#### First Term - Full Portion Test

9th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 65

Part-A

5 x 1 = 5
1. if $\frac { 1 }{ 7 }$ = $0.\bar { 142857 }$ then the value of $\frac { 5 }{ 7 }$

(a)

$0.\overline { 142857 }$

(b)

$0.\overline { 714285 }$

(c)

$0.\overline { 571428 }$

(d)

0.714285

2. Find the odd one out of the following

(a)

$\sqrt { 32 } \times \sqrt { 2 }$

(b)

$\frac { \sqrt { 27 } }{ \sqrt { 3 } }$

(c)

$\sqrt { 72 } \times \sqrt { 8 }$

(d)

$\frac { \sqrt { 54 } }{ \sqrt { 18 } }$

3. It is not possible to construct a triangle when its sides are

(a)

8.2 cm, 3.5 cm, 6.5 cm

(b)

6.3 cm, 3.1 cm, 3.2 cm

(c)

7 cm, 8 cm, 10 cm

(d)

4 cm, 6 cm, 6 cm

4. Point (–3,5) lie in the ________ quadrant

(a)

I

(b)

II

(c)

III

(d)

IV

5. Point (0, –7) lies ________________________________

(a)

on the x-axis

(b)

(c)

on the y-axis

(d)

6. Part - B

8 x 2 = 16
7. Insert the appropriate symbol $\subseteq$ or $\nsubseteq$ in each blank to make a true statement.
{p, q, r} _____ {w, x, y, z}

8. If A={1, 2, 6} and B={2, 3, 4} , find A∪B.

9. Let U= {x : -3 : << 4} A = {-1,2,3} B = {0,1,2,3} C = {-3;-2,-1,0,1,2}. Find (i) A' UB' (ii) (A ∩ B)' (iii) (A ⋂ C)'

10. Express the following in the form  ${p\over q},$  where p and q are integers and q $\ne$ 0.
$0.5\overline {7}$

11. Find the value of x

12. Which ones are not quadrilaterals?

13. Procedure: Cut off a quadrilateral ABCD in a paper with prescribed dimensions. Mark the mid points P, Q, R and S of the sides AB, BC, CD and DA respectively. By folding the sides appropriately cut off the quadrilateral PQRS. Fold the quadrilateral (i) Does PQ lie on SR? similarly fold the other way and verify QR lies on PS.
Observation
(i) What do you conclude?
(ii) Name the resulting figure?
Draw the following quadrilaterals and join the mid points of all its sides. Find the resultant shape and complete the table.

 Name of the quadrilateral Shape obtained by joining the midpoints Parallelogram Rectangle Square Kite Trapezium Rhombus
14. In which quadrant does the following points lie?(–1,–3)

15. Part-C

7 x 3 = 21
16. Represent $\sqrt { 9.3 }$ on a number line

17. Identify monomials, binomials and trinomial from the following expression.
(i) -8 abc
(ii) 3a2bc+8-9a2
(iii) -9
(iv) a2+b2+c2-k2
(v) a+b
(vi) 7ab3
(vii) -z+$\sqrt{3}$z3

18. Your friend draws a figure such as this on a piece of paper.
You don't know what it is, and stand at the board. She has to describe the figure to you so that you draw exactly the same figure on the board.
You both know rectangles, so it is easy to describe and draw a rectangle. The rest are not easy.
Can we describe any such shape we can ever think of, in a way that another person
hearing it can reproduce it exactly?
Yes, yes, yes! Now, isn't that exciting? The answer is so simple that it is breathtaking.
We describe different shapes by their properties.

19. Take three different colour sheets; place on over the other and draw a triangle on the top sheet. Cut the sheets to get triangles of different colour which are identical. Mark the vertices and the angles as shown. Place the interior angles ㄥ1, ㄥ2 and ㄥ3 on a straight line, adjacent to each other, without leaving any gap. What can you say about the total measure of the three angles ㄥ1, ㄥ2 and ㄥ3?

Can you use the same figure to explain the "Exterior angle property" of a triangle?
If a side of a triangle is stretched, the exterior angle so formed is equal to the sum of the two remote interior angles.

20. Determine whether the given set of points in each case are collinear or not (–2, –8), (2,–3) (6,2)

21. Show that the following points taken in order form an isosceles triangle A (6,–4), B (–2, –4), C (2,10)

22. Plot the following points on a graph sheet by taking the scale as 1cm = 1 unit.
Find how far the points are from each other?
A (1,0) and D (4, 0). Find AD and also DA.
You plot another set of points and verify your Result.

23. Part-D

4 x 5 = 20
24. Consider the ten real numbers
$\sqrt { 2 } ,\frac { 7 }{ 9 }$,-1.32,$\frac { 6 }{ 9 } ,-\sqrt { 3 }$ , 2.151155 .....,$\frac { 23 }{ 6 } ,\frac { 48 }{ 5 }$, -3.010010001... and 12.353553555.
(i) Arrange the ten real numbers in the given boxes in ascending order.

(ii) Arrange the same numbers in the boxes given below in descending order

25. Classify the following polynomials based on their degree.

26. Without actual division , prove that f(x) = 2x4-6x3+3x2+3x-2  is exactly divisible by x2 –3x + 2

27. Plot the points A( 1, 0), B ( -7, 2), C (-3, 7) on a graph sheet and join them to form a triangle.
Plot the point G ( -3, 3).
Join AG and extend it to intersect BC at D.
Join BG and extend it to intersect AC at E.
What do you infer when you measure the distance between BD and DC and the distance between CE and EA?
Using distance formula find the lengths of CG and GF, where F in on AB.

28. Part-E

3 x 1 = 3
29. 7x - 5y + 3 has __________ terms

()

3

30. A rhombus is a quadrilateral with _____ of equal length

()

sides

31. A square has sides of equal length and angles of equal measures, so it is not a ______ polygon.

()

regular