KENDRIYA VIDYALAYA, H.V.F., AVADI 2014-2015
CLASS-IX
HOLIDAY HOMEWORK- MATHEMATICS
PART-A MCQ:
1.Which of the following represent a line parallel to y-axis?
(a) x-y=7 (b) 2x+3y=13
(c) x+5=0
(d)3y-3=2y+2
2.The solution of a linear equation 3x-y=2 is
(a) (1,3)
(b) (3,-1)
(c) (1,1)
(d) (-1,-1)
3. The equation of x axis is
(a) x=0
(b) y=0
(c) x+y=0
(d) x=y
4. Which of the following is not true for a parallelogram?
(a) Opposite sides are equal.
(b) Opposite angles are equal.
(c) Diagonals bisect each other.
(d) Opposite angles are bisected by diagonals.
5. Which of the following statement is correct?
(a) a trapezium is a parallelogram.
(b) every rectangle is a parallelogram.
(c) every parallelogram is a rectangle.
(d) every rhombus is a square.
6. In the figure ‫ ے‬AOB = 100º and ‫ے‬ABC = 25º, then ‫ے‬CAB = ?
(a) 50º
(b) 75º
(c) 105º
(d) 125º
7. A median of a triangle divides it into two
(a) Isosceles triangle
(b) Congruent triangles.
(c) Triangles of equal area. (d) Right triangles
8. D and E are the midpoints of the sides AB and AC respectively of triangle ABC. If
BC=10cm then the measure of DE is
(a) 6cm
(b) 4cm
(c) 5cm
(d) 3cm
9. Given ar(∆ ABC) = 48
. AD is a median of triangle ABC and BE is a median of triangle
ABD. Then ar(∆ ABE) is
(a) 24
(b) 12
(c) 6
(d 3
10. The number of circles which can be drawn through three non collinear points are
(a)1
(b) 2
(c) infinte (d) none of these
PART-B
1. If the point (4,-6) lies on the graph of 5x-ay+4=0, find the value of a.
2. Express the equation 5x= – 9y in the form of ax+by+c=0 and indicate the values of
a,b and c.
3. In triangle ABC, median AM is produced to D such that AM=MD. Prove that ABDC is a
parallelogram.
4. The angles of a quadrilateral are in the ratio 3:4:6:7, find all the four angles of a quadrilateral.
5. The area of a parallelogram is 338cm2. If its base is twice the corresponding altitude,
determine the base and altitude.
7. If the diagonals of a parallelogram are equal then show that it is a rectangle.
8. Find the length of the chord of a circle, of radius 13 cm, at a distance of 5 cm from the centre.
9. In the figure 1, O is the centre of the circle. QS=SR and ‫ے‬SQR=25º. Find ‫ے‬QPR.
Figure 1
Figure 2
Figure 3
10. In the fig 2, ‫ے‬ACB=59º and ‫ے‬DBA=35º. Find ‫ے‬DAB.
11. In the fig 3, O is the centre of the circle. If ‫ے‬PAO=15º and ‫ے‬PBO=20º, then find ‫ے‬AOB.
12. Solve the equation 2y+1=y –3 and represent the solution on
(i) the number line
(ii) the Cartesian plane
13. In the fig. PM and RN are respectively the
bisectors of the opposite angles P and R
of a parallelogram PQRS. Show that
PM || NR
14. ABCD is a rhombus and P,Q,R,S are mid points of the sides AB,BC,CD and DA
respectively. Show that the quadrilateral PQRS is a rectangle.
15. In the fig 1, CD || AO || TG. Prove that
ar(COT)=ar(DAG).
fig 1
fig 2
16. In the fig 2, AB || DC. Show that ar(BDE) = ar(ACED).
17. In the fig 3, AD and BE are medians of ∆ ABC and BE || DF. Prove that CF= AC
18. Prove that equal chords of a circle subtend equal angles at
the centre.
19. Draw the graph of the equation x-2y=3. From the graph find
the coordinates of the point when (i) x = -5
(ii) y = 0
20. Draw the graph of 2x +y =7. Write the points where the line
meets x and y axes.
21. Prove that a diagonal of a parallelogram divides it into two congruent triangles.
22. Construct a triangle a ABC in which BC=7 cm, ‫ے‬B=75º and AB+AC=12 cm.
23. In the figure P is a point in the interior of a parallelogram ABCD. Show that
(i) ar(APB) + ar(PCD) =
ar(ABCD)
(ii) ar(APD) + ar(PBC) = ar(APB) + ar(PCD)
(Hint: Through P, draw a line parallel to AB)
fig 3
24. Prove that the angle subtended by an arc at the centre is double the angle subtended by it at
any point on the remaining part of the circle.
25. Construct a triangle PQR in which
º, ‫ے‬R=75º and its perimeter is 11cm. Write the
steps of construction.
26. Construct a triangle ABC in which BC=5 cm, ‫ے‬C = 60º and AC-AB=1.5 cm.
27. Construct a right triangle ABC, right angled at B, in which BC= 4 cm and AC+AB= 8 cm.
28. Draw the graph of the linear equation 5x–2y=10. At what points, the line cuts the x-axis and
the y-axis.
29. PQ is a line parallel to side BC of a triangle ABC. If BE || AC and CF || AB meet PQ at E and
F respectively, show that ar(ABE)=ar(ACF).
30. If two intersecting chords of a circle make equal angles with the diameter passing through
their point of intersection, prove that the chords are equal.
31. Construct a triangle ABC in which ‫ے‬A=60º, ‫ے‬B=90º and AB+BC+CA=13cm.
32. ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ‫ے‬DBC=55º and
‫ے‬BAC= 45º, Find ‫ے‬BCD.
33. Draw the graph of the equation 5y = 3x+18. From the graph check whether (-2,4) is the
solution of the linear equation or not.
34. Show that if the diagonals of a quadrilateral bisect each other at right angles then it is a
rhombus
35. Diagonal AC of a parallelogram ABCD bisects ‫ے‬A. Show that
(i) it bisects ‫ے‬C also.
(ii) ABCD is a rhombus.
36. Show that the diagonals of a square are equal and perpendicular to each other.
37. Prove that each angle of a rectangle is a right angle.
38. Prove that parallelograms on the same base and between the same parallels are equal in area.
Figure 1
Figure 2
39. In the fig 1, O is the centre of the circle with radius 5 cm. OP ┴ AB , OQ ┴ CD, AB║CD,
AB=6 cm and CD=8 cm. Determine PQ.
40. In the fig 2, PS=SR, ‫ے‬RPS=54º and ‫ے‬PRQ=26º. Calculate
(i) ‫ے‬TQR
(ii) ‫ے‬RTQ