Maths Sample Paper Class 10 Term 2 Exam with Solutions

Maths Sample Paper Class 10 Term 2

CBSE Class 10  Term 2 Maths Sample Paper: CBSE has released the CBSE Class 10 Maths Sample Paper for Term 2 Exam for giving ease to the 10th class students to understand and be familiar with the new pattern to be followed. CBSE has scheduled CBSE Class 10 Maths Term 2 Exam for 05th May 2022 (Thursday) and students must prepare well for the examination. The duration of the test will be 120 minutes (2 hours) and it will cover only the rationalized syllabus of Term II only (i.e. approx. 50% of the entire syllabus). The CBSE Class 10 Maths Sample Paper 2021-22 are now available at CBSE’s academic website i.e. cbseacademic.nic.in or you can also download Class 10 Maths Term 2 Sample Papers for Basic & Standard Mathematics from the direct links provided in the article. 

Sample Paper Class 10 Term 2 Maths

The pattern for CBSE Class 10 Maths Term 2 (Basic & Standard) has been discussed along with the Class 10 Maths Sample Paper which is as follows-

For Basic Maths Syllabus- Class 10 Term 2 Basic Maths Exam will consist of 14 questions divided into 3 sections A, B, C. Section A comprises of 6 questions of 2 marks each, Section B comprises of 4 questions of 3 marks each, and Section C comprises of 4 questions of 4 marks each. 

For Standard Maths Syllabus- Class 10 Term 2 Standard Maths Exam will consist of 14 questions divided into 3 sections A, B, C. Section A comprises of 6 questions of 2 marks each, Section B comprises of 4questions of 3 marks each, and Section C comprises of 4 questions of 4 marks each. 

Maths Class 10 Term 2 Answer Key 2022- Click Here

Class 10 Maths Term 2 Sample Paper PDF

To give students a clear vision for the Class 10 Mathematics Term 2 Exam, CBSE has uploaded sample question papers for CBSE Class 10th Maths Sample Paper 2022 Term 2 (Basic & Standard) on its official website https://cbseacademic.nic.in/index.html. CBSE Class 10 Maths Term 2 Sample Paper with Solutions PDF can be downloaded directly from here along with the answer key containing detailed solutions to the Class 10 Maths Term 2 Sample Papers. 

CBSE Class 10 Term 2 Maths Syllabus-Click to Check

Maths Sample Paper Class 10 Term 2 with Solutions

Below are the questions that have been mentioned in the CBSE Class 10 Term-2 Maths Sample Paper with Solutions. 

SECTION A

Question 1- Find the roots of the quadratic equation 3x² − 7𝑥 − 6 = 0.

Solution- 3x² − 7𝑥 − 6 = 0 

⇒ 3x² − 9𝑥 + 2𝑥 − 6 = 0 

⇒ 3𝑥(𝑥 − 3) + 2(𝑥 − 3) = 0 

⇒ (𝑥 − 3)(3𝑥 + 2) = 0 

∵ 𝑥 = 3, − 2/3 

OR

Find the values of k for which the quadratic equation 3x² + 𝑘𝑥 + 3 = 0 has real and equal roots.

Solution- Since the roots are real and equal, 

∴ 𝐷 = b² − 4𝑎𝑐 = 0 

⇒ k² – 4×3×3 = 0 (∵ 𝑎 = 3, 𝑏 = 𝑘, 𝑐 = 3) 

⇒ k² = 36 

⇒ k = 6 𝑜𝑟 −6

Question 2- Three cubes each of volume 64cm³ are joined end to end to form a cuboid. Find the total surface area of the cuboid so formed?

Solution- Let 𝑙 be the side of the cube and L, B, H be the dimensions of the cuboid

Since b³ = 64cm³ ∴ 𝑙 = 4 𝑐𝑚

Total surface area of cuboid is 2[𝐿𝐵 + 𝐵𝐻 + 𝐻𝐿], Where L=12, B=4 and H=4

=2(12 × 4 + 4 × 4 + 4 × 12) cm² = 224 cm²

Question 3- An inter-house cricket match was organized by a school. The distribution of runs made by the students is given below. Find the median runs scored.

Solution- 

Total frequency (N) = 22 

𝑁/2 = 11; So 40-60 is the median class. 

Median = 𝑙 + ( 𝑁/2 )−𝑐𝑓/𝑓 × ℎ 

= 40 + 11−10/5 x 20 

= 44 runs

Question 4- Find the common difference of the AP 4,9,14,… If the first term changes to 6 and the common difference remains the same then write the new AP.

Solution- The common difference is 9 - 4=5

If the first term is 6 and the common difference is 5, 

then the new AP is, 6, 6+5, 6+10…

=6,11,16…

Question 5- The mode of the following frequency distribution is 38. Find the value of x.

Solution- ∵ Mode = 38. 

∴ The modal class is 30-40. 

Mode = 𝑙 + 𝑓1− 𝑓0 /2𝑓1−𝑓0−𝑓2 × ℎ

=30 + 16−12/ (32−12−𝑥 )x10 = 38

 4/ 20−𝑥 x 10 =8 

8(20-x) = 40 

20-x= 5 

X= 15 

Question 6- XY and MN are the tangents drawn at the endpoints of the diameter DE of the circle with centre O. Prove that XY || MN.

Solution- ∵XY is the tangent to the circle at the point D

∴ OD ⟂ XY  ⇒ ㄥODX = 90° ⇒ ㄥEDX = 90°

Also, MN is the tangent to the circle at E

∴ OE ⟂ MN ⇒ ㄥOEN = 90° ⇒  ㄥDEN = 90°

ㄥEDX = ㄥ DEN (𝑒𝑎𝑐ℎ 90°).

which are alternate interior angles.

∴ XY ॥ MN

OR

In the given figure, a circle is inscribed in the quadrilateral ABCD. Given AB=6 cm, BC=7 cm and CD=4 cm. Find AD.

Solution- ∵Tangent segments drawn from an external point to a circle are equal 

∴ BP=BQ 

CR=CQ 

DR=DS 

AP=AS

⇒ BP+CR+DR+AP = BQ+CQ+DS+AS

⇒ AB+DC = BC+AD 

∴ AD= 10-7= 3 cm

SECTION B

Question 7- An AP 5, 8, 11…has 40 terms. Find the last term. Also find the sum of the last 10 terms.

Solution- First Term of the AP(a) = 5

Common difference (d) = 8-5=3

Last term =  a40 = a+(40-1) d

= 5 + 39 × 3 = 122

Also 𝑎31 = 𝑎 + 30𝑑 = 5 + 30 × 3 = 95

Sum of last 10 terms = 𝑛/2 (𝑎31 + 𝑎40)

= 10/2 (95 + 122)

= 5 × 217 = 1085

Question 8- A tree is broken due to the storm in such a way that the top of the tree touches the ground and makes an angle of 30° with the ground. The length of the broken upper part of the tree is 8 meters. Find the height of the tree before it was broken.

Solution- Let, AB be the tree broken at C, 

Also let 𝐴𝐶 = 𝑥 

In ∆ CAD, sin30° = 𝐴𝐶 𝐷𝐶 

⇒ 1/2 = 𝑥/8 ⇒ 𝑥 = 4 𝑚 

⇒ the length of the tree is = 8+4 =12m

OR

Two poles of equal height are standing opposite each other on either side of the road 80m wide. From a point between them on the road the angles of elevation of the top of the two poles are respectively 60° and 30° . Find the distance of the point from the two poles.

Solution- Let AB and CD be two poles of height h meters also let P be a point between them on the road which is x meters away from foot of first pole AB, PD= (80-x) meters.

In ∆ABP, 𝑡𝑎𝑛60° = ℎ/𝑥 ⇒ ℎ = 𝑥√3       .…(1)

In ∆CDP, 𝑡𝑎𝑛 30° = ℎ/80−𝑥 ⇒ ℎ =80−𝑥/√3    ….(2)

𝑥√3 = 80 − 𝑥/√3 [∵ 𝐿𝐻𝑆(1) = 𝐿𝐻𝑆(2), 𝑠𝑜 𝑒𝑞𝑢𝑎𝑡𝑖𝑛𝑔 𝑅𝐻𝑆]

⇒ 3𝑥 = 80 − 𝑥 ⇒ 4𝑥 = 80 ⇒ 𝑥 = 20𝑚

So, 80 − 𝑥 = 80 − 20 = 60𝑚

Hence the point is 20m from one pole and 60 meters from the other pole.

Question 9- PA and PB are the tangents drawn to a circle with centre O. If PA= 6 cm and ∠APB=60° , then find the length of the chord AB.

Solution- PA = PB (Tangent segments drawn to a circle from an external point are equal)

∴ In ∆𝐴𝑃𝐵, ㄥPAB = ㄥPBA

Also, ㄥAPB = 60°

In ∆𝐴𝑃𝐵, sum of three angles is 180°

Therefore, ㄥPAB + ㄥPBA = 180°

∴ ㄥAPB= 180° – 60° = 120°

ㄥPAB = ㄥPBA = 60°(∴ ㄥPAB = ㄥPBA)

∵ ∆𝐴𝑃𝐵 is an equilateral triangle.

So, 𝐴𝐵 = 6cm

Question 10- The sum of the squares of three positive numbers that are consecutive multiples of 5 is 725. Find the three numbers.

Solution- Let the three consecutive multiples of 5 be 5x, 5x+5, 5x+10.

Their squares are (5𝑥)², (5𝑥 + 5)² and(5𝑥 + 10)²

(5𝑥)²+ (5𝑥 + 5)²+ (5𝑥 + 10)²= 725

⇒25𝑥²+ 25𝑥²+ 50x + 25 + 25𝑥²+ 100x + 100 = 725

⇒ 75𝑥²+ 150𝑥 − 600 = 0

⇒ 𝑥² + 2𝑥 − 8 = 0

⇒ (𝑥 + 4)(𝑥 − 2) = 0

⇒ 𝑥 = −4, 2

⇒ 𝑥 = 2 (ignoring –ve value)

So the numbers are 10, 15 and 20

Question 11- Construct two concentric circles of radii 3cm and 7cm. Draw two tangents to the smaller circle from a point P which lies on the bigger circle.

Solution- Draw two concentric circles with centre O and radii 3 cm and 7 cm respectively. 

⇒Join OP and bisect it at 𝑂 ′, so 𝑃𝑂′ = 𝑂 ′𝑂 

⇒Construct circle with centre 𝑂 ′ and radius 𝑂 ′𝑂 

⇒Join PA and PB

OR

Draw a pair of tangents to a circle of radius 6cm which are inclined to each other at an angle of 60° . Also, find the length of the tangent.

Solution- Draw a circle of radius 6cm 

⇒Draw OA and Construct ∠ 𝐴𝑂𝐵 = 120° 

⇒Draw ∠ 𝑂𝐴𝑃 = ∠ 𝑂𝐵𝑃 = 90° 

⇒PA and PB are required tangents 

⇒Join OP and apply tan∠𝐴𝑃𝑂 = tan 30° = 6 𝑃𝐴 ⇒ Length of tangent = 6√3 cm

Question 12- The following age-wise chart of 300 passengers flying from Delhi to Pune is prepared by the Airlines staff. Find the mean age of the passengers.

Solution- Converting the cumulative frequency table into exclusive classes, we get:

Mean age = 𝑥̅= ∑ 𝑓𝑖𝑥𝑖/ ∑ 𝑓𝑖 = 12600/300

 𝑥̅= 42 

Question 13- A lighthouse is a tall tower with light near the top. These are often built on islands, coasts or on cliffs. Lighthouses on water surface act as a navigational aid to the mariners and send warning to boats and ships for dangers. Initially wood, coal would be used as illuminators. Gradually it was replaced by candles, lanterns, electric lights. Nowadays they are run by machines and remote monitoring. Prongs Reef lighthouse of Mumbai was constructed in 1874-75. It is approximately 40 meters high and its beam can be seen at a distance of 30 kilometres. A ship and a boat are coming towards the lighthouse from opposite directions. Angles of depression of flash light from the lighthouse to the boat and the ship are 30° and 60° respectively.

i) Which of the two, the boat or the ship is nearer to the lighthouse. Find its distance from the lighthouse? 

ii) Find the time taken by the boat to reach the lighthouse if it is moving at the rate of 20 km per hour.

Solution (i) The ship is nearer to the lighthouse as its angle of depression is greater.

In ∆ ACB, tan 60° = AB/BC

⇒√3 = 40/BC

∴ BC = 40/√3 = 40√3/3 m

Solution (ii) In ∆ ADB, tan 30° = AB/BC

⇒ 1/ √3 = 40/DB

∴ DB = 40√3m

Time taken to cover this distance = ( 60/ 2000 × 40√3) minutes 

= 60√3/100 = 2.076 minutes

Question 14- Krishnanagar is a small town in the Nadia District of West Bengal. Krishnanagar clay dolls are unique in their realism and the quality of their finish. They are created by modeling coils of clay over a metal frame. The figures are painted in natural colours and their hair is made either from sheep’s wool or jute. Artisans make models starting from fruits, animals, God, goddesses, farmers, fishermen, weavers to Donald Duck and present comic characters. These creations are displayed in different national and international museums.

Here are a few images (not to scale) of some clay dolls of Krishnanagar.

The ratio of diameters of red spherical apples in Doll-1 to that of spherical oranges in Doll-2 is 2:3. In Doll-3, a male doll of blue colour has a cylindrical body and a spherical head. The spherical head touches the cylindrical body. The radius of both the spherical head and the cylindrical body is 3cm and the height of the cylindrical body is 8cm. 

Based on the above information answer the following questions: 

i) What is the ratio of the surface areas of red spherical apples in Doll-1 to that of spherical oranges in Doll-2.? 

ii) The blue doll of Doll-3 is melted and its clay is used to make the cylindrical drum of Doll-4. If the radius of the drum is also 3cm, find the height of the drum.

Solution- (i) Let 𝑟1𝑎𝑛𝑑 𝑟2 be respectively the radii of apples and oranges

∵ 2𝑟1: 2𝑟2 = 2: 3 ⇒ 𝑟1: 𝑟2 = 2: 3

4𝜋𝑟1²: 4𝜋𝑟2² = (𝑟1/𝑟2)² = (2/3)²

= 4: 9

Solution- (ii) Let the height of the drum be h.

The volume of the drum = volume of the cylinder + volume of the sphere

π3²h = (π3²× 8 + 4/3 π3³) 𝑐𝑚³

⇒ ℎ = (8 + 4)𝑐𝑚

⇒ ℎ = 12𝑐𝑚

Class 10 Maths Term 2 Sample Paper- Standard Maths

Question 1- Find the value of a25 - a15 for the AP: 6, 9, 12, 15, ………..

Solution- a = 6, d = 3        ; a25 = 6 + 24(3) = 78 

a15 = 6 + 14(3) = 48             ; a25 - a15 = 78 - 48 = 30 

OR 

If 7 times the seventh term of the AP is equal to 5 times the fifth term, then find the value of its 12th term.

Solution- 7(𝑎 + 6𝑑) = 5(𝑎 + 4𝑑) 

⇒2𝑎 + 22𝑑 = 0 

⇒ 𝑎 + 11𝑑 = 0 

⇒ 𝑡12 = 0

Question 2- Find the value of 𝑚 so that the quadratic equation 𝑚𝑥(5𝑥 − 6) = 0 has two equal roots.

Solution- 5mx² - 6mx + 9 = 0

b² - 4ac = 0 ⇒ (-6m)² - 4(5m)(9) = 0

⇒ 36m(m - 5) = 0

⇒ m = 0, 5 ; rejecting m=0, we get m = 5

Question 3- From a point P, two tangents PA and PB are drawn to a circle C(0, r). If OP = 2r, then find ∠𝐴𝑃𝐵. What type of triangle is APB?

Solution- let ∠𝐴𝑃𝑂 = 𝜃 

𝑆𝑖𝑛𝜃 = 𝑂𝐴/ 𝑂𝑃 = 1/ 2 ⇒ 𝜃 = 30° 

⇒ ∠𝐴𝑃𝐵 = 2𝜃 = 60° 

Also ∠𝑃𝐴𝐵 = ∠𝑃𝐵𝐴 = 60° 

(∵ 𝑃𝐴 = 𝑃𝐵) 

⇒△ 𝐴𝑃𝐵 is equilateral

Question 4- The curved surface area of a right circular cone is 12320 cm². If the radius of its base is 56 cm, then find its height.

Question 5- Mrs. Garg recorded the marks obtained by her students in the following table. She calculated the modal marks of the students of the class as 45. While printing the data, a blank was left. Find the missing frequency in the table given below

Question 6- If Ritu were younger by 5 years than what she really is, then the square of her age would have been 11 more than five times her present age. What is her present age? 

OR 

Solve for x: 9x² - 6px + (p² - q²) = 0

Question 7- Following is the distribution of the long jump competition in which 250 students participated. Find the median distance jumped by the students. Interpret the median

Question 8- Construct a pair of tangents to a circle of radius 4cm, which are inclined to each other at an angle of 60°.

Question 9- The distribution given below shows the runs scored by batsmen in one-day cricket matches. Find the mean number of runs.

Question 10- Two vertical poles of different heights are standing 20m away from each other on the level ground. The angle of elevation of the top of the first pole from the foot of the second pole is 60° and angle of elevation of the top of the second pole from the foot of the first pole is 30°. Find the difference between the heights of two poles. (Take √3 = 1.73) 

OR 

A boy 1.7 m tall is standing on a horizontal ground, 50 m away from a building. The angle of elevation of the top of the building from his eye is 60°. Calculate the height of the building. (Take √3 = 1.73)

Question 11- The internal and external radii of a spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid cylinder of diameter 14cm, find the height of the cylinder. Also find the total surface area of the cylinder. (Take 𝜋 = 22/7 )

Question 12- Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact to the centre. 

OR 

Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2∠OPQ

Question 13- Trigonometry in the form of triangulation forms the basis of navigation, whether it is by land, sea or air. GPS a radio navigation system helps to locate our position on earth with the help of satellites. A guard, stationed at the top of a 240m tower, observed an unidentified boat coming towards it. A clinometer or inclinometer is an instrument used for measuring angles or slopes(tilt). The guard used the clinometer to measure the angle of depression of the boat coming towards the lighthouse and found it to be 30°.

(Lighthouse of Mumbai Harbour. Picture credits - Times of India Travel) i) Make a labelled figure on the basis of the given information and calculate the distance of the boat from the foot of the observation tower. ii) After 10 minutes, the guard observed that the boat was approaching the tower and its distance from tower is reduced by 240(√3 - 1) m. He immediately raised the alarm. What was the new angle of depression of the boat from the top of the observation tower?

Question 14- Push-ups are a fast and effective exercise for building strength. These are helpful in almost all sports including athletics. While the push-up primarily targets the muscles of the chest, arms, and shoulders, support required from other muscles helps in toning up the whole body.

Nitesh wants to participate in the push-up challenge. He can currently make 3000 push-ups in one hour. But he wants to achieve a target of 3900 push-ups in 1 hour for which he practices regularly. With each day of practice, he is able to make 5 more push-ups in one hour as compared to the previous day. If on first day of practice he makes 3000 push-ups and continues to practice regularly till his target is achieved. 

Keeping the above situation in mind answer the following questions: 

i) Form an A.P representing the number of push-ups per day and hence find the minimum number of days he needs to practice before the day his goal is accomplished? 

ii) Find the total number of push-ups performed by Nitesh up to the day his goal is achieved.

Steps to download CBSE Class 10 Maths Sample Paper 2021-22

Download the CBSE Maths Sample Paper 2022 Class 10 by following the below-mentioned steps

Step I- Visit the official website of CBSE Academic @ www.cbseacademic.nic.in. 

Step II- Click on the notification appearing in the academic section- “Sample Question Papers of Classes X for Term 2 Exams 2022”.

Step III- Now click on the link mentioned under “Sample Papers Class X”.

Step IV- The list of all subjects “Class X Sample Question Paper & Marking Scheme for Exam 2022” appears on the screen. 

Step V- Click on “SQP” for “Maths” and download CBSE Class 10th Maths Sample Paper Term 2 pdf along with Answer Key. 

Step VI- Check the marking scheme after attempting each subject CBSE Class 10th Maths Sample Paper 2022 Term 2.

CBSE Class 10 Term 2 Admit Card 2022 Out- Click to Download

CBSE Class 10 Term 2 Date Sheet 2022 Out- Click to Check