CBSE Class 10 Mathematics 2022
102 questions · 295 marks · 98 with the board’s own marking-scheme answer, 4 with no official answer on the site.
Marks by chapter
Counted from the 102 questions listed below, as the 2022 papers print them. CBSE allocates marks per unit, not per chapter — this is what was observed, not an official CBSE weightage. Every year compared →
| Chapter | Marks | Share |
|---|---|---|
| Circles21 questions | 66 | 22.4% |
| Statistics22 questions | 60 | 20.3% |
| Some Applications of Trigonometry16 questions | 55 | 18.6% |
| Surface Areas and Volumes12 questions | 36 | 12.2% |
| Arithmetic Progressions14 questions | 33 | 11.2% |
| Quadratic Equations10 questions | 23 | 7.8% |
| Areas Related to Circles2 questions | 6 | 2.0% |
| Coordinate Geometry2 questions | 6 | 2.0% |
| Introduction to Trigonometry1 question | 4 | 1.4% |
| Pair of Linear Equations in Two Variables1 question | 4 | 1.4% |
| Real Numbers1 question | 2 | 0.7% |
102 questions from 2022
- Q1The mode of a grouped frequency distribution is 75 and the modal class is 65-80. The frequency of the class preceding…2 mk
- Q1Solve the quadratic equation: x^2+2 √2 x-6=0 for x.2 mk
- Q1Find the sum of first 30 terms of AP: - 30, - 24, - 18,...... OR In an AP if S_n=n(4 n+1), then find the AP.2 mk
- Q1Find the value of 'k' for which the quadratic equation 2 k x^2-40 x+25=0 has real and equal roots. OR Solve for x: 5/2…2 mk
- Q1Solve the quadratic equation for x: x^2-2 a x-(4 b^2-a^2)=0 OR If the quadratic equation (1+a^2) x^2+2 a b…2 mk
- Q1In Figure 1, PQ and PR are tangents to the circle centred at O. If ∠ OPR=45^°, then prove that ORPQ is a square. Figure…2 mk
- Q2In Fig. 1, AB is diameter of a circle centered at O. BC is tangent to the circle at B. If OP bisects the chord AD and ∠…2 mk
- Q2A solid metallic sphere of radius 10 · 5 cm is melted and recast into a number of smaller cones, each of radius 3.5 cm…2 mk
- Q2Which term of the A.P. -11/2,-3,-1/2, … is 49/2? OR Find a and b so that the numbers a, 7, b, 23 are in A.P.2 mk
- Q2How many natural numbers are there between 1 and 1000 which are divisible by 5 but not by 2?2 mk
- Q2Find the sum of first 20 terms of an AP in which d=5 and a_20=135.2 mk
- Q3Find the value of m for which the quadratic equation (m-1) x^2+2(m-1) x+1=0 has two real and equal roots. OR Solve the…2 mk
- Q3Find the sum of the first twelve 2-digit numbers which are multiples of 6. OR In an AP, if a_2=26 and a_15=-26, then…2 mk
- Q3A solid piece of metal in the form of a cuboid of dimensions 11 cm × 7 cm × 7 cm is melted to form 'n' number of solid…2 mk
- Q3In an A.P. if the sum of third and seventh term is zero, find its 5^th term. OR Determine the A.P. whose third term is…2 mk
- Q3If the sum of the roots of the quadratic equation ky^2-11 y+(k-23)=0 is 13/21 more than the product of the roots, then…2 mk
- Q3Find the common difference 'd' of an AP whose first term is 10 and the sum of the first 14 terms is 1505.2 mk
- Q3Find the mode of the given frequency distribution:2 mk
- Q4In Fig. 1, AB is diameter of a circle centered at O. BC is tangent to the circle at B. If OP bisects the chord AD and ∠…2 mk
- Q4A cone of height 28 cm and radius of base 7 cm is made up of modelling clay. A child reshapes it in the form of a…2 mk
- Q4150 spherical marbles, each of diameter 1 · 4 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some…2 mk
- Q4Find the mode of the following frequency distribution:2 mk
- Q4Find the sum of all 11 terms of an A.P. whose 6^th term is 30.2 mk
- Q4Find the mean of the following frequency distribution:2 mk
- Q4For what value of m, the quadratic equation m x^2-2(m-1) x+(m+2)=0 has two real and equal roots? OR The diagonal of a…2 mk
- Q4If the first term of an A.P. is 5, the last term is 15 and the sum of first n terms is 30, then find the value of n.2 mk
- Q5Solve the quadratic equation: x^2-2 a x+(a^2-b^2)=0 for x.2 mk
- Q5In Fig. 1, there are two concentric circles with centre O. If ARC and AQB are tangents to the smaller circle from the…2 mk
- Q5Find the median of the following distribution:2 mk
- Q5The product of Rehan's age (in years) 5 years ago and his age 7 years from now, is one more than twice his present age.…2 mk
- Q5If mode of the following frequency distribution is 55, then find the value of x.2 mk
- Q5For what value of 'n', are the n ^th terms of the APs: 9, 7, 5,..... and 15,12,9, …. the same?2 mk
- Q5For the following frequency distribution, find the mode:2 mk
- Q6If the mean of the following frequency distribution is 18, then find the missing frequency ' f '.2 mk
- Q6Find the sum of first 20 terms of an A.P. whose n^th term is given as a_n=5-2 n.2 mk
- Q6150 spherical marbles, each of diameter 1.4 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some…2 mk
- Q6The curved surface area of a right circular cylinder is 176 sq cm and its volume is 1232 cu cm. What is the height of…2 mk
- Q6Two concentric circles are of radii 4 cm and 3 cm. Find the length of the chord of the larger circle which touches the…2 mk
- Q6In Figure 2, PQ and PR are tangents to the circle centred at O. If ∠ OPR=45^°, then prove that ORPQ is a square. Figure…2 mk
- Q7Two boats are sailing in the sea 80 m apart from each other towards a cliff AB. The angles of depression of the boats…3 mk
- Q7An aeroplane at an altitude of 200 metres observes the angles of depression of opposite points on the two banks of a…3 mk
- Q7A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle of…3 mk
- Q7Heights of 50 students of class X of a school are recorded and following data is obtained: Find the median height of…3 mk
- Q7For what value of x, is the median of the following frequency distribution 34•5?3 mk
- Q7Construct a pair of tangents to a circle of radius 4 cm which are inclined to each other at an angle of 60°.3 mk
- Q7Draw a line segment AB of length 8 cm and locate a point P on AB such that AP: PB=1: 5. OR Draw a circle of radius 3…3 mk
- Q7Draw two concentric circles of radii 2 cm and 5 cm. From a point on the outer circle, construct a pair of tangents to…3 mk
- Q8In Fig. 3, AB is tower of height 50 m. A man standing on its top, observes two cars on the opposite sides of the tower…3 mk
- Q8Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from…3 mk
- Q8The percentage of marks obtained by 100 students in an examination are given below: Determine the median percentage of…3 mk
- Q8The sum of the first three terms of an A.P. is 33. If the product of first and third term exceeds the second term by…3 mk
- Q8Draw a line segment AB=7 cm. Divide it in the ratio 3: 2.3 mk
- Q8The tops of two poles of heights 20 m and 28 m are connected with a wire. The wire is inclined to the horizontal at an…3 mk
- Q8Find the value of 'p' for which the quadratic equation p(x-4)(x-2)+ (x-1)^2=0 has real and equal roots. OR Had Aarush…3 mk
- Q8From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30°…3 mk
- Q9The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top…3 mk
- Q9For what value of x, is the median of the following frequency distribution 34•5?3 mk
- Q9If the median of the following data is 33 then, find the value of m:3 mk
- Q9Two men on either side of a cliff 75 m high observe the angles of elevation of the top of the cliff to be 30° and 60°.…3 mk
- Q9The weights (in kg) of 50 wild animals of a National Park were recorded and the following data was obtained: Find the…3 mk
- Q9There is a small island in the middle of a 100 m wide river and a tall tree stands on the island. P and Q are points…3 mk
- Q9The mean of the following frequency distribution is 25. Find the value of f. OR Find the mean of the following data…3 mk
- Q9An aeroplane when flying at a height of 3125 m from the ground passes vertically below another plane at an instant when…3 mk
- Q10Heights of 50 students of class X of a school are recorded and following data is obtained: Find the median height of…3 mk
- Q10The following table gives the production yield of wheat of farms of a village: Find the mean production yield, using…3 mk
- Q10Construct a pair of tangents to a circle of radius 4 cm from a point P lying outside the circle at a distance of 6 cm…3 mk
- Q10In an A.P., the sum of first n terms is n/2(3 n+5). Find the 25^th term of the A.P.3 mk
- Q10Construct a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.3 mk
- Q10If the last term of an A.P. of 30 terms is 119 and the 8^th term from the end (towards the first term) is 91, then find…3 mk
- Q10For the following frequency distribution, find the median:3 mk
- Q10Construct a pair of tangents to a circle of radius 3 cm which are inclined to each other at an angle of 60°.3 mk
- Q10Construct a pair of tangents to a circle of radius 5 cm, which are inclined to each other at an angle of 60°.3 mk
- Q10Following is the daily expenditure on lunch by 30 employees of a company: Find the mean daily expenditure of the…3 mk
- Q10Find the mean of the following frequency distribution:3 mk
- Q11In Figure 1, a right triangle ABC in which ∠ B=90^°, AB=12 cm and BC=5 cm is shown. Find the radius of the circle…4 mk
- Q11In Fig.-2, if a circle touches the side QR of PQR at S and extended sides PQ and PR at M and N, respectively, then Fig.…4 mk
- Q11In Figure 3, two circles with centres at O and O' of radii 2r and r respectively, touch each other internally at A. A…4 mk
- Q11The angle of elevation of an aeroplane from a point on the ground is 60°. After a flight of 30 seconds, the angle of…4 mk
- Q11From the top of an 8 m high building, the angle of elevation of the top of a cable tower is 60^° and the angle of…4 mk
- Q11The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60^°. From a point Y, 40 m…4 mk
- Q11The sum of two numbers is 34. If 3 is subtracted from one number and 2 is added to another, the product of these two…4 mk
- Q11In Fig. 4, PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q meet at a point T. Find the…4 mk
- Q11From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and same radius is hollowed…4 mk
- Q12From the top of an 8 m high building, the angle of elevation of the top of a cable tower is 60^° and the angle of…4 mk
- Q12From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and same radius is hollowed…4 mk
- Q12In Figure 2, from a solid cube of side 7 cm, a cylinder of radius 2 · 1 cm and height 7 cm is scooped out. Find the…4 mk
- Q12In Figure 3, two circles with centres at O and O^′ of radii 2 r and r respectively, touch each other internally at A. A…4 mk
- Q12In Figure 4, two circles with centres at O and O' of radii 2 r and r respectively, touch each other internally at A. A…4 mk
- Q12In Figure 1, a triangle ABC with ∠ B=90^° is shown. Taking AB as diameter, a circle has been drawn intersecting AC at…4 mk
- Q12A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of…4 mk
- Q12Prove that a parallelogram circumscribing a circle is a rhombus.4 mk
- Q12A 2-digit number is such that the product of its digits is 24. If 18 is subtracted from the number, the digits…4 mk
- Q13In the picture given below, one can see a rectangular in-ground swimming pool installed by a family in their backyard.…4 mk
- Q13Yoga is an ancient practice which is a form of meditation and exercise. By practising yoga, we not even make our body…4 mk
- Q13Case Study-1: Kite festival is celebrated in many countries at different times of the year. In India, every year 14^th…4 mk
- Q13In Mathematics, relations can be expressed in various ways. The matchstick patterns are based on linear relations.…4 mk
- Q13Khurja is a city in the Indian state of Uttar Pradesh famous for the pottery. Khurja pottery is traditional Indian…4 mk
- Q14Khurja is a city in the Indian state of Uttar Pradesh famous for the pottery. Khurja pottery is traditional Indian…4 mk
- Q14Gadisar Lake is located in the Jaisalmer district of Rajasthan. It was built by the King of Jaisalmer and rebuilt by…4 mk
- Q14John planned a birthday party for his younger sister with his friends. They decided to make some birthday caps by…4 mk
- Q14Yoga is an ancient practice which is a form of meditation and exercise. By practising yoga, we not even make our body…4 mk
- Q14Case Study - 2 A 'circus' is a company of performers who put on shows of acrobats, clowns etc. to entertain people…4 mk
Other Mathematics years
Answers come from CBSE’s own marking schemes. How we source them.