CBSE Mathematics Sample Papers for Class 10

The Central Board of Secondary Education have released the Sample paper for Mathematics for class 10th students. This CBSE Sample paper will definitely help Class 10th CBSE students to prepare their mathematics papers in a right manner & will give them the idea of the questions going to be asked in March 2018 CBSE board examination.

For more CBSE sample papers & practice material along with the solutions, visit HERE.

NOTE - These Sample papers have been released by the CBSE Board to help students for March 2018 board exam.

General Instructions :

• All questions are compulsory.
• The question paper consists of 31 questions divided into four sections - A, B, C and D.
• Section A contains 4 questions of 1 mark each. Section B contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each and Section D contains 11 questions of 4 marks each.
• Use of calculators is not permitted.

SECTION A

Question numbers 1 to 4 carry 1 mark each.

1. What is the common difference of an A.P. in which a₂₁ - a₇ = 84 ?
2. If the angle between two tangents drawn from an external point P to a circle of radius a and centre O, is 60°, then find the length of OP.
3. If a tower 30 m high, casts a shadow 10√3 m long on the ground, then what is the angle of elevation of the sun ?
4. The probability of selecting a rotten apple randomly from a heap of 900 apples is 0·18. What is the number of rotten apples in the heap ?

SECTION B

Question numbers 5 to 10 carry 2 marks each.

5. Find the value of p, for which one root of the quadratic equation px² - 14x + 8 = 0 is 6 times the other.
6. Which term of the progression 20, 19*1∕4, 18*1∕2, 17*3∕4, ... is the first negative term ?
7. Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord.
8. A circle touches all the four sides of a quadrilateral ABCD. Prove that
   AB + CD = BC + DA
9. A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, -5) is the mid-point of PQ, then find the coordinates of P and Q
10. If the distances of P(x, y) from A(5, 1) and B(-1, 5) are equal, then prove that 3x = 2y.

SECTION C

Question numbers 11 to 20 carry 3 marks each.





If a∦bc, then prove that the equation
(a² + b²) x² + 2 (ac + bd) x + (c² + d²) = 0 has no real roots.
The first term of an A.P. is 5, the last term is 45 and the sum of all its terms is 400. Find the number of terms and the common difference of the A.P.
On a straight line passing through the foot of a tower, two points C and D are at distances of 4 m and 16 m from the foot respectively. If the angles of elevation from C and D of the top of the tower are complementary, then find the height of the tower.
A bag contains 15 white and some black balls. If the probability of drawing a black ball from the bag is thrice that of drawing a white ball, find the number of black balls in the bag.
 In what ratio does the point (24/11, y) the line segment joining the points P(2, -2) and Q(3, 7) ? Also find the value of y.
Three semicircles each of diameter 3 cm, a circle of diameter 4·5 cm and a semicircle of radius 4·5 cm are drawn in the given figure. Find the area of the shaded region.
 
In the given figure, two concentric circles with centre O have radii 21 cm and 42 cm. If ∠AOB = 60° , find the area of the shaded region. [ Use π = 22/7 ]

Water in a canal, 5·4 m wide and 1·8 m deep, is flowing with a speed of 25 km/hour. How much area can it irrigate in 40 minutes, if 10 cm of standing water is required for irrigation ?
The slant height of a frustum of a cone is 4 cm and the perimeters of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum.
The dimensions of a solid iron cuboid are 4·4 m * 2·6 m * 1·0 m. It is melted and recast into a hollow cylindrical pipe of 30 cm inner radius and thickness 5 cm. Find the length of the pipe.


SECTION D
Question numbers 21 to 31 carry 4 marks each.





Solve for x :

Two taps running together can fill a tank in 3*1/13 hours. If one tap takes 3 hours more than the other to fill the tank, then how much time will each tap take to fill the tank ?
If the ratio of the sum of the first n terms of two A.Ps is (7n + 1) : (4n + 27), then find the ratio of their 9th terms.
Prove that the lengths of two tangents drawn from an external point to a circle are equal.
In the given figure, XY and X′Y′ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C, is intersecting XY at A and X′Y′ at B. Prove that∠AOB = 90°.

 Construct a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠ A = 105°. Then construct another triangle whose sides are 3/4 times the corresponding sides of the △ ABC.
An aeroplane is flying at a height of 300 m above the ground. Flying at this height, the angles of depression from the aeroplane of two points on both banks of a river in opposite directions are 45° and 60° respectively. Find the width of the river. [Use √3 = 1·732]
If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k - 1, 5k) are collinear, then find the value of k.
Two different dice are thrown together. Find the probability that the numbers obtained have


•  even sum, and
• even product.





 In the given figure, ABCD is a rectangle of dimensions 21 cm * 14 cm. A semicircle is drawn with BC as diameter. Find the area and the perimeter of the shaded region in the figure.

In a rain-water harvesting system, the rain-water from a roof of 22 m * 20 m drains into a cylindrical tank having diameter of base 2 m and height 3·5 m. If the tank is full, find the rainfall in cm. Write your views on water conservation.

CBSE Help Books-The Perfect Reference Source for Students

The CBSE syllabus tends to change periodically from year to year. But one problem which is often faced by students of CBSE schools is that they lack clarity of certain concepts of chapters of individual subjects. Therefore, they look for reference books which discuss all concepts and principles with clarity. In recent times, publishing houses have come up with CBSE support books of different subjects.

Here are some of the major ways in which these support books can be of great help to students:-

Content developed according to the newest syllabus

The content of the reference books for CBSE boards which have been launched in the market is according to the latest CBSE syllabus. Therefore students can to a great extent get acquainted with the main concepts of each subject. These books can therefore help them to create a clear idea of all the subjects which are taught at school. Therefore they can perform much better way in their exams at school and also in board exams.

The CBSE help books have been developed by subject matter experts who have years of experience in writing books in subjects of their expertise. They are well aware of the questioning pattern of the CBSE board and have developed the contents according. The students therefore will have a good knowhow of all those areas where they had doubts before they came across before consulting these books.

Students get to know short cuts 

For certain subjects such as Maths, there are several ways through which a sum can be solved. However, sometimes students fail to answer their entire question paper because of the lack of time. Therefore, a number of publishing houses have come up with CBSE help books & guides with short cuts which help students to save an ample amount of their time. Their skills in solving complex sums within minimum amount of time will also develop within a considerably short period of time.

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One common problem which students of CBSE board often face is that certain parts of a chapter are often inadequately covered. Using the reference books, they can be sure that they have a clear understanding of those sections and can answer questions based on them clearly. Using the cbsesample papers along with text books will help them to prepare for their exams in a better manner. Their grades will also show considerable improvement as a result.