Download subject: mathematics - Vijaya Vittala Vidyashala

Class & section: VIII _____
Roll No : _____________________
Name of the Student : ______________
Signature of the invigilator : ____________
Summative Assessment I 2015
Mathematics
I. Choose the correct answer & fill the blanks: [1x8=8]
1. Remainder of a perfect square divided by 5 is __
a. 0 ,1, 3 b. 0, 1, 4
c. 0, 1, 3
d. 1, 2, 3
3
2. The additive inverse and multiplicative inverse of 2 is ___
3
3
3
2
3
2
2
3
Time: 2 ½ hours
Marks Obtained :
Total Marks : 80
Signature of the evaluator :________
_____________________
_____________________
a. − 2 , 2
b. 2 , 3
c. − 2 , 3
d. 3 , − 2
2
3. What should be added to 𝑥 + 9 to make it a perfect square. __
____________________
a. 2x
b. 3x
c. 6x
d. 9x
2
4. Facatorizing 𝑥 + 6𝑥 + 8 we get ____
___________________
a. (𝑥 + 3)(𝑥 + 4) b. (𝑥 + 3)(𝑥 + 2) c. (𝑥 + 6)(𝑥 + 2) d. (𝑥 + 4) (𝑥 + 2)
5. The difference of (0.7)2 – (0.3)2 simplifies to ___
___________________
a. 0.4
b. 0.49
c.
d. 0.56
6. The correct identity to evaluate 53 x 54 is ____
__________________
a. (𝑎 + 𝑏)2 b. (𝑎 − 𝑏)2 c. 𝑎2 − 𝑏 2 d. (𝑥 + 𝑎)(𝑥 + 𝑏)
7. Seven times a number if increased by 11 is 81. The equation of this is __
__________________
a. 7x + 81 = 11
b. 7x + 11 = 81
c. 7x – 11 = 81 d. 7x = 81
8. If the sum of two integers is − 12 and their product is 32, the numbers are _
________________
a. +8, +4 b. – 8, +4 c. +8, − 4 d. – 8, − 4
II. Do as directed : [1x8=8]
1. Express 144 as a sum of odd numbers.
2. Represent
3
8
on the number line.
3. Find the nearest integer to the square root of 824.
4. Subtract : 2𝑥 3 − 𝑥 2 + 4 𝑥 − 6 from 𝑥 3 + 5𝑥 2 − 4 𝑥 + 6.
5. Find the product of
6𝑥
5
(𝑎3 − 𝑏 3 )
1
6. Expand (𝑥 + 𝑥)2.
7. Solve: (2𝑥 − 5) = 3(𝑥 − 5).
2𝑥
2𝑥
8. Find the product of ( 3 + 1) ( 3 − 1) using the correct identity.
III. Answer the following: [2x8=16]
2
3
1. Write a rational number between 5 and 5 having the same denominator.
2. Simplify using the distributive property:
3.
4.
5.
6.
7.
8.
2 1
2
( + 5)
5 9
2
Classify the following into rational and irrational numbers.: 3 , √2 , 
̅ , 0.32415……….
Find the sum of 12th and 13th triangular number, find their sum and verify.
Find the cube root of 10648 by prime factorisation.
The base and altitude of a triangle are (6𝑥 − 8𝑦) and (5𝑥 − 7𝑦) respectively find the area.
Factorise 4𝑥 2 + 12 𝑥𝑦 + 5𝑦 2
2𝑥+7
3𝑥+11
2𝑥+8
Solve 5 − 2 = 3 − 5
IV. Solve: [3x6=18]
1. Factorise: 𝑥 4 + 5𝑥 2 + 9 by making a perfect square.
2. A sum of Rs 2304 is equally distributed among several people. Each gets as many rupees as the
number of persons. How much does each gets?
3. State closure property and associative property of rational numbers under addition give
an example for each.
4. The area of a square field is 7396𝑚2 find the perimeter.
5. If a = (3𝑥 − 5𝑦), 𝑏 = (6𝑥 − 3𝑦) 𝑎𝑛𝑑 𝑐 = (2𝑦 − 4𝑥) 𝑓𝑖𝑛𝑑 (2𝑎 − 3𝑏 + 4𝑐)
1
6. (𝑥 + 𝑥) = 6 find (𝑥 2 +
1
𝑥2
) 𝑎𝑛𝑑 (𝑥 4 +
1
𝑥4
)
Geometry:
I. I. Choose the correct answer & fill the blanks: [1x3=3]
1. The measure of an angle which is 3 times its supplement is ____
________________
a. 45° b. 135° c. 90° d. 145°
2. Two circles are said to be congruent if they have same ___
________________
a. length
b. radius c. diameter d. both b and c
3. In ∆ ABC,  B =  C = 45°, then the triangle is ___
_________________
a. acute angled triangle b. obtuse angled triangle c. right angled triangle d. equilateral triangle.
II. Answer as directed: [1x3=3]
1. How many obtuse angles can be there in a triangle? Why?
2. Find the values of x and y in the given figure:
3. Are these two triangles congruent? Justify.
III. Do as directed: [2x5=10]
1. Compute the value of ‘x’ in the given figure:
2. In the adjoining figure, if  𝐶𝑂𝐴 −  𝐵𝑂𝐶 = 50° , find the angles.
3. Identify the corresponding sides and angles in the following figure:
4. The sum of two angles of a triangle is equal to its third angle. Determine the measure
of the third angle.
5. In the figure, diagonal AC of a quadrilateral ABCD bisects  𝐴 𝑎𝑛𝑑  𝐶 .
Prove that AB = AD and CB=CD.
III. Solve: [3x2=6]
1. State and prove exterior angle theorem.
2. i] In the adjoining figure AB=CD, AD=BC. Show that  1 =  2
Ii] Find ‘y’ in the given figure:
V. Solve: [4x2=8]
1. State SAS postulate. Prove that in a triangle the angles opposite to equal sides are equal.
2. i] In the figure, QT ┴ PR.  𝑇𝑄𝑅 = 40° ,  𝑆𝑃𝑅 = 30°, find  𝑇𝑅𝑆 𝑎𝑛𝑑 𝑃𝑆𝑄
i] In ∆ABC,  𝐴 is a right angle,  𝐵 =35°, find  𝐶.
OR
i] Prove that if two parallel lines are cut by a transversal then each pair of alternate angles are equal.
Ii] Find all the angles in the given figure.
……………………………………………………………………………………………………………………………
Class & section: IX _____
Summative Assessment I 2015
Time: 2 ½ hours
Roll No : _____________________
Marks Obtained :
Name of the Student : ______________
Total Marks : 80
Signature of the invigilator : ____________
Mathematics
Signature of the evaluator :________
I. Choose the correct answer & fill the blanks: [1x4=4]
1. A Polynomial whose degree is zero is a ___
a. constant polynomial
____________________
b. linear polynomial
c. real polynomial
d. quadratic polynomial
2. If √332929 is 577, then √0.00332929 is __
a. 05.77
b. 0.577
c. 0.0577
____________________
d. 0.00577
3. The HCF of a2 – 1 and 3a – 3 is ___
a. 3(𝑎 − 1)
b. (𝑎 − 1)
_____________________
c. (𝑎 − 1)2
d. (𝑎 + 1) (𝑎 − 1)
3
4. The simplest form of √108 is __
3
3
a. 4√3
b.3 √3
3
c. 2 √4
_____________________
3
d. 3 √4
II. Answer as directed: [1x6=6]
1. Simplify: [16]−0.75 x [64]4/3
2. Factorise: a2 – b2 – a+b .
3. If A = { a, b, c, d } find A∪ ∅
4. Simplify: (3𝑎 − 2)2 - (2𝑎 − 3)2
5. Write the periodic part and the length for the given decimal expansion: 0.0714285714285714285………….
6. Expand : (𝑎 − 𝑏 + 𝑐)2
III.
1.
2.
3.
4.
Do as directed: [2x10=20]
Find the square root of 2.0164.
Factorise x2 + 10x + 20 by adding and subtracting appropriate quantity.
̅̅̅̅.
Find the rational number whose decimal expansion is 0.214
If a+b+c=2s prove that 𝑠(𝑠 − 𝑎) + 𝑠(𝑠 − 𝑏) + 𝑠(𝑠 − 𝑐) = 𝑠2
5
3
5. Reduce √2 , √2 , and √5 to the same order.
6. Factorise √3 a2 + 2a - 5√3 .
7. Locate 1 + √5 on the number line.
8. Find the volume of the cuboid with dimensions (𝑥 − 1), (𝑥 − 2) and (𝑥 − 3).
9. For any set B, A  B, show that A ∪ B = B and A ∩ B = A.
𝑥
𝑥
𝑥2
𝑥4
𝑥8
10. Prove that (1 + 𝑦) (1 − 𝑦) (1 + 𝑦 2 ) (1 + 𝑦 4 ) + 𝑦 8 = 1
IV. Answer as directed: [3x4=12]
1. A square garden has an area of 900 m2. Additional land measuring equal area surrounding it has been
added to it . If the resulting plot is in the form of a square, what is its side, correct to ‘3’ decimal places?
2. If a + b + c = 0, prove that 𝑎(𝑏 − 𝑐)2 + 𝑏(𝑐 − 𝑎)2 +c (𝑎 − 𝑏)2 = - 9abc .
3
3
3. Classify the following into like surds: √243, √128, √75
4. Facatorise: (𝑥 2 − 2𝑥)2 - 23 (𝑥 2 − 2𝑥)+ 120.
3
√72,
3
√54, √48.
V. Solve: [4x2=8]
1. Suppose the polynomials P(𝑦)=(𝑦 − 1)(2𝑦 2 +ay+2) and q(𝑦)=(𝑦 + 2)(3𝑦 2 - by+1) have their HCF
h(𝑦)= 𝑦 2 + 𝑦 − 2, find the values of a and b.
2. If A = { 1, 2, 3, 4 }, B= { 3, 4, 6, 7 } and ∪ = { 1, 2, 3, 4, 5, 6, 7, 8 }, find i] 𝐴| in ∪ ii] A ∪ B
iii] A ∩ B iv] A ∆ B and represent all the operations through Venn diagram.
OR
If A = { a, b, c, d }, B = { c, d, e, f } and ∪ = { a, b, c, d, e, f, g, h } then find
i] Find the relation between A∩B and B∩A. ii] Find A ∪ 𝐴1 iii] Write the power set of A
iv] Find 𝐴| 𝑖𝑛 ∪ and represent through Venn diagram.
Geometry:
I. Choose the correct answer: [1x3=3]
1. Number of sides a polygon has if the sum of its interior angles is 8 right angles is __
___________
[ 8, 6, 10, 12 ]
2. Each exterior angle of regular polygon with side 30 is ___ [ 12°, 24°, 60° , 30° ]
___________
3. If the diagonals of a parallelogram are perpendicular to each other, the parallelogram is a _
[ Rectangle, Trapezium, Rhombus, Kite ]
_____________
II. Fill in the blanks: [1x2]
1. If each exterior angle of a regular polygon is equal to twice its adjacent interior angle,
then the number of sides is ___________
2. The area of a parallelogram is 153.6 cm2 . The base measures 19.2 cm. Then the height of
parallelogram is ______________
III. Answer the following : [2x5=10]
1. Prove that if the diagonals of a parallelogram are equal then the figure is a rectangle.
2. The angles of a convex polygon are in the ratio 2:3:5:9:11. Find each angle.
3. Construct a Rhombus ABCD with AB = 3.2cm AC = 4.8cm.
4. A polygon has n sides. Two of its angles are right angles. Each of the remaining angles measures 144°.
Find n.
5. Construct a parallelogram ABCD. AD=4.3cm CD = 5.7cm and BD = 7cm.
6. Construct a Quadrilateral ABCD. AB= 7cm BC=5cm AC=6cm.  ACD = 30°,  CAD = 40°. [3x2=6]
Measure BD.
7. Define a Polygon. Differentiate between concave and convex polygons.
8. Prove that the parallelograms on the same base & between same parallels are equal in area. [4x2=8]
9. Suppose E, F are the midpoints respectively of the oblique sides PS , QR of the trapezium PQRS.
Prove that EF is parallel to SR & EF =
𝑃𝑄+𝑅𝑆
2
.
…………………………………………………………………………………………………..
SUMMATIVE ASSESSMENT – I - 2015-16
Class & section: X ___
Roll No: _________
Name of the Student: ___________________
Signature of the invigilator: ________
Time: 2½ hours
Marks Obtained:_______
Total Marks:
80
Signature of the evaluator: _______
SUBJECT: MATHEMATICS
I. Choose the correct answer:
3
1x8=8
3
1. If 3√2 + 𝑥 3√𝑦 = √192 ,then values of x and y are ___________________________________
a) x=3 and y=2
b) y=3 and x=2
2. If A={ 3,4,5,6,7} and B={1,3,5,8} then B A
a) ∅
3. if 17200=
b) {3,5}
x
y
z
1,
2
3
p p, p
c)x=3 and y=6
d) x=6 and y=18
B is ___________________________________
c){1,3,5,8}
d){1,8}
then the values of P1 , P2 , P3 and x, y, z are__________________ respectively.
a) Primes and 23 , 34 , 52 b) 2,3,5 and 3,4,2
c) 2,3,5 and 23 , 34 , 52 d) None of these.
4. If Tn—3 = 5n—6 then then Tn is __________________________ a) 5n +6 , b)5n—3
c)5n+9
d)5n+9
5. In a G.P, the ratio of the sum of first three terms to the sum of first six terms is 27:35, then the
Common ratio is _________________________
a) 27:8
3
6. The rationalizing factor of √18 is_______________________
7.
b) 3:2
3
c)2:3
3
d) 35:27
3
3
a)√12 𝑏)√324 𝑐)√4 𝑑)√18
in the given, graphical representation of a polynomial, the number of zeroes are _____________
a) 2
b) 3
c) nil
d) not possible to identify the zeroes.
8. The formula to find Pythagorean triplets is ______________________________________________________
a) ( hyp)2 = the sum of squares on the other two sides b) 2n, n2—1 , and n2+1
c) 2(n2+1), 2n and 2n—1
d) 2n, (n2+1), and 2n2+1
II. Solve the following:
6x1=6
9. If f(x)= 4x2 –7x+2, find f( −3/2).
10. Find the product of 3√2 − 4 and its conjugate.
11. (x-a), is it a factor of the polynomial x6 –a6
12.
in the given figure, what is the length of AD.
13.
In the figure ‘O’ is the centre and PQ is a tangent. If PQ=18cms and PR=12cms then
What is the radius of the circle?
14.
In the given ∆𝐴𝐵𝐶, YX ‖ BC. Write the conclusion on base of basic proportionality
Theorem
III. Do as directed:
18x2=36
15. Show that the sum of an A P whose first term is ‘P’, second term is ‘q’ and the last term is ‘r’
(𝑝+𝑞)(𝑞+𝑟−2𝑝)
Is equally to
2(𝑞−𝑝)
16. A person saved every year three-fourth as much he saved the previous year. If he totally saved
24,992 in 5 years. How much did he save in the first year?
17. There are 75 roses and 45 lily flowers. They are to be made into bouquets containing both the
Flowers. All the bouquets should contain the same number of flowers. Find the number of each
Kind of flowers in them.
18. If ‘a’ is the arithmetic mean of ‘b’ and ‘c’. ‘b’ is the geometric mean of ‘a’ and ‘c’ then prove
That ‘c’ will be the harmonic mean of ‘a’ and ‘b’.
19. In class of 136 student , 95 student want to play cricket and 65 students are interested in cultural
Programme. 48 students participated both. How many of them participated in neither of these.
20. If 6+6x+6x2+6x3+……….=9. Find the value of ‘x’
21. Find the quotient and remainder by synthetic division method, given P(x)=6x4—29x3+4x2—12
And g(x)=(x—3).
22. What must be added to 6x4+13x3+13x2+28x—20 so that resulting is exactly divisible by 3x2+2x+5.
3
4
23. Find the product of √3 𝑎𝑛𝑑 √4.
24. if x3+ax2—bx+10 is divisible by x2—3x+2. Find the values of ‘a’ and ‘b’.
25. on dividing 2x3 –5x2+x+a and ax3+2x2—3 by (x—2) , the obtained remainder are R1 and R2
Respectively . if R1=2R2, find the value of ‘a’
26. Solve by factor method; √24 − 10𝑥 = 3 − 4𝑥.
27. PQRS is a trapezium, in which PQ ‖ RS, 2PQ=3RS. Prove that the ratio between ∆POR ~ ∆SOR =9:4
28. Construct a pair of tangents to a circle of radius 4.5cms from an external point which is 2.5cms
away from the centre
29. The sides of a right angled triangle are in A P, then Show that the sides are in the ratio 3:4:5.
30. Prove the converse of basic proportionality theorem.
31. Ina circle of radius 4.5cms, draw a chord AB of length 7cms. Construct tangent at the ends of the Chord AB.
In ∆𝐴𝐵𝐶, DE ‖ BC and CD ‖ EF. Prove that AD2=AF x AB
32.
IV. Solve the following:
6x3=18
33. Using Euclid’s division algorithm show that cube of any positive integer is of the form 9m, 9m+1 or
9m+8, for some integer ‘m’.
34. In a A P, the sum of 4 terms is 44 and the product of extremes is 85. Find the terms.
35. Simplify:
7√3
4√3
− 6+2
√10−√3
√
36. Solve by completing the square; 3x2 –5x—6 .
37. Prove that, in a right angled triangle, the square on the hypotenuse is equal to the sum of squares
on the other two sides.
∆𝐴𝐵𝐶, right angled at A and AD  BC. If AB=5cms and AC=12cms. Find the length of AD.
38.
V. Do as directed:
4 x 4=16
39. a) U is a set of multiples of 3 between 9 and 38. A and B are the subsets of U, A={x/x is a multiple of
6 and 12 ≤ 𝑥 < 30} and B={ x /x is a multiple of 9 and 12 < 𝑥 ≤ 36 }. Verify De Morgan’s law.
b) P= The set of digits which are multiple of 2, Q= The set of natural number which
are perfect square digit. Verify commutative property under union of sets
𝑥
40. a) solve: 𝑥+1 +
𝑥+1
𝑥
34
𝑙
= 15 b) if = 2 √𝑔 , Solve for ‘g’.
41. Construct transverse common tangents to a pair of circles of radii 4.5cms and 2.5cms so that circles are 4cms apart.
Measure their lengths and verify.
42. Prove that in two triangles, if respective angles are equal then the respective sides are in the same ratio.