01.08.22
Monday
Time: 1 hour
Periodic Test 1
Class IX
Mathematics
M.M: 40
General Instructions :
1. This question paper consists of 12 questions printed on 2 pages.
2. Question 1 contains 5 MCQ’s of 1 mark each.
3. Question 2 contains 5 very short questions of 1 mark each.
4. Question 3 to 5 are of 2 marks each.
5. Question 6 to 9 are of 3 marks each.
6. Questions 10 to 12 are of 4 marks each ( one case study).
1. (i) Value of ( 343)-2/3 is
(a) 1/7
(b) 3/7
(c) 1/49
(d) None of these.
(ii) If m and n are two natural numbers and mn = 32 then nmn is
(a) 510
(b) 52
(c) 512
(d) 53 .
(iii) Which of the following is true?
(a) Every whole number is a natural number.
(b) Every integer is a rational number.
(c) Every rational number is an integer.
(d) Every integer is a whole number.
(iv) Abscissa of all points on the x axis is
(a) 0
(b) 1
(c) -1
(d) None of these.
(v) Any point on the line y = x is of the form
(a) ( x, x )
(b) ( 0, x )
(c) ( x, 0 )
(d) ( x, -x )
2. (i) What is the point of intersection of lines x = 3 and y = 4?
(ii) What is the equation of y axis?
(iii) How many irrational numbers lie between two distinct rational numbers?
(iv) The decimal expansion of the number √2 is _____________.
(v) Write two irrational numbers whose sum and product are rational.
3. Express 0.163 as a fraction in simplest form.
4. Add 3√𝟐 + 7 √𝟑 and √2 - 5√𝟑.
5. Find the value of k if x = 3 and y = 1 is a solution of the equation 2x + 5y = k.
6. If 4 + √𝟓 = a + b √𝟓 , find the values of a and b.
4 - √𝟓
7. If a = 2 + √3 then find the value of a2 + 1 .
a2
8 Simplify (I) 22/3 X 21/3.
(ii) ( 0.001)-3/4
9 Without plotting the given points on a graph paper indicate the quadrants in which they lie if
(I) Ordinate = 6, abscissa = -3 (ii) ordinate = 3, abscissa = 5 (iii) ordinate = -5, abscissa = -7.
10 Represent √5.6 on number line.
11 The linear equation that converts Farenheit ( F ) to celsius ( C ) is given by the relation
C = 5F - 160
9
(I) If the temperature is 860 F, what is the temperature in celsius.
(II) If the temperature is 350 C, what is the temperature in farenheit.
(III) If the temperature is 00 F, what is the temperature in celsius.
(IV) What is the numerical value of the temperature which is same in both the scales?
12 Case study : A book store shopkeeper gives books on rent for reading. He has variety of
books in his store related to fiction, stories and quizzes etc. He takes a fixed charge for the
first two days and additional charge for each subsequent day. Assume that the fixed charge
be ₹ x and additional charge (per day) be ₹ y. Amrita paid ₹ 22 for a book and kept it for 6
days while Radhika paid ₹ 16 for keeping the book for 4 days.
(i) The situation of the amount paid by Radhika is algebraically represented by
(a) x - 4y = 16 (b) x + 4y = 16
(c ) x - 2y = 16 (d) x + 2y = 16
(ii) The situation of the amount paid by Amrita is algebraically represented by
(a) x - 2y = 11 (b) x - 2y = 22
(c ) x + 4y = 22 (d) x - 4y = 11
(iii) Which of the following points lie on graph of equation of amount paid by Amrita
(a) ( 6,6 )
(b) ( 10,3 )
(c ) ( 4,4 )
(d) none of these.
(iv) Which of the following points lie on graph of equation of amount paid by Radhika
(a) ( 10,3 )
(b) ( 3,10 )
(c ) ( 6,6 )
(d) none of these
27.09.22
Half Yearly Examination 2022 - 23
Tuesday
Class VIII
Time: 3 hrs
Mathematics
Name :____________
M.M : 80
General Instructions:
1. All questions are compulsory.
2. Section A consists of 20 questions of 1 mark each.
3. Section B consists of 8 questions of 2 marks each.
4. Section C consists of 8 questions of 3 marks each.
5. Section D consists of 5 questions of 4 marks each.
6. This question paper consists of 41 questions on 3 pages.
Section A
MCQ’s
1. Which of the following can not be the unit digit of a perfect square number ?
(I) 6
(ii) 1
(iii) 9
(iv) 8
2. If n is odd then ( 1 + 3 + 5 + 7 + 9 + 11 + ------ n terms) is equal to
(I) n2 + 1
(ii) n2 - 1
(iii) n2
(iv) 2n2 + 1.
3. Which of the following is the cube of odd number?
(I) 343
(ii) 1728
(iii) 4096
(iv) 512.
4. ( 0.8 )3 = _________
(I) 51.2
(ii) 5.12
(iii) 0.512
(iv) none of these.
5. A monomial multiplied by a monomial always gives a
(I) Monomial (ii) Binomial (iii) Trinomial (iv) None of these.
Fill in the blanks
6. Product of two rational numbers is always a __________.
7. The cube of a negative integer is always __________.
8. __________ is the interest calculated on previous year’s amount.
9. a x a2 X a3 X a4 = ________.
10. Area of a rectangle with length 3mn and breadth 4np is ________.
One word answer
11. Which rational number is its own additive inverse?
12. Name the quadrilaterals whose diagonals are equal.
13. What could be the possible ones of the square root of 998001?
14. If 16% of a number is 72, find the number.
15. Find the sum of 7x , -3x , 5x , -x and -2x.
True/ False
16. 0 is a whole number but it is not a rational number.
17. All parallelograms are trapeziums.
18. 6 hours = 25% of a day.
19. ( 5a - 9b ) - ( - 6a + 2b ) = ( -a - 7b ).
20. The square of a prime number is always prime.
Section B
21. State the name of a regular polygon of (I) 4 sides
(ii) 6 sides.
22. Find the measure of each exterior angle of a regular polygon of 15 sides.
23. GUNS is a parallelogram where GU = ( 3y - 1 )cm , UN = 18cm , SN = 26cm , GS = 3x cm.
Find the value of x and y.
24. Write a pythagorean triplet whose one member is 16.
25. Find the smallest whole number by which 2925 should be divided to make it a perfect
square. Also find the square root of the square number so obtained.
26. Find the value of (I)
( 21 )3
(ii) (
−𝟐 3
).
𝟑
27. A machinery worth ₹ 10,500 depreciated by 5%. Find its value after 1 year.
28. What must be subtracted from 3a2 - 6ab - 3b2 - 1 to get 4a2 - 7ab - 4b2 +1?
Section C
29. The sum of two rational numbers is -2. If one number is -14/5, find the other.
30. The length of a rectangle is 8cm and each of its diagonal measures 10cm. Find its breadth.
31. Name the parallelogram:
(I) The diagonals are equal and adjacent sides are unequal.
(II) All the sides are equal and one angle is 600.
(III) The diagonals are equal and the adjacent sides are equal.
32. Find the smallest square number that is divisible by each of the numbers 4, 9, 10.
33. Find √𝟎. 𝟗 upto two decimal places.
34. Find the smallest number by which 1323 must be multiplied so that the product is a perfect
cube.
35. Salim bought an article for ₹ 784 which includes GST of 12%. What was the price of the
article before GST was added?
36. Simplify 3y ( 2y - 7 ) - 3 ( y - 4 ) - 63 for (I) y = 0 and (ii) y = - 2.
Section D
37. Simplify using properties:
2 X -3
5
7
_
1 _ 3 X 3
14
7
5
38. The area of a square field is 60025m2. A man cycles along its boundary at 18 km/hr. In how
much time will he return to the starting point?
39. Kamala borrowed ₹ 26400 from a bank to buy a scooter at a rate of 15% p.a. compounded
yearly. What amount will she pay at the end of 2 year 4 months to clear the loan?
40. A picnic is being planned in a school for class VIII. Girls are 60% of the total number of
students and are 18 in number. The picnic site is 55km from the school and the transport
company if charging at the rate of ₹12 per km. The total cost of refreshments will be
₹4280.Find
(I) The ratio of number of girls to the number of boys in the class.
(II) The cost per head if two teachers are also going with the class.
41. (i) Multiply ( 2.5p - 0.5q ) ( 2.5p + 0.5q + 3)
(ii) Simplify ( a + b ) ( 2a - 3b + c ) - ( 2a - 3b )c.
10.09.22
Saturday
Time: 3 hr 15 mins
Half Yearly Examination 2022-23
M.M : 80
Class IX
Mathematics
Name : ____________
General Instructions :
1. This question paper contains total 24 questions printed on 3 pages.
2. Question 1 contains 5 MCQ’s of 1 mark each.
3. Question 2 contains 5 true / false of 1 mark each.
4. Question 3 contains 5 very short questions of 1 mark each.
5. Question 4 contains 5 fill ups of 1 mark each.
6. Questions 5 to 10 are of 2 marks each.
7. Questions 11 to 18 are of 3 marks each.
8. Questions 19 to 24 are of 4 marks each. ( 2 case study based questions)
Section A
1 . MCQ’s
a) The decimal representation of a rational number is
(I) Always terminating
(ii) either terminating or repeating
(iii) either terminating or non repeating
(iv) neither terminating nor repeating
b) If x < 0 and y > 0 then the point ( x , y ) lies in
(I) Quadrant 1 (ii) Quadrant 2 (iii) Quadrant 3
c) y = 0 is the equation of
(I) X axis
(ii) y axis
(iv) Quadrant 4
(iii) a line parallel to x axis
(iv) a line parallel to y axis.
d) The graph of the linear equation 4x + 3y = 12 cuts the x axis at the point
(I) ( 2 , 0 )
(ii) ( 0 , 2 )
(iii) ( 0 , 3 )
(iv) ( 3 , 0 )
e) If the angles of a triangle are in ratio 1:2:7, then the triangle is
(I) an isosceles triangle
(ii) an acute angled triangle
(iii) an obtuse angled triangle (iv) a right angled triangle
2. True / False
a) Every real number is an irrational number.
b) The point ( -5 , 0 ) lies on x axis.
c) All the points ( 2 , 0 ) , ( -3 , 0 ) , ( 4 , 2 ) , ( 0 , 5 ) lie on the x axis.
d) The edges of a surface are lines.
e) Sum of two complementary angles is 1800.
3. Very short answers
a) Write the name of the point where x - axis and y - axis intersect.
b) Can two unequals be equal to the same thing?
c) How many dimensions does, a solid has?
d) If bisector of angle A is at right angle to the side BC , then evaluate ∠𝐁 - ∠𝐂
e) Diagonals of a quadrilateral bisect each other. If ∠𝐀 = 350, find ∠𝐁.
4. Fill in the blanks
a) ( 125 ) = ___________.
b) The point ( 0 , 7 ) _________ on the graph of 7x + y = 7.
c) The graph of equations x = 4 and x = 0 has _______ points in common.
d) _________ many points can be drawn through a point.
e) The quadrilateral with only one pair of parallel sides is called a _________.
Section B
5. Express 0. 324 as a fraction in simplest form.
6. Simplify ( 5 + √𝟕) ( 2 + √√𝟓).
7. Lines PQ and RS intersect each other at point O. If ∠𝐏𝐎𝐑 : ∠𝐑𝐎𝐐 = 5 : 7. Find all angles.
8. The supplement of an angle is six times its complement . What is the measure of this angle.
Or
Find the angle which is four times its complement.
9. ABC is a right angled triangle in which ∠𝐀 = 900 and AB = AC. Find ∠𝐁 and ∠𝐂.
10. ABCD is a rectangle . Diagonals AC and BD intersect each other at point O. If ∠𝐁𝐎𝐂 = 500
then find ∠𝐎𝐀𝐃.
Section C
11. Find the values of a and b
5-√6 =a-b√6
5+√6
12. Without plotting the given points on graph paper indicate the quadrants in which the given
points lie.
(I) Ordinate = 6 , abscissa = - 3 (ii) ordinate = - 6 , abscissa = 4
(iii) ordinate = 3 , abscissa = 5.
13. Write three solutions of the equation 2x + y = 7.
Or
Find the value of k if x = 2 , y = 1 is a solution of the equation 2x + 3y = k.
14. POQ is a line . Ray OR is perpendicular to line PQ. OS is another ray lying between rays
OP and OR . Prove that ∠𝐑𝐎𝐒 = 1/2 ( ∠𝐐𝐎𝐒 - ∠𝐏𝐎𝐒 ).
15. AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that
(I) AD bisects BC
(ii) AD bisects ∠𝐀.
Or
In an isosceles triangle ABC with AB = AC, D and E are the points on BC
such that BE = CD. Show that AD = AE.
16. Prove that “ Angles opposite to equal sides of an isosceles triangle are equal”.
17. The sides of a triangular park are in ratio of 3 : 5 : 7 and its perimeter is 300m. Find its area.
18. Find the area of the triangle whose sides are of length 36cm, 48cm and 60cm. Also find the
height corresponding to the longest side.
SECTION D
19. Ray OS stands on a line POQ. Ray OR and OT are angle bisectors of ∠𝐏𝐎𝐒 and ∠𝐒𝐎𝐐
respectively . If ∠𝐏𝐎𝐒 = x , find ∠𝐑𝐎𝐓.
20. AB is a line segment . P and Q are points on opposite sides of AB such that each of them
is equidistant from the points A and B . Show that the line PQ is perpendicular bisector of AB.
21. Show that the diagonals of a square are equal and bisect each other at right angles.
Or
Show that the line segments joining the mid points of the opposite sides of a quadrilateral
bisect each other.
22. ABCD is a rhombus and P , Q , R , S are the mid points of the sides AB , BC , CD and DA
respectively. Show that the quadrilateral PQRS is a rectangle.
Case Study
23. If the temperature of a liquid can be measured in Kelvin units as x0k or in Fahrenheit units
as y0F , the relation between the two systems of measurements of temperature is given by the
linear equation
𝟗
y = 𝟓 ( ( x - 273) + 32
(i) Find the temperature of the liquid in Fahrenheit if the temperature of the liquid is 313 0k.
(ii) If the temperature is 1580F , then find the temperature in kelvin.
24. There is a triangular children park with sides AB = 7m , BC = 8m and Ac = 5m. AD is
perpendicular to BC, D lying on BC. Trees are planted at A, B, C, D.
(i) Find the area of the park.
(ii) Find the distance between the trees at A and D.