Download Class : IX (2016-17) - Adharsheela Global School

ADHARSHEELA GLOBAL SCHOOL
QUESTION BANK (TERM – I)
Class : IX (2016-17)
Chapter- Number Systems
1. Identify a rational number among the following numbers :
2. Simplify :
25
,
6
20
, 2.27 , 2. 3
4
8 √3 – 2 √3 + 4 √3
3. Express 0.2353535… in the form of
p
, where p and q are integers and q  0 .
q
4. If a = √3 - √2 and b = √3 + √2 , find the value of a2 + b2 – 5ab.
√3 + √2
√3 - √2
5. Find the value of : √1089 - 660 .
√400
400
6. Add: (2 √2 + 5 √3) and (√2 – 3 √3) . Is the sum a rational number or an irrational number ?
7. Simplify : 271/3 [ 271/3 – 272/3]
8. If a = 1 - √7 and b = 1 + √7, then find the value of a2 + ab + b2 .
1 + √7
1 - √7
a2 – ab + b2
Chapter- Polynomials
2
1. Prove that x + 6x + 15 has no zero.
2. If the polynomials px3 + 4x2 + 3x - 4 and x3 - 4x + p are divided by x - 3, then the remainder in each case is
the same. Find the value of p.
3. Factorise : x3 - 6x2 + 11x - 6
4. If (2x - 5) is a factor 2x3 - 3x2 - 17x + 30, then find its other factors.
a
5. If 3a – 1 = 9 and 4b + 2 = 64, find the value of .
b
6. Write the zeroes of the polynomial : x2x(2 + x).
7. Factorise : 3x2 + 10x + 3
8. Prove that:
a-1
+
-1
-1
a +b
a-1
a-1 -
=
b-1
2b2
.
2
–a .
b2
9. Find the value of x3 - y3 - 18xy - 216, when x – y = 6
10. If ab + c0, then prove that a4b4c42(b2c2c2a2a2b2)
11. Find the value of k, if (x – 3) is a factor of p(x) = 2x3 - 5x2 + 3x + k.
12. Divide polynomial p(x) = x44x34x23x + 4 by q(x) = x – 1 and find what should be added in
p(x) so that it is divisible by q(x).
Chapter- Coordinate Geometry
1. Plot two points A(0, 4) and B(4, 0)on the graph paper. Now, plot point C so that OBCA is a square. Draw
diagonals and write the coordinates of the point of intersection of the diagonals.
2. In the figure, the co-ordinates of certain vertices are missing. Find them.
3. In which quadrants the points A (3, 4) and B ( –2 , – 1 ) lie ?
4. Write the distance of point C(- 2, - 4) from x-axis.
5. Which of the following pairs of points determine a line parallel to x-axis ?
6. (i)
(iii)
(4, 5) and (10, 5)
(ii)
 1 2 , 1 3 and  2, 1 3
(8, 0) and (8, 5)
(iv)
(5, 8) and (5, 5)
Chapter- Triangles
1. In figure ABAC. D is a point in the interior of ABC such that angle DBC= angle DCB. Prove that AD bisects
angle BAC.
2. In figure AB || CD and O is midpoint of AD. Show that O is midpoint of BC.
3. Prove that two triangle are congruent if two angles and the included side of one triangle is equal to two
angles and the included side of the other triangle.
4. In figure, in ABC, AE is bisector of BAC and ADBC. Show that DAE =
1
(C +B).
2
5. In an isosceles triangle ABC, if AB = AC and AP  BC, then prove that BAP = CAP.
6. Prove that “angles opposite to equal sides of an isosceles triangle are equal”.
7. ABCD is a square and BX = BY prove that :
(i) DCX DAY (ii)
DY = DX(iii) DXC = DYA
8. In two right angled triangles, one side and acute angle of one triangle are equal to one side and the
corresponding acute angle of the other triangle, prove that the two triangles are congruent.
9. E and F are respectively the mid-points of equal sides AB and AC of ABC. Show that BF = CE.
10. In ABC, BD and CD are internal bisector of  B and  C respectively. Prove that 180y = 2x.
11. In the figure, ABC and DBC are two isosceles triangles on the same base BC. Prove that ABD = ACD.
Heron’s Formula
1. Suman has a piece of land, which is in the shape of a rhombus. She wants her two sons to work on
the land and produce different crops. She divides the land in two equal parts by drawing a
diagonal. If its perimeter is 400 m and one of the diagonals is of length 120 m, how much area each
of them will get for his crops ?
2. Length of a rectangular field is 15 m and diagonal is of length 17 m. Find its area and the perimeter.
3. A park is in the shape of a quadrilateral ABCD in which AB  9 m,
BC 12 m, CD = 5 m, AD = 8 m and C 90. Find the area of the park.
4. The sides of a triangle are in the ratio 3 : 4 : 5. If perimeter of the triangle is 360 m, find its area using
Heron’s formula.
5. In the given figure, ABCD is rectangle in which AB= 8 cm, BC = 6 cm and the diagonals intersect each other at
O. Find the area of the shaded region by using Heron’s formula.
Lines & Angles
1. Is triangle ABC possible, if A = 600, B = 80o and C = 40o ?
2. In the given figure; if 1=3, 2=4 and 3=4, write the relation between 1 and 2 by using an Euclid’s
axiom. Write the axiom.
3. In given fig, two lines AB and CD intersect each other at a point E. Find the values of x, y, z.
4. In given figure, GM and HL are bisectors of AGH and GHD respectively, such that GM || HL. Show that
AB ||CD.
5. As shown in figure, three towns form a triangle on a map. The angle formed at the point designating A is 48 o,
at B 60o, and at C 72o. Which distance among AB, BC and AC is largest and why ?
Govind is travelling from Place A to B to C. He asked driver to use CNG gas instead of Petrol and diesel. Why
do you think he opted for CNG ? What value is he showing by doing so?
6. A transversal l intersects two lines m and n such that a pair of alternate interior angles is equal.
Then, what can you say about the lines m and n ?
7. Consider two postulates given below :
(i) Given any two distinct points R and S, there exists a third point T which is in between R and S.
(ii) There exist at least three points which are not in the same straight line and answer the
following questions :
(a) Do these postulates contain any undefined terms ?
(b) Do they follow from Euclid’s postulates ? Explain.
8. If a transversal intersects two parallel lines, then prove that bisectors of alternate interior angles are
parallel.
9. In the figure, if AB||CD, EFCD, find AGE, GEF and CFE.
10. In figure AB = AD,  1 = 2 and  3 = 4. Prove that AP = AQ.