CBSE Class 10 Math Important Questions 2023-24

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CBSE Class 10 Math Important Questions 2023-24: The Central Board of Secondary Education is conducting the CBSE 10th Board Exam 2024 from February 15 to April 10, 2024, in a single shift and an offline mode. Students who are appearing for the CBSE Class 12 exam 2024 are advised to complete the CBSE Class 10 syllabus 2023-24 early to get enough time for revision. Students can check out the important questions or the repeated questions that have a high chance of coming to the CBSE 12th Exam 2024 to perform well. In this article, we have provided weightage-wise CBSE 10th Mathematics important questions along with chapter-wise important questions with which students can improve their scores significantly.

Additionally, students must also solve the CBSE Class 10 Previous Year Questions and sample papers within the allotted time regularly. Not only will this improve their confidence level but also will enable them to get an overview of the important questions of the CBSE 10th Mathematics Exam 2024.  

CBSE Class 10 Math Important Questions 2023-24: High Weightage Questions

In the CBSE class 10 question paper, Section D will have the maximum weightage questions. There will be a total of 4 questions each carrying 5 marks. Here are some of the highest weightage carrying important questions of the CBSE 10th Math Exam 2024:

Question 1: A container open at the top and made up of a metal sheet, is in the form of a frustum of a cone of height 14 cm with radii of its lower and upper circular ends as 8 cm and 20 cm. respectively. Find the capacity of the container.

Question 2: Two water taps together can fill a tank in 9 3/8 hours. The tap of a larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank. 

Question 3: A tent is in the shape of a cylinder surmounted by a conical top. If the height and radius of the cylindrical part are 3 m and 14 m respectively, and the total height of the tent is 13.5 m, find the area of the canvas required for making the tent, keeping a provision of 26 m2 of canvas for stitching and wastage. Also, find the cost of the canvas to be purchased at the rate of ₹ 500 per m2. 

Question 4: A rectangular park is to be designed whose breadth is 3 m less than its length. Its area is to be 4 square meters more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude 12 m. Find the length and breadth of the park.

Question 5: A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.

CBSE Class 10 Math Important Questions 2023-24: 3 Mark Questions

Section C will contain 6 questions each carrying 3 marks questions. Below are the 3 marks questions that are important for the upcoming CBSE Class 10 Math exam 2024.

Question 1: The sum of a two digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there?  

Question 2: A shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days, and an additional charge for each day thereafter. Latika paid Rs 22 for a book kept for six days, while Anand paid Rs 16 for a book kept for four days. Find the fixed charges and the charge for each extra day.

Question 3: If A(–2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides. 

Question 4: Construct a triangle with its sides 4 cm, 5 cm and 6 cm. Then construct a triangle similar to it whose sides are 2 3 of the corresponding sides of the first triangle. 

Question 5: A plane left 30 minutes late than its scheduled time and in order to reach the destination 1500 km away in time, it had to increase its speed by 100 km/h from the usual speed. Find its usual speed. 

CBSE Class 10 Math Important Questions 2023-24: 1 Mark Questions

Section A will comprise 1 mark or multiple choice questions. Here are some of the important 1 mark CBSE class 10 Math questions:

Question 1: If two positive integers a and b are written as a = x3y2 and b = xy3, where x, y are prime numbers, then the result obtained by dividing the product of the positive integers by the LCM (a, b) is (a) xy (b) xy2 (c) x3y3 (d) x2y2

Question 2:  If HCF of 510 and 92 is 2, then the LCM of 510 & 92 is 32460 

Reason: as HCF(a,b) x LCM(a,b) = a x b 

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A). 

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A). 

(c) Assertion (A) is true but Reason (R) is false. 

(d) Assertion (A) is false but Reason (R) is true.

Question 3: If a pair of linear equations is consistent, then the lines represented by them are 

(A) parallel (B) intersecting or coincident (C) always coincident (D) always intersecting Answer: Correct 

Answer: (B) intersecting or coincident If a pair of linear equations is consistent, then the lines represented by them are intersecting or coincident.

Question 4: If x = 3 is one root of the quadratic equation x 2 – 2kx – 6 = 0, then find the value of k. 

Question 5: What is the HCF of smallest prime number and the smallest composite number?

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CBSE Class 10 Math Important Questions 2023-24: Chapter-wise Questions

As per the CBSE class 12 mathematics marking scheme 2023-24, the high weightage carrying units are given below. 

Unit 2: Algebra (20 marks)

Question 1:  If the distance between points (5, 2) and (1, a) is 5, then find the value of a, If (a < 0).

Ans: Distance = {(5-1)2+2-a2}

=>5= {(4)2+2-a2}

=>25 = 16+2-a2

=>25-16 = 2-a2

=>9=2-a2

As value of a is negative.

=>2-a=3

=>a = 2-3 = -1

Question 2: A circle with its center at O (x,11) has a radius of 26  units. Point P (3,-13)  lies on the circle. Also, x> 10. Find x.

Ans:

As O is at (x, 11) and p (3, – 13)

=> OP = x-32+(11--132)

=> OP = (x-3)^2+24^2

=>OP = (x-3)^2+576

=>262 = x-32+576

=>676 = x-32 +576

=>x-32= 100

=>(x-3) = 10

=>x = 13 (As x > 10)

Question 3: What will be the sum of the first 21 terms of the AP 4, 7, 10, …..?

Ans:

AP = 4, 7, 10, ……

Here, a = 4

d = 7-4 = 3

Number of terms = n = 21

So, sum of first 21 terms of AP will be Sn =n2 (2a+(n-1)d)

=>Sn =212 * [2*4 +(21-1)*3]

=>Sn =212 * [8+60]

=>Sn =212 * 68

=>Sn = 21*34 = 714

Unit 4: Geometry (15 marks)

Question 1: Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.

Question 2: If A (-2,1), B (a, 0), C (4, b) and D (1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides.

Question 3: Find the centre and radius of the circumcircle (i.e., circumcentre and circum-radius) of the triangle whose vertices are (-2, 3), (2, -1) and (4, 0).

Unit 5: Trigonometry (12 marks)

Question 1: If sec θ + tan θ = 7, then evaluate sec θ – tan θ. 

Ans: We know that,

sec2θ – tan2θ = 1

(sec θ + tan θ) (sec θ – tan θ) = 1

(7) (sec θ – tan θ) = 1 …[sec θ + tan θ = 7; (Given)

∴ sec θ – tan θ = 

1/7

Question 2: What happens to value of cos when increases from 0° to 90°? (2015)

Ans: cos 0° = 1, cos 90° = 0

When θ increases from 0° to 90°, the value of cos θ decreases from 1 to 0.

Question 3: Evaluate: sin2 19° + sin771°. 

Ans: sin2 19° + sin2 71°

= sin219° + sin2 (90° – 19°)…[∵ sin(90° – θ) = cos θ

= sin2 19° + cos2 19° = 1 …[∵ sin2 θ + cos2 θ = 1

The questions provided above in the article are important looking at the past few years' CBSE Class 10 Math question Papers. Students must practice these questions and the questions similar to these to score well in the CBSE 10th Board exam 2024.

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