{"id":843017,"date":"2024-09-20T17:54:24","date_gmt":"2024-09-20T12:24:24","guid":{"rendered":"https:\/\/leverageedu.com\/discover\/?p=843017"},"modified":"2024-09-20T17:54:24","modified_gmt":"2024-09-20T12:24:24","slug":"study-prep-maths-questions-for-class-9","status":"publish","type":"post","link":"https:\/\/leverageedu.com\/discover\/indian-exams\/study-prep-maths-questions-for-class-9\/","title":{"rendered":"100+ Maths Questions for Class 9 with Answers for Competitive Exams: Download Free PDF"},"content":{"rendered":"\n

This blog post presents a collection of over 100 carefully curated math questions for Class 9 for competitive exams. These questions cover a wide range of topics, from basic arithmetic to more advanced concepts like algebra, geometry, and trigonometry. By practising these questions, you can enhance your problem-solving skills, improve your understanding of mathematical concepts, and gain confidence in your ability to tackle challenging problems. Also, you can download the Maths questions for Class 9 with answers PDF here. Keep reading!!<\/p>\n\n\n\n\n\n\n

Sample Maths Questions for Class 9 with Answers<\/h2>\n\n\n\n

Solve Maths Questions for Class 9 of number systems, polynomial equations, coordinate geometry, lines and angles, triangles, quadratic equations, menstruation, statistics, and probability.\u00a0<\/p>\n\n\n\n

Number Systems<\/h3>\n\n\n\n

1. Simplify:<\/strong> 3\u221a27\u200b\u00d73\u221a8\u200b<\/p>\n\n\n\n

Solution:<\/strong> 3\u00d72=6<\/p>\n\n\n\n

2. Rationalize the denominator:<\/strong> 1\/(\u221a5\u200b\u22122)\u200b<\/p>\n\n\n\n

Solution:<\/strong> \u221a5+2 \/ (\u221a5\u200b\u22122)(\u221a5\u200b+2) = \u221a5\u22124\/5\u200b+2\u200b = \u221a5\u200b+2<\/p>\n\n\n\n

Polynomials<\/h3>\n\n\n\n

3. Find the product:<\/strong> (x+3)(x\u22122)<\/p>\n\n\n\n

Solution:<\/strong> x2<\/sup>\u22122x+3x\u22126 = x2<\/sup>+x\u22126<\/p>\n\n\n\n

4. Factorize:<\/strong> x2<\/sup>\u22129<\/p>\n\n\n\n

Solution:<\/strong> (x+3)(x\u22123)<\/p>\n\n\n\n

5. Divide:<\/strong> (x3<\/sup>\u22123x2<\/sup>+2x+5)\u00f7(x\u22122)<\/p>\n\n\n\n

Solution:<\/strong> Using synthetic division, we get a quotient of x2<\/sup>\u2212x+1 and a remainder of 7.<\/p>\n\n\n\n

Coordinate Geometry<\/h3>\n\n\n\n

6. Find the distance between points A(2, 3) and B(5, 7).<\/strong><\/p>\n\n\n\n

Solution:<\/strong> d = \u221a(5\u22122)2<\/sup>+(7\u22123)2<\/sup>\u200b = \u221a9+16 \u200b= 5<\/p>\n\n\n\n

7. Find the midpoint of the line segment joining points A(3, 5) and B(7, 9).<\/strong><\/p>\n\n\n\n

Solution:<\/strong> M=((3+7)\/2\u200b,(5+9)\/2\u200b) = (5,7)<\/p>\n\n\n\n

Lines and Angles<\/h3>\n\n\n\n

8. If two lines intersect, prove that the vertically opposite angles are equal.<\/strong><\/p>\n\n\n\n

Solution:<\/strong> This is a standard geometry proof that involves using the properties of linear pairs and adjacent angles.<\/p>\n\n\n\n

9. If the angles in a triangle are in the ratio 2:3:7, find the angles.<\/strong><\/p>\n\n\n\n

Solution:<\/strong> Let the angles be 2x, 3x, and 7x. Since the sum of angles in a triangle is 180\u00b0, we get 12x = 180, so x = 15. Therefore, the angles are 30\u00b0, 45\u00b0, and 105\u00b0.<\/p>\n\n\n\n

Triangles<\/h3>\n\n\n\n

10. In a right-angled triangle, the hypotenuse is 13 cm and one of the legs is 5 cm. Find the length of the other leg.<\/strong><\/p>\n\n\n\n

Solution:<\/strong> Using the Pythagorean theorem, we get a2<\/sup>+52<\/sup>=132, so a2<\/sup>=144 and a = 12 cm.<\/p>\n\n\n\n

11. Prove that the angles opposite to equal sides of an isosceles triangle are equal.<\/strong><\/p>\n\n\n\n

Solution:<\/strong> This is another standard geometry proof that involves drawing a perpendicular bisector of the base.<\/p>\n\n\n\n

Quadratic Equations<\/h3>\n\n\n\n

13. Solve the quadratic equation:<\/strong> x2<\/sup>\u22125x+6=0<\/p>\n\n\n\n

Solution:<\/strong> Factoring, we get (x\u22122)(x\u22123)=0, so x = 2 or x = 3.<\/p>\n\n\n\n

14. Find the discriminant of the quadratic equation:<\/strong> 2x2<\/sup>\u22123x+1=0<\/p>\n\n\n\n

Solution:<\/strong> The discriminant is b2<\/sup>\u22124ac=(\u22123)2<\/sup>\u22124(2)(1)=1.<\/p>\n\n\n\n

Area of Parallelogram and Triangle<\/h3>\n\n\n\n

15. Find the area of a parallelogram with base 12 cm and height 8 cm.<\/strong><\/p>\n\n\n\n

Solution:<\/strong> Area = base \u00d7 height = 12 cm \u00d7 8 cm = 96 cm\u00b2<\/p>\n\n\n\n

16. The area of a triangle is 24 cm\u00b2. If the base is 8 cm, find the height.<\/strong><\/p>\n\n\n\n

Solution:<\/strong> Height = (2 \u00d7 Area) \/ base = (2 \u00d7 24 cm\u00b2) \/ 8 cm = 6 cm<\/p>\n\n\n\n

Mensuration<\/h3>\n\n\n\n

17. Find the volume of a cube with a side 5 cm.<\/strong><\/p>\n\n\n\n

Solution:<\/strong> Volume = side\u00b3 = 5\u00b3 cm\u00b3 = 125 cm\u00b3<\/p>\n\n\n\n

18. Find the total surface area of a sphere with a radius 7 cm.<\/strong><\/p>\n\n\n\n

Solution:<\/strong> Total surface area = 4\u03c0r\u00b2 = 4 \u00d7 \u03c0 \u00d7 7\u00b2 cm\u00b2 = 616\u03c0 cm\u00b2<\/p>\n\n\n\n

Statistics<\/h3>\n\n\n\n

19. Find the mean, median, and mode of the data: 2, 4, 5, 3, 2, 5, 4, 6.<\/strong><\/p>\n\n\n\n

Solution:<\/strong> Mean = (2+4+5+3+2+5+4+6)\/8 = 3.75, Median = 4, Mode = 4 and 5.<\/p>\n\n\n\n

20. Draw a histogram for the following frequency distribution:<\/strong> <\/p>\n\n\n\n

| Class Interval | Frequency | |\u2014|\u2014| | 0-10 | 5 | | 10-20 | 8 | | 20-30 | 12 | | 30-40 | 6 |<\/p>\n\n\n\n

Solution:<\/strong> A histogram can be drawn using the given data, with the x-axis representing the class intervals and the y-axis representing the frequency.<\/p>\n\n\n\n

Probability<\/h3>\n\n\n\n

21. A coin is tossed twice. Find the probability of getting two heads.<\/strong><\/p>\n\n\n\n

Solution:<\/strong> The total possible outcomes are HH, HT, TH, and TT. The probability of getting two heads is 1\/4.<\/p>\n\n\n\n