# Sample Paper for Class 9 Maths

Class IX develops your basics and prepares you for competitive examinations. If your basics of maths aren’t clear and strong, you would struggle a lot in higher classes. Maths requires consistent practice for improvement.  Solving sample paper for class 9 is the best way to practice maths. It provides you variety of questions and improves your speed. NTSEGURU faculties have developed incredible cbse class 9 maths sample paper for the students to practice from. You can access all the sample papers, NCERT solutions, examination files and a lot more in study material section of NTSEGuru.

Meanwhile, here’s a sample question paper of class 9 maths by NTSE Guru you can practice from.

## Sample Question Paper Class 9 Maths

MATHEMATICS

IX – EXAM ZONE – 01

GENERAL INSTRUCTION

1.    All Questions arc compulsory to attempt.

2.    The questions paper consists of 30 questions divided into four sections A, B. C and D.

3.    Section A comprises 6 questions of I mark each. Section B comprises 6 questions of 2 marks each. Section C comprises 10 questions of 3 marks each. Section D comprises 8 questions of 4 marks each.

4.    There is no overall choice. However, an internal choice has been provided in two questions of 1 mark each, two questions of 2 marks each, four questions of 3 marks each and three questions of 4 mark each. You have to attempt only one of the alternatives in all such questions.

5.    Use of calculators is not permitted.

SYLLABUS & MARKING SCHEME:

 Unit No. Unit Marks I Number system 10 II Algebra 13 III Co-ordinate geometry 04 IV Geometry 35 V Mensuration 08 VI Statistics and Probability 10 Total 80

SECTION – A

1.    Evaluate ${{(125)}^{1/3}}$.   [1]

OR

If $\left(&space;\sqrt{15-x\sqrt{14}}&space;\right)=\sqrt{8}-\sqrt{7},$ then find the value of x.

2.    Write the degree of polynomial $({{x}^{2}}+x+1)({{x}^{2}}+1)$.     [1]

OR

Factorize: ${{a}^{3}}-{{b}^{3}}+1+3ab$.

3.    If the co-ordinate of two points are P (- 2.3) and Q (- 3,5) then (abscissa of P) – (abscissa of Q) is.  [1]

4.    Euclid divided his book “Elements” into how many chapter.  [1]

5.    A die is thrown once. Find the probability of getting a prime number.  [1]

6.    Find the curved surface area of a right circular cone, whose slant height is 25 cm and the radius of the base is 7 cm.  [1]

SECTION – B

7.     Represent $\sqrt{5}$ on number line.

OR

Evaluate: ${{2}^{55}}\times&space;{{2}^{60}}-{{2}^{97}}\times&space;{{2}^{18}}$

8.    Find the value of k, if (x – 1) is a factor of $4{{x}^{3}}+3{{x}^{2}}-4x+k$.
9.    If diagonal AC of a quadrilateral ABCD bisect $\angle&space;A$ and $\angle&space;C$. prove that AB = AD and CB = CD.  [2]

OR

If the diagonal of a parallelogram are equal, then show that it is a rectangle.

10.    The semi-peri meter of a triangle i> 96 cm and its side are in the ratio of 3 : 4 : 5. Find the area of triangle.  [2]

11.    For what value of x. the mode of the following data is 13.       [2]

(13, 24, 13, 27, 17, 16, 17, x, 22, 21, 13, 17)

12.    Prove that the bisector of pair of vertically opposite angle’s are in the same straight line.

SECTION – C

13.    Simplify: $\frac{2\sqrt{3}-\sqrt{2}}{2\sqrt{2}+3\sqrt{3}}$ by retionolizing the denominator.

OR

If $x=\frac{1}{2}\left(&space;\sqrt{a}+\frac{1}{\sqrt{a}}&space;\right),$ then show that $\frac{\sqrt{{{x}^{2}}-1}}{x-\sqrt{{{x}^{2}}-1}}\,=\frac{a-1}{2}$.

14.    Factorize:${{x}^{3}}+13{{x}^{2}}+31x-45$.             [3]

15.    Find the value of k. if x = 2k – 1 and y = k is a solution of the equation $3x-5y-7=0$.    [3]

OR

If $x+y+z=0,$ then show that ${{x}^{3}}+{{y}^{3}}+{{z}^{3}}=3xyz$.

16.    Draw the quadrilateral with vertices (-4, 4), (-6, 0), (-4, -4) and (-2, 0). Also name the type of quadrilateral and find its area.   [3]

17.    In the figure $\angle&space;POY={{90}^{o}}$. and a : b = 2 : 3 then find value of c.    [3]

18.    A triangle and parallelogram have the same base and the same area. If the side of the triangle are 26 cm, 28 cm, and 30 cm and parallelogram stand on the base 28 cm. Find the height of the parallelogram.

OR

In the figure D and E are two points on BC such that BD = DE = EC. Show that $ar(ABD)=ar(ADE)=ar(AEC)$.

19.    Construct a triangle ABC the length of whose medians are 6 cm. 7 cm and 6 cm.  [3]

20.    A semi circular thin sheet of metal pf diameter 28 cm in bent and an open conical cup is made find the capacity of the cup.  [3]

21.    ABCD is an isosceles trapezium whose parallel sides AD and BC measure 10 cm and 25 cm respectively and AB = DC = 15 cm. find the area of trapezium.  [3]

22.    Find the mean salary of 60 worker’s of factory from the following table.  [3]

 Salary (in Rs.) No. of worker’s 3000 16 4000 12 5000 10 6000 8 7000 6 8000 4 9000 3 10000 1

OR

In a English test given to 15 student’s, the following marks (out of 100) are recorded.

41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60

Find mean, median and mode of this data.

SECTION – D (Marks – 4)

23.   If both (x – 2) and $\left(&space;x-\frac{1}{2}&space;\right)$ are factor’s of $p{{x}^{2}}+5x+r,$ show that p = r.

24.    Prove that $\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+....+\frac{1}{\sqrt{8}+\sqrt{9}}=2$

OR

A library take charge of 5 for issue a book for one day and 1 per day thereafter. If Ritu had taken 2 book for x day’s and y be the total amount’s need to be paid, write the linear equation in two variable’s for this situation. Plot its graph and find the amount to be paid for 5 day’s.

25.    The image of an object placed at a point A before a plane mirror LM is seen at the point B by an observer at D as shown in fig. Prove that the image is as far behind the mirror as the object is in front of the mirror.    [4]

26.    Prove that the line segment joining the midpoint’s of the diagonal of a trapezium are parallel to each of the parallel side and is equal to half the difference of these side.

OR

A circular park of radius 20 m is situated in a colony, three boy’s Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hand’s to talk each other, find the length of the string of each phone.

27.    P and Q are respectively the mid points of sides AB and BC of a triangle ABC and R is the midpoint of AP, show that.

(i) $ar\left(&space;PQR&space;\right)=\frac{1}{2}ar\left(&space;ARC&space;\right)$

(ii) $ar(RQC)=\frac{3}{8}ar(ABC)$

(iii) $ar(PBQ)=ar(ARC)$

28.    AC and BD are chord’s of a circle which bisect each other, prove that  [4]

(i) AC and BD are diameter’s

(ii) ABCD is a rectangle

29.    The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm3 of wood has a mass of 0.6 g  [4]

OR

A hollow sphere of internal and external diameter 4 cm and 88 cm respectively in melted into a shape of cylinder of base circumference 8 cm. Find the height of the cylinder

30.    A random survey of the number of children of various age group’s playing in a park was found as follows:

 Age (in years) No. of children 1 – 2 5 2 – 3 3 3 – 5 6 5 – 7 12 7 – 10 9 10 – 15 10 15 – 17 4

Draw a histogram to represent the data above.

This CBSE class 9 maths sample paper is based on subject- Maths only. You can appear in this test before seeing the video lectures of this subject too. This will give you an idea of your current level of preparation.

After seeing the video lecture, when you appear in this test again, you can see the progress – the effect of learning on your results.