Shree Bharathi Vidyalaya
Summative Assessment 1 -2024
Subject: Mathematics
Class: IX (State) Max. Marks: 80
General Instructions:
1. Answers to this paper must be written on the paper provided separately.
2. Omission of essential working will result in loss of marks
3. The intended marks for questions or parts of questions are given in brackets.
4. This question paper consists of 4 printed pages.
5. All questions are Compulsory.
6. Read the questions thoroughly before you attempt.
I. Choose the correct answer. 8X1=8
1. Which of the following is an irrational number?
a) √16 b) √(12/3) c) √12 d) √100
2. The value of 1251/3 is:
a) 5 b) 25 c) 45 d) 35
3. 3√6 + 4√6 is equal to _______
a) 6√6 b) 7√6 c) 4√12 d) 7√12
4. Two lines PQ and RS intersect at O. If ∠POR = 500, then value of ∠ROQ is
(a) 1200 (b) 1300 (c) 900 (d) 1500
5. Two straight lines AB and CD cut each other at O. If ∠BOD = 63°, then ∠BOC = _____
(a) 63° (b) 117° (c) 17° (d) 153°
6. A binomial of degree 20 in the following is _______.
(a) 20x + 1 (b) x/20 + 1 (c) x20 +1 (d) x2+20
7.The rationalizing factor of 7 + 2 √3 is
(a) 7 + 2 √3 (b) 7 - 2 √3 (c) 5 + 2 √3 (d) 4 - 2 √3
8. The name of the vertical line in the cartesian plane which determines the position of a point is
called:
(a) Origin (b) X-axis (c) Y-axis (d) Quadrants
II. Answer the following questions. 8X1=8
9.Find the value of 322/5.
10. Multiply 6 √5 by 2 √5.
11. Write the degree of 4 – y2
1
12. Find the value of p(x) = 6x – 3x2 + 4 for x = 2.
13. Find the zero of p(x) = 3x - 2
14. If the coordinates of a point are (-3, 4), In which quadrant lies?
15. Point (3, 4) lies on the graph of the equation 3y = kx + 7. Find the value of k
16. It is known that x + y = 10 and that x = z. Show that z + y = 10.
III. Do as directed. 8X2=16
17. In the given figure, if AC = BD, then prove that AB = CD.
OR
In the Figure, if PQ || ST, ∠PQR = 110° and ∠RST = 130°, find ∠QRS.
[Hint: Draw a line parallel to ST through point R.]
18. Write four solutions for 3x + 2y = 12 .
19. Classify the following as rational and irrational :
i) √23 ii) √225 iii) 7.478478…… iv) 1.101001000
20. Find P(0)and P(2) p(t) = 2 + t+ 2t2 – t3.
21. Factorise 27q3– 125p3– 135q2p + 225qp2
22. In the figure, PQR is a line, |POR = 4x and |ROQ = 2x. Find x .
23. Which of the following points lie on the x-axis?
i)(3,4) ii) (7, 0) iii) (0, 8) iv) (-9, 0)
24. Find six rational numbers between 3 and 4.
IV. Solve the following: 9 X 3=27
25. Plot the points in a graph and check whether they are collinear or not:
(i) (1, 3), (– 1, – 1), (– 2, – 3)
2
26. Find i) 71/5 ii) 163/4 iii) 22/3 . 21/5
71/3
27. Evaluate the following using identities: i) (3a + 4b + 5c)2 ii) (5p + 3q)3
OR
Evaluate the following products using identity: (i) 103×107 ii) 104×96
28. In the Figure, if AB || CD, EF ⊥ CD and ∠GED = 126°, find ∠AGE, ∠GEF and ∠FGE.
29. Expand each of the following using suitable identities: (i) (x+2y+4z)2 ii) (2a−3b)3
30. Show how √5 can be represented on the number line.
31. In the given figure, OP, OQ, OR and OS are four rays. Prove that |POQ + QOR + |SOR +
|POS = 3600.
OR
32. In Fig. |PQR = |PRQ ,then prove that |PQS = |PRT.
33. Show that 0.235353535........... can be expressed in p/q form.
34. Find the value of K, if x – 1 is a factor of P(x) in each case of the following cases.
i) P(x) = kx2 - √2𝑥 + 1 ii) x2 + 3x2 + 1
3
V. Solve the following: 4 X 4=16
35. Plot the following points and check whether they are collinear or not:
(i) (1, 3), (– 1, – 1), (– 2, – 3)
(ii) (1, 1), (2, – 3), (– 1, – 2)
(iii) (0, 0), (2, 2), (5, 5)
36. i) In Fig. lines AB and CD intersect at O. If ∠AOC +∠BOE = 70°
and ∠BOD = 40°, find ∠BOE and reflex ∠COE.
ii) In Fig, find the values of x and y and then show that AB || CD.
37. i) Factorise: x3–2x2–x+2
ii) Using identity simplify (3x+4) (3x–5)
38. i) Check which of the following are solutions of the equation x – 2y = 4 and which are not:
(i) (0, 2) (ii) (2, 0) (iii) (4, 0) (iv) ( 2 , 4 )
ii) Factorise: 64a3 -27b3 – 144a2b + 108ab2
OR
i) Simplify : (√5 - √2 ) (√5 + √2 )
ii) Rationalise the denominator of 1
2 + √3
VI. Solve: 1 X 5 =5
39. Without plotting the points indicate the quadrant in which they will lie, if
(i) the ordinate is 5 and abscissa is – 3
(ii) the abscissa is – 5 and ordinate is – 3
(iii) the abscissa is – 5 and ordinate is 3
(iv) the ordinate is 5 and abscissa is 3
(v) the ordinate is 0 and abscissa is 0
