About this Class 9 Math practice test

This Class 9 Math practice test helps students learn to solve polynomials, find coordinates, understand parallel lines, and calculate surface areas or volumes of 3D shapes easily.

Class 9 Math Practice Test sample questions

These starter questions help you launch a math mock test quickly. Swap them with your own worksheet, notebook, or textbook questions any time.

1. 1. State whether √9 is a rational or an irrational number.

2. 2. Between which two consecutive integers does √20 lie?

3. 3. Find the degree of the polynomial: 7x^4 - 3x^3 + x - 5.

4. 4. Find the zero of the linear polynomial p(x) = 3x - 9.

5. 5. Using the Remainder Theorem, find the remainder when x^3 - 2x^2 + x - 1 is divided by (x - 1).

6. 6. Using the Factor Theorem, check whether (x - 1) is a factor of the polynomial x^3 - 3x^2 + 3x - 1.

7. 7. Simplify the surd expression √45 + √20 into a single combined radical.

8. 8. Simplify using laws of exponents: (3^4 × 3^-2) ÷ 3^1.

9. 9. Express the recurring decimal 0.333... as a fraction in simplest form.

10. 10. Find the value of x if 5^(2x) = 125.

11. 11. In which quadrant does the point (-4, -2) lie?

12. 12. What are the coordinates of a point that lies exactly on the x-axis?

13. 13. Find one solution of the linear equation in two variables: 2x + y = 7.

14. 14. If (2, k) is a solution of the equation 3x - y = 4, find the value of k.

15. 15. Does the point (0, 5) lie on the y-axis or the x-axis?

16. 16. Write the equation 2x = 10 in the standard two-variable form ax + by + c = 0.

17. 17. A shopkeeper marks up an item's cost price of 800 rupees by 25% to set the selling price. Find the selling price.

18. 18. Find the simple interest on 4000 rupees at a rate of 5% per annum for 3 years.

19. 19. If x and y vary directly and y = 15 when x = 5, find y when x = 9.

20. 20. In how many years will 6000 rupees amount to 7200 rupees in simple interest at a rate of 4% per annum?

21. 21. Using Euclid's parallel postulate, if two lines are each parallel to a third line, what can you conclude about the two lines?

22. 22. Two parallel lines are cut by a transversal. If one co-interior angle measures 70 degrees, find its paired co-interior angle.

23. 23. Which triangle congruence criterion proves two triangles congruent when two sides and the included angle are equal?

24. 24. In triangle ABC, AB = AC and angle B = 50 degrees. Find angle C.

25. 25. Find the area of a triangle with sides 13 cm, 14 cm, and 15 cm using Heron's formula.

26. 26. Find the curved surface area of a cone with radius 7 cm and slant height 10 cm. Take pi = 22/7.

27. 27. Find the volume of a sphere with radius 3 cm. Take pi = 22/7.

28. 28. An angle inscribed in a semicircle is always which type of angle?

29. 29. A die is thrown once. What is the probability of getting a number greater than 4?

30. 30. In a survey of 50 families, 20 own a car. Find the experimental probability that a randomly selected family owns a car.

Answer key & quick explanations

Short answers for the sample questions above. Use this to self-check before generating a fresh AI-built mock test.

1. 1. State whether √9 is a rational or an irrational number.

   Rational

   √9 equals 3, a whole number that can be written as the fraction 3/1, so it satisfies the definition of a rational number.

2. 2. Between which two consecutive integers does √20 lie?

   Between 4 and 5

   Since 4² = 16 and 5² = 25, and 16 < 20 < 25, the square root of 20 must fall strictly between 4 and 5.

3. 3. Find the degree of the polynomial: 7x^4 - 3x^3 + x - 5.

   4

   The degree of a polynomial is the highest power of the variable present. Here, the highest power of x is 4, in the term 7x^4.

4. 4. Find the zero of the linear polynomial p(x) = 3x - 9.

   x = 3

   A zero of a polynomial is the value of x that makes p(x) = 0. Setting 3x - 9 = 0 gives 3x = 9, so x = 3.

5. 5. Using the Remainder Theorem, find the remainder when x^3 - 2x^2 + x - 1 is divided by (x - 1).

   -1

   The Remainder Theorem states that dividing p(x) by (x - a) leaves a remainder equal to p(a). Substituting x = 1: 1 - 2 + 1 - 1 = -1.

6. 6. Using the Factor Theorem, check whether (x - 1) is a factor of the polynomial x^3 - 3x^2 + 3x - 1.

   Yes, it is a factor

   By the Factor Theorem, (x - 1) is a factor of p(x) exactly when p(1) = 0. Substituting x = 1 gives 1 - 3 + 3 - 1 = 0, confirming it is a factor.

7. 7. Simplify the surd expression √45 + √20 into a single combined radical.

   5√5

   √45 simplifies to 3√5 (since 45 = 9 × 5) and √20 simplifies to 2√5 (since 20 = 4 × 5). Adding the like surds: 3√5 + 2√5 = 5√5.

8. 8. Simplify using laws of exponents: (3^4 × 3^-2) ÷ 3^1.

   3

   When multiplying or dividing powers with the same base, exponents add or subtract: 3^(4 + (-2) - 1) = 3^1 = 3.

9. 9. Express the recurring decimal 0.333... as a fraction in simplest form.

   1/3

   Letting x = 0.333..., multiplying by 10 gives 10x = 3.333.... Subtracting the original equation removes the repeating part: 9x = 3, so x = 3/9 = 1/3.

10. 10. Find the value of x if 5^(2x) = 125.

    x = 3/2 (or 1.5)

    Since 125 = 5^3, the equation becomes 5^(2x) = 5^3. Comparing exponents gives 2x = 3, so x = 3/2.

11. 11. In which quadrant does the point (-4, -2) lie?

    Third quadrant

    A point with a negative x-coordinate and a negative y-coordinate always lies in the third quadrant of the Cartesian plane.

12. 12. What are the coordinates of a point that lies exactly on the x-axis?

    (a, 0) — any point with a y-coordinate of 0

    Every point on the x-axis has zero vertical distance from it, meaning its y-coordinate is always 0, while the x-coordinate can be any value.

13. 13. Find one solution of the linear equation in two variables: 2x + y = 7.

    x = 1, y = 5 (or any pair satisfying 2x + y = 7)

    A linear equation in two variables has infinitely many solutions. Substituting x = 1 gives 2(1) + y = 7, so y = 5, which is one valid solution among many.

14. 14. If (2, k) is a solution of the equation 3x - y = 4, find the value of k.

    k = 2

    Substituting x = 2 and y = k into the equation gives 3(2) - k = 4, so 6 - k = 4, which means k = 2.

15. 15. Does the point (0, 5) lie on the y-axis or the x-axis?

    The y-axis

    A point with an x-coordinate of 0 lies exactly on the y-axis, regardless of its y-coordinate.

16. 16. Write the equation 2x = 10 in the standard two-variable form ax + by + c = 0.

    2x + 0y - 10 = 0

    Even though the equation 2x = 10 involves only one variable visibly, it can be written in the two-variable standard form by including y with a coefficient of 0: 2x + 0y - 10 = 0.

17. 17. A shopkeeper marks up an item's cost price of 800 rupees by 25% to set the selling price. Find the selling price.

    1000 rupees

    A 25% markup adds (25/100) × 800 = 200 rupees to the cost price, giving a selling price of 800 + 200 = 1000 rupees.

18. 18. Find the simple interest on 4000 rupees at a rate of 5% per annum for 3 years.

    600 rupees

    Simple interest is calculated as (Principal × Rate × Time) / 100. Substituting the values: (4000 × 5 × 3) / 100 = 60000 / 100 = 600 rupees.

19. 19. If x and y vary directly and y = 15 when x = 5, find y when x = 9.

    27

    In direct proportion, y/x stays constant. Here, y/x = 15/5 = 3, so when x = 9, y = 3 × 9 = 27.

20. 20. In how many years will 6000 rupees amount to 7200 rupees in simple interest at a rate of 4% per annum?

    5 years

    The interest earned is 7200 - 6000 = 1200 rupees. Using Time = (Interest × 100) / (Principal × Rate): (1200 × 100) / (6000 × 4) = 120000 / 24000 = 5 years.

21. 21. Using Euclid's parallel postulate, if two lines are each parallel to a third line, what can you conclude about the two lines?

    They are parallel to each other

    Euclid's parallel axiom implies that two lines parallel to the same line never meet each other either, so they must be parallel to one another.

22. 22. Two parallel lines are cut by a transversal. If one co-interior angle measures 70 degrees, find its paired co-interior angle.

    110 degrees

    Co-interior (allied) angles formed between two parallel lines cut by a transversal are always supplementary, so the paired angle is 180 - 70 = 110 degrees.

23. 23. Which triangle congruence criterion proves two triangles congruent when two sides and the included angle are equal?

    SAS (Side-Angle-Side)

    The SAS criterion states that if two sides and the angle between them in one triangle equal the corresponding two sides and included angle in another, the triangles are congruent.

24. 24. In triangle ABC, AB = AC and angle B = 50 degrees. Find angle C.

    50 degrees

    In an isosceles triangle, the angles opposite the equal sides are themselves equal. Since AB = AC, the angles opposite them (angle C and angle B) are equal, so angle C = 50 degrees.

25. 25. Find the area of a triangle with sides 13 cm, 14 cm, and 15 cm using Heron's formula.

    84 square centimeters (cm2)

    The semi-perimeter is s = (13 + 14 + 15)/2 = 21. Heron's formula gives Area = √(s(s-a)(s-b)(s-c)) = √(21 × 8 × 7 × 6) = √7056 = 84 cm2.

26. 26. Find the curved surface area of a cone with radius 7 cm and slant height 10 cm. Take pi = 22/7.

    220 square centimeters (cm2)

    The curved surface area of a cone is pi × r × l. Substituting the values: (22/7) × 7 × 10 = 22 × 10 = 220 cm2.

27. 27. Find the volume of a sphere with radius 3 cm. Take pi = 22/7.

    ≈113.14 cubic centimeters (792/7 cm3)

    The volume of a sphere is (4/3) × pi × r^3. Substituting the values: (4/3) × (22/7) × 27 = 2376/21 = 792/7, which is approximately 113.14 cm3.

28. 28. An angle inscribed in a semicircle is always which type of angle?

    A right angle (90 degrees)

    This is a standard circle theorem: any angle subtended by a diameter at a point on the circle is always a right angle.

29. 29. A die is thrown once. What is the probability of getting a number greater than 4?

    1/3

    The numbers greater than 4 on a standard die are 5 and 6, giving 2 favorable outcomes out of 6 total outcomes: 2/6 = 1/3.

30. 30. In a survey of 50 families, 20 own a car. Find the experimental probability that a randomly selected family owns a car.

    2/5 (or 0.4)

    Experimental probability is the number of favorable observations divided by the total number of observations: 20/50, which simplifies to 2/5.

Curriculum Mapping & Learning Guide

Use this breakdown to identify which skills each question tests and guide post-test review.

Class 9 Math chapters covered

1. Chapter 1: Number Systems: Classifying rationals and irrationals, and simplifying surd expressions.
2. Chapter 2: Polynomials: Finding degree and zeros, and applying the Remainder and Factor Theorems.
3. Chapter 3: Coordinate Geometry: Locating quadrants and plotting points on a Cartesian plane.
4. Chapter 4: Linear Equations in Two Variables: Finding and checking solutions, and standard form.
5. Chapter 5: Euclid's Geometry & Lines: Postulates, parallel lines, and transversal angle pairs.
6. Chapter 6: Triangles & Circles: Congruence criteria, isosceles properties, and circle theorems.
7. Chapter 7: Mensuration & Probability: Heron's formula, cone and sphere volumes, and simple probability.

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