SUMMATIVE ASSESSMENT – 1 
SUBJECT – MATHEMATICS 
CLASS: IX 
Time: 3Hrs  M.M: 90 
General Instruction: 
1. All questions are compulsory.
2. The paper consists of 31 questions divided into four sections A, B, C and D. Section A
comprises of 4 questions of 1 marks 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.
4. Use of calculator is not permitted.
SECTION A 
1. Is the number (3 7)(3 7) - + rational or irrational?
2. Write the coefficient of y in the expansion of
2
(5 ) . y - 3. In the given fir. For what value of x + y which make ABC ? a straight line:
For Visually impaired 
Write the Euclid’s first postulates. 
4. Find the perpendicular distance of the points P (5, 7) from the y – axis.
SECTION B 
5. If the coordinates of two points are P(-2, 3) and Q(-3, 5) then find (abscissa of P) –
(abscissa of Q).
6. Without actually calculating the cubes, find the value of 48
3
 – 30
3
 – 18
3
.
7. In given fig. if AC = BD. Using an Euclid’s axiom show that AB = CD.
For visually impaired 
If the ratio between two complementary angles is 2:3, then find the angles. 
Page 2


SUMMATIVE ASSESSMENT – 1 
SUBJECT – MATHEMATICS 
CLASS: IX 
Time: 3Hrs  M.M: 90 
General Instruction: 
1. All questions are compulsory.
2. The paper consists of 31 questions divided into four sections A, B, C and D. Section A
comprises of 4 questions of 1 marks 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.
4. Use of calculator is not permitted.
SECTION A 
1. Is the number (3 7)(3 7) - + rational or irrational?
2. Write the coefficient of y in the expansion of
2
(5 ) . y - 3. In the given fir. For what value of x + y which make ABC ? a straight line:
For Visually impaired 
Write the Euclid’s first postulates. 
4. Find the perpendicular distance of the points P (5, 7) from the y – axis.
SECTION B 
5. If the coordinates of two points are P(-2, 3) and Q(-3, 5) then find (abscissa of P) –
(abscissa of Q).
6. Without actually calculating the cubes, find the value of 48
3
 – 30
3
 – 18
3
.
7. In given fig. if AC = BD. Using an Euclid’s axiom show that AB = CD.
For visually impaired 
If the ratio between two complementary angles is 2:3, then find the angles. 
8. Find two rational numbers between – 2 and 5.
9. The sides of a triangle are 8cm, 15cm and 17cm. Find the area.
10. An exterior angle of a is 
0
110 ? and its two interior opposite angles are equal. Find each of
these equal angles.
SECTION C 
11. Plot the following points and check whether they are collinear or not:(-1, 1), (-3, 3), (-5,5).
12. By actual division, find the quotient and remainder when
4 3
3 4 3 1 x x x - - - is divide by
x+1.
13. Locate 3 on the number line.
14. In fig, line CB and FD intersect at A. If
0
POX=90 ? and a:b = 2:3, find c.
For visually impaired 
The angles of a triangle are in the ratio 6 : 7 : 2. Find the angles of the triangle. 
15. Prove that angles opposite to equal sides of a triangle are equal.
16. The perimeter of an isosceles triangle is 32cm. The ratio of the equal side to its base is
3:2. Find the area of the triangle.
17. Factorize:
3 2
2 3 17 30 x x x - - +
18. Prove that the sum of the angles of triangle is 180
o
.
19. Simplify:
1 1
3 2
1 2
6 3
9 27
3 3
- - ×
×
20. In fig., we have ABC = ACB ? ? and 3 = 4. ? ?
Show that 1 = 2. ? ?
Page 3


SUMMATIVE ASSESSMENT – 1 
SUBJECT – MATHEMATICS 
CLASS: IX 
Time: 3Hrs  M.M: 90 
General Instruction: 
1. All questions are compulsory.
2. The paper consists of 31 questions divided into four sections A, B, C and D. Section A
comprises of 4 questions of 1 marks 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.
4. Use of calculator is not permitted.
SECTION A 
1. Is the number (3 7)(3 7) - + rational or irrational?
2. Write the coefficient of y in the expansion of
2
(5 ) . y - 3. In the given fir. For what value of x + y which make ABC ? a straight line:
For Visually impaired 
Write the Euclid’s first postulates. 
4. Find the perpendicular distance of the points P (5, 7) from the y – axis.
SECTION B 
5. If the coordinates of two points are P(-2, 3) and Q(-3, 5) then find (abscissa of P) –
(abscissa of Q).
6. Without actually calculating the cubes, find the value of 48
3
 – 30
3
 – 18
3
.
7. In given fig. if AC = BD. Using an Euclid’s axiom show that AB = CD.
For visually impaired 
If the ratio between two complementary angles is 2:3, then find the angles. 
8. Find two rational numbers between – 2 and 5.
9. The sides of a triangle are 8cm, 15cm and 17cm. Find the area.
10. An exterior angle of a is 
0
110 ? and its two interior opposite angles are equal. Find each of
these equal angles.
SECTION C 
11. Plot the following points and check whether they are collinear or not:(-1, 1), (-3, 3), (-5,5).
12. By actual division, find the quotient and remainder when
4 3
3 4 3 1 x x x - - - is divide by
x+1.
13. Locate 3 on the number line.
14. In fig, line CB and FD intersect at A. If
0
POX=90 ? and a:b = 2:3, find c.
For visually impaired 
The angles of a triangle are in the ratio 6 : 7 : 2. Find the angles of the triangle. 
15. Prove that angles opposite to equal sides of a triangle are equal.
16. The perimeter of an isosceles triangle is 32cm. The ratio of the equal side to its base is
3:2. Find the area of the triangle.
17. Factorize:
3 2
2 3 17 30 x x x - - +
18. Prove that the sum of the angles of triangle is 180
o
.
19. Simplify:
1 1
3 2
1 2
6 3
9 27
3 3
- - ×
×
20. In fig., we have ABC = ACB ? ? and 3 = 4. ? ?
Show that 1 = 2. ? ?
For visually impaired 
If two lines intersect each other, then the vertically opposite angles are equal. 
SECTION D 
21. Factories the following:
(i)
2
2
9
y
x - (ii) 
2
2 7 15 x x - - 22. Pooja distributed Cuboidal gifts to the children in an orphanage on her birthday. What are
the possible expression for the dimensions of the cuboid if the volume is
2
3 2 5 . Kx Kx k + - What value of Pooja is depicted here?
23. If
5 3 3
3,
7 4 3
a b
+
= +
+
find the values of a and b. 
24. Prove that the sum of any two sides of a triangle is greater than twice the median drawn
to the third side.
25. ABC ? in an isosceles triangle in which AB = AC. Side BA is produced to D such that AD =
AB. Show that BCD ? is a right angles.
26. In fig. the side QR of PQR ? is produced to a point S. If the bisector of PQR ? and PRS ?
meet at a point T then prove that
1
QTR= QPR
2
? ?
Page 4


SUMMATIVE ASSESSMENT – 1 
SUBJECT – MATHEMATICS 
CLASS: IX 
Time: 3Hrs  M.M: 90 
General Instruction: 
1. All questions are compulsory.
2. The paper consists of 31 questions divided into four sections A, B, C and D. Section A
comprises of 4 questions of 1 marks 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.
4. Use of calculator is not permitted.
SECTION A 
1. Is the number (3 7)(3 7) - + rational or irrational?
2. Write the coefficient of y in the expansion of
2
(5 ) . y - 3. In the given fir. For what value of x + y which make ABC ? a straight line:
For Visually impaired 
Write the Euclid’s first postulates. 
4. Find the perpendicular distance of the points P (5, 7) from the y – axis.
SECTION B 
5. If the coordinates of two points are P(-2, 3) and Q(-3, 5) then find (abscissa of P) –
(abscissa of Q).
6. Without actually calculating the cubes, find the value of 48
3
 – 30
3
 – 18
3
.
7. In given fig. if AC = BD. Using an Euclid’s axiom show that AB = CD.
For visually impaired 
If the ratio between two complementary angles is 2:3, then find the angles. 
8. Find two rational numbers between – 2 and 5.
9. The sides of a triangle are 8cm, 15cm and 17cm. Find the area.
10. An exterior angle of a is 
0
110 ? and its two interior opposite angles are equal. Find each of
these equal angles.
SECTION C 
11. Plot the following points and check whether they are collinear or not:(-1, 1), (-3, 3), (-5,5).
12. By actual division, find the quotient and remainder when
4 3
3 4 3 1 x x x - - - is divide by
x+1.
13. Locate 3 on the number line.
14. In fig, line CB and FD intersect at A. If
0
POX=90 ? and a:b = 2:3, find c.
For visually impaired 
The angles of a triangle are in the ratio 6 : 7 : 2. Find the angles of the triangle. 
15. Prove that angles opposite to equal sides of a triangle are equal.
16. The perimeter of an isosceles triangle is 32cm. The ratio of the equal side to its base is
3:2. Find the area of the triangle.
17. Factorize:
3 2
2 3 17 30 x x x - - +
18. Prove that the sum of the angles of triangle is 180
o
.
19. Simplify:
1 1
3 2
1 2
6 3
9 27
3 3
- - ×
×
20. In fig., we have ABC = ACB ? ? and 3 = 4. ? ?
Show that 1 = 2. ? ?
For visually impaired 
If two lines intersect each other, then the vertically opposite angles are equal. 
SECTION D 
21. Factories the following:
(i)
2
2
9
y
x - (ii) 
2
2 7 15 x x - - 22. Pooja distributed Cuboidal gifts to the children in an orphanage on her birthday. What are
the possible expression for the dimensions of the cuboid if the volume is
2
3 2 5 . Kx Kx k + - What value of Pooja is depicted here?
23. If
5 3 3
3,
7 4 3
a b
+
= +
+
find the values of a and b. 
24. Prove that the sum of any two sides of a triangle is greater than twice the median drawn
to the third side.
25. ABC ? in an isosceles triangle in which AB = AC. Side BA is produced to D such that AD =
AB. Show that BCD ? is a right angles.
26. In fig. the side QR of PQR ? is produced to a point S. If the bisector of PQR ? and PRS ?
meet at a point T then prove that
1
QTR= QPR
2
? ?
For visually impaired 
If a transversal intercepts two lines such that the bisectors of a pair of corresponding 
angles are parallel, then prove that the two parallel. 
27. In ABC ? and sides AB and AC of ABC ? are produced to points E and D respectively of
bisectors BO and CO of CBE ? and BCD ? respectively meet at point O, then prove that
0
1
BOC=90 A.
2
? - ? 
28. If a, b, c are all non – zero and a + b+ c = 0 prove that
2 2 2
3
a b c
bc ca cb
+ + = 
29. Find the value of a and b so that x + 1 and x – 1 are factors of
2 3 2
2 3 . x ax x x b + + - +
30. Represent 9.3 on number line prove it.
31. In right triangle ABC, right angles at C. M is the mid point of hypotenuse AB. C is joined to
M and produced to a point D such that DM = CM. Point D is joined to point B.
Show that
(i) AMC BMD ? ? ?
(ii) DBC ? is a right angle
(iii) DBC ACB ? ? ?
(iv) 
1
CM= AB
2
For visually impaired 
Prove that if in two triangles, two angles and the included side of one triangle are equal to 
two angles and the included side of other triangle, then two triangles are congruent.