Class 10 CBSE Term2 Maths Specimen 2022

BOARD -

CLASS -

SUBJECT -

CBSE

10th

MATHEMATICS

Paper Pattern for Written Term-I

TIME -

MARKS -

2 hour

40

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Solved Specimen Paper Semester-2 2022

Question 1 [MATHEMATICS Specimen Paper Semester-2 2022]

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

Solution

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

Question 2 [MATHEMATICS Specimen Paper Semester-2 2022]

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

Solution

Question 3 [MATHEMATICS Specimen Paper Semester-2 2022]

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

Question 4 [MATHEMATICS Specimen Paper Semester-2 2022]

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

Solution

Question 5 [MATHEMATICS Specimen Paper Semester-2 2022]

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

Marks 0-20 20-40 40-60 60-80 80-100
No. of students 5 10 6 --- 3

Solution

Question 6 [MATHEMATICS Specimen Paper Semester-2 2022]

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?

Solution

OR

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

Solution

Question 7 [MATHEMATICS Specimen Paper Semester-2 2022]

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

Distance 0-1 1-2 2-3 3-4 4-5
No. of students 40 80 62 38 30

Solution

Question 8 [MATHEMATICS Specimen Paper Semester-2 2022]

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

Solution

Question 9 [MATHEMATICS Specimen Paper Semester-2 2022]

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

Runs scored 0-40 40-80 80-120 120-140 140-180
No. of batmans 12 20 35 30 23

Solution

Question 10 [MATHEMATICS Specimen Paper Semester-2 2022]

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)

Solution

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)

Solution

Question 11 [MATHEMATICS Specimen Paper Semester-2 2022]

The internal and external radii of a spherical shell are 3cm and 5cm 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 )

Solution

Question 12 [MATHEMATICS Specimen Paper Semester-2 2022]

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.

Solution

OR

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

Solution

Question 13 [MATHEMATICS Specimen Paper Semester-2 2022]

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?

Solution

Question 14 [MATHEMATICS Specimen Paper Semester-2 2022]

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.

Solution

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