# CBSE 10th Maths Board Exam 2019: Important Questions, Theorems, Chapter-wise Weightage

Check important questions for upcoming CBSE Class 10 Maths Board Exam 2019. Check chapter-wise weightage (of 10th Maths NCERT textbook), important questions, theorems & topics for upcoming CBSE 10th Maths Board Exam 2019. As per CBSE Date Sheet 2019, this paper is scheduled to be held on Thursday, 07th March from 10:30 AM to 1:30 PM. Questions and theorems mentioned in this article are important and expected to be asked in the upcoming CBSE 10th Maths Board Exam 2019. You can access solutions of almost all the questions mentioned in this article from the links given at the end of this article.

## CBSE 10th Maths Board Exam 2019: Chapter-wise important questions, theorems, topics & weightage

Chapter-wise important questions, theorems, topics & weightage for upcoming CBSE 10th Maths Board Exam 2019 are given below

### Chapter 1: Real Numbers [Expected - 6 Marks: 1 Mark + 2 Marks + 3 Marks]

Example: 1 Mark

Question: After how many decimal places will the decimal expansion of 23/(24 × 53) terminate?

Example: 2 Marks

Question: The HCF and LCM of two numbers are 9 and 360 respectively. If one number is 45, find the other number.

Question: Show that 7 − √5 is irrational, give that √5 is irrational.

Example: 3 Marks

Question: Use Euclid’s Division Algorithm to find HCF of 726 and 275.

## CBSE Class 10 Mathematics Exam 2019: Important questions with solutions

### Chapter 2: Polynomials [Expected - 3 Marks: 1 Question]

Example: 3 Marks

Question: Find the zeroes of the following polynomial: 5√5 x2 + 30 x + 8√5.

Question: Divide 3x2x3 ‒ 3x + 5 by x ‒ 1 ‒ x2 and verify the division algorithm.

CBSE Sample Papers 2019 for 10th and 12th with Answers & Marking Scheme: All Subjects [Issued by CBSE - Check this link]

### Chapter 3: Pair of Linear Equations in Two Variables [Expected - 5 Marks: 2 Marks + 3 Marks]

Example: 2 Marks

Question: For what value of p will the following pair of linear equations have infinitely many solutions

(p ‒ 3)x + 3 y = p

px + py = 12

Example: 3 Marks

Question:

Places A and B are 80 km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in same direction they meet in 8 hours and if they move towards each other they meet in 1 hour 20 minutes. Find the speed of cars.

### Chapter 4: Quadratic Equations [Expected - 5 Marks: 1 Mark + 4 Marks]

Example: 1 Mark

Question: Find the value of k, for which one root of the quadratic equation kx2 ‒14x + 8 = 0 is 2.

Question: Find the value(s) of k for which the equation x2 + 5 kx + 16 = 0 has real and equal roots.

Example: 4 Mark

Question: A train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/h from its usual speed. Find the usual speed of the train.

Question: Solve for x: 1/(a + b + x) = [1/a + 1/b + 1/x], [a ≠ 0, b ≠ 0, x ≠ 0, x ≠ ‒ (a + b)]

CBSE Class 10 Mathematics NCERT Exemplar Problems and Solutions: All Chapters

### Chapter 5: Arithmetic Progressions [Expected - 7 Marks: 1 Mark + 2 Marks + 4 Marks]

Example: 1 Mark

Question: If nth term of an A.P. is (2n+1), what is the sum of its first three terms?

Example: 2 Marks

Question: Find the 20th term from the last term of the AP 3, 8, 13,…., 253.

Question: If 7 times the 7th term of an A.P is equal to 11 times its 11th term, then find its 18th term.

Example: 4 Marks

Question: An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.

### Chapter 6: Triangles [Expected - 8 Marks: 1 Mark + 3 Marks + 4 Marks]

Example: 1 Mark

Question:

In figure if AD = 6cm, DB = 9cm, AE = 8cm and EC = 12cm and ∠ADE = 48. Find ∠ABC .

Example: 3 Marks

Question:

In figure ∠ 1 = ∠ 2and ∆NSQ ≅ ∆MTR, then prove that ∆PTS~∆PRQ.

Question:

In ∆ABC, if AD is the median, then show that AB2+AC2 = 2(AD2 + BD2).

Example: 3 Marks

Important Theorems:

• Prove that in a right angled triangle square of the hypotenuse is equal to sum of the squares of other two sides.

• If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

• The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

• In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.

• In a triangle, if the square on one side is equal to sum of the squares on the other two sides, the angles opposite to the first side is a right angle.

NCERT Exemplar Problems and Solutions for CBSE Class 10 Science: All chapters

### Chapter 7: Coordinate Geometry [Expected – 6 Marks: 1 Mark + 2 Marks + 3 Marks]

Example: 1 Mark

Question:

Find the value of a, for which point P (a/3, 2) is the mid-point of the line segment joining the points Q (-5, 4) and R (-1, 0).

Chapter 15: Probability [Expected - 4 Marks: 2 Marks + 2 Marks]

Example: 2 Marks

Question:

A card is drawn at random from a well shuffled deck of 52 cards. Find the probability of getting neither a red card nor a queen.

Question:

Two dice are thrown at the same time and the product of numbers appearing on them is noted. Find the probability that the product is a prime number.

These questions are taken from latest CBSE 10th Maths Sample Paper 2019. You can check solutions of these questions from the links given below

Question:

Find the coordinates of the point P which divides the join of A (- 2, 5) and B (3, - 5) in the ratio 2:3.

Question:

Find the coordinates of the point P which divides the join of A (- 2, 5) and B (3, - 5) in the ratio 2:3.

Example: 3 Marks

Question:

The points A (1, -2), B (2, 3), C (k, 2) and D (-4, -3) are the vertices of a parallelogram. Find the value of k.

Question:

The value of k for which the points (3k ‒ 1, k ‒ 2), (k, k ‒ 7) and (k ‒ 1, ‒ k ‒ 2) are collinear.

### Chapter 8: Introduction to Trigonometry, Expected - 8 Marks: [1 Mark + 3 Marks  + 4 Marks]

Example: 1 Mark

Question:

Write the value of cot2 θ ‒ (1/sin2θ).

Example: 3 Marks

Question:

In sin θ = cos θ, then find the value of 2 tan θ + cos2 θ.

Question:

Prove that cot θ ‒ tan θ = (2 cos2 ‒ 1)/(sin θ cos θ).

Question:

Prove that sin θ (1 + tan θ) + cos θ (1 + cot θ) = sec θ + cosec θ.

Example: 4 Marks

Question:

If sec θ + tan θ = p, then find the value of cosec θ.

### Chapter 9: Some Applications of Trigonometry [Expected - 4 Marks: 1 Question]

Example: 4 Marks

Question:

A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from 30 to 45, how long will the car take to reach the observation tower from this point?

Question:

The angle of elevation of a cloud from a point 60 m above the surface of the water of a lake is 30 and the angle of depression of its shadow from the same point in water of lake is 60. Find the height of the cloud from the surface of water.

### Chapter 10: Circles [Expected - 3 Marks: 1 Question]

Example: 3 Marks

Question:

The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the bigger circle and BD is a tangent to the smaller circle touching it at D and intersecting the larger circle at P on producing. Find the length of AP.

Important Theorems:

• The tangent at any point of a circle is perpendicular to the radius through the point of contact.

• The lengths of tangents drawn from an external point to a circle are equal.

### Chapter 11: Constructions [Expected - 4 Marks: 1 Question]

Example: 4 Marks

Question:

Draw a ∆ ABC with sides 6cm, 8cm and 9 cm and then construct a triangle similar to ∆ABC whose sides are 3/5 of the corresponding sides of ∆ ABC.

### Chapter 12: Areas Related to Circles [Expected - 3 Marks: 1 Question]

Example: 3 Marks

Question:

Find the area of the minor segment of a circle of radius 42cm, if length of the corresponding arc is 44cm.

### Chapter 13: Surface Areas and Volumes [Expected - 7 Marks: 3 Marks + 4 Marks]

Example: 3 Marks

Question: A solid sphere of radius 3 cm is melted and then recast into small spherical balls each of diameter 0.6 cm. Find the number of balls.

Question: Water is flowing at the rate of 15 km per hour through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. Find the time in which the level of water in the tank will rise by 21 cm

Example: 4 Marks

Question: The radii of circular ends of a bucket of height 24 cm are 15 cm and 5 cm. Find the area of its curved surface

### Chapter 14: Statistics [Expected 7 Marks: 3 Marks + 4 Marks]

Example: 3 Marks

Question:

The table shows the daily expenditure on grocery of 25 households in a locality. Find the modal daily expenditure on grocery by a suitable method.

Example: 4 Marks

Question:

The median of the following data is 525. Find the values of x and y if the total frequency is 100.

### Chapter 15: Probability [Expected - 4 Marks: 2 Marks + 2 Marks]

Example: 2 Marks

Question:

A card is drawn at random from a well shuffled deck of 52 cards. Find the probability of getting neither a red card nor a queen.

Question:

Two dice are thrown at the same time and the product of numbers appearing on them is noted. Find the probability that the product is a prime number.

These questions are taken from latest CBSE 10th Maths Sample Paper 2019. You can check solutions of these questions from the links given below

CBSE Class 10 Mathematics Sample Paper 2019: Marking Scheme (All Questions are available in this paper)

Chapter 15: Probability [Expected - 4 Marks: 2 Marks + 2 Marks]

Example: 2 Marks

Question:

A card is drawn at random from a well shuffled deck of 52 cards. Find the probability of getting neither a red card nor a queen.

Question:

Two dice are thrown at the same time and the product of numbers appearing on them is noted. Find the probability that the product is a prime number.

These questions are taken from latest CBSE 10th Maths Sample Paper 2019. You can check solutions of these questions from the links given below