Why maths practice needs to show its work

A maths answer without steps teaches nothing — a student who gets a mark scheme question wrong usually made an error in one specific step (a sign flip, a missed unit conversion, a wrong substitution), not in the whole method. That's why every generated question here comes with a full working, not just a final number: it lets you find the exact line where a method breaks down instead of just re-reading the question and guessing what went wrong.

Paste questions from a single chapter to drill one technique (factoring, trigonometric ratios, calculus rules), or mix chapters to simulate how board and competitive papers actually combine topics in a single multi-step problem.

Class 10 & JEE Foundation Mathematics Starter Set

Click the button below to translate these algebraic and geometric samples into an active practice test.

1. Find the roots of the quadratic equation: x² - 5x + 6 = 0
2. A cylinder has a radius of 7 cm and height of 10 cm. Find its volume. (Use π = 22/7)
3. If sin θ = 3/5, find cos θ and tan θ.
4. Two trains start from stations A and B simultaneously. Train A travels at 60 km/h and Train B at 80 km/h. If the distance between A and B is 280 km, in how many hours will they meet?
5. Find the value of: log₂(64)
6. Find the HCF and LCM of 24 and 36.
7. A fair die is rolled once. What is the probability of getting an even number?
8. Find the distance between the points A(2, 3) and B(5, 7).
9. Find the compound interest on ₹10,000 at 10% per annum for 2 years (compounded annually).
10. Solve the simultaneous equations: 2x + 3y = 12 and x − y = 1.
11. Find the sum of the first 20 natural numbers.
12. Find the surface area of a sphere of radius 7 cm. (Use π = 22/7)
13. Solve: |x − 3| = 5
14. Find the mean of the data: 5, 8, 12, 15, 20.
15. Differentiate y = x³ + 2x² − 5x + 7 with respect to x.
16. Find the area of a triangle with base 12 cm and height 9 cm.
17. Solve the quadratic equation using the quadratic formula: 2x² − 7x + 3 = 0.
18. A ladder 10 m long rests against a vertical wall with its foot 6 m from the wall. Find the height at which the top touches the wall.
19. Find the 10th term of the arithmetic progression: 3, 7, 11, 15, ...
20. Simplify: (2x³y²) × (3x²y⁴).
21. If the perimeter of a rectangle is 60 cm and its length is 18 cm, find its width and area.
22. Evaluate: ∫(4x³ − 6x + 5) dx.
23. Find the median of the data set: 12, 15, 9, 21, 18, 7, 24.
24. Two dice are rolled together. Find the probability of getting a sum of 8.
25. Find the value of x: 2ˣ = 32.
26. Find the curved surface area of a cone with radius 7 cm and slant height 10 cm. (Use π = 22/7)
27. Solve for x and y: x + y = 10 and x − y = 4.
28. Find the discriminant of the quadratic equation x² + 4x + 4 = 0 and state the nature of its roots.
29. A number is increased by 25% and then decreased by 20%. Find the net percentage change.
30. Find the length of the diagonal of a rectangle with sides 8 cm and 6 cm.

Feel free to input your own challenging equations to construct custom drills of similar complexity.

Answer key & worked solutions

Detailed worked examples and formulas for each sample problem. Study these steps, then activate the generator to practice similar variations.

• Q1: Factorise: x² − 5x + 6 = (x − 2)(x − 3) = 0. Roots are x = 2 and x = 3.
• Q2: Volume of a cylinder V = πr²h = (22/7) × 7² × 10 = (22/7) × 49 × 10 = 1540 cm³.
• Q3: For a 3-4-5 right triangle, if sin θ = 3/5 then cos θ = 4/5 and tan θ = sin θ / cos θ = 3/4.
• Q4: They move toward each other, so relative speed = 60 + 80 = 140 km/h. Time to meet = 280 / 140 = 2 hours.
• Q5: 64 = 2⁶, therefore log₂(64) = 6.
• Q6: 24 = 2³ × 3 and 36 = 2² × 3². HCF = 2² × 3 = 12. LCM = 2³ × 3² = 72.
• Q7: Even outcomes: {2, 4, 6} = 3 favourable. Total outcomes = 6. Probability = 3/6 = 1/2.
• Q8: Distance = √[(5 − 2)² + (7 − 3)²] = √(9 + 16) = √25 = 5 units.
• Q9: Amount A = P(1 + R/100)ⁿ = 10000 × (1.1)² = 10000 × 1.21 = ₹12,100. Compound interest = 12100 − 10000 = ₹2,100.
• Q10: From x − y = 1 ⇒ x = y + 1. Substitute: 2(y + 1) + 3y = 12 ⇒ 5y = 10 ⇒ y = 2, x = 3.
• Q11: Sum = n(n + 1)/2 = 20 × 21 / 2 = 210.
• Q12: Surface area = 4πr² = 4 × (22/7) × 49 = 616 cm².
• Q13: |x − 3| = 5 ⇒ x − 3 = 5 or x − 3 = −5 ⇒ x = 8 or x = −2.
• Q14: Mean = (5 + 8 + 12 + 15 + 20) / 5 = 60 / 5 = 12.
• Q15: dy/dx = 3x² + 4x − 5.
• Q16: Area = ½ × base × height = ½ × 12 × 9 = 54 cm².
• Q17: Using x = [−b ± √(b² − 4ac)] / 2a with a=2, b=−7, c=3: x = [7 ± √(49 − 24)] / 4 = [7 ± 5] / 4, giving x = 3 or x = 0.5.
• Q18: By Pythagoras' theorem: height² = 10² − 6² = 100 − 36 = 64, so height = 8 m.
• Q19: First term a = 3, common difference d = 4. 10th term = a + (n−1)d = 3 + 9(4) = 3 + 36 = 39.
• Q20: (2x³y²) × (3x²y⁴) = 6x⁵y⁶ (multiply coefficients, add exponents of like bases).
• Q21: Perimeter = 2(l + w) ⇒ 60 = 2(18 + w) ⇒ 30 = 18 + w ⇒ w = 12 cm. Area = 18 × 12 = 216 cm².
• Q22: ∫(4x³ − 6x + 5) dx = x⁴ − 3x² + 5x + C, where C is the constant of integration.
• Q23: Arrange in order: 7, 9, 12, 15, 18, 21, 24. With 7 values, the median is the 4th value = 15.
• Q24: Pairs summing to 8 out of 36 total outcomes: (2,6),(3,5),(4,4),(5,3),(6,2) = 5 outcomes. Probability = 5/36.
• Q25: 32 = 2⁵, so 2ˣ = 2⁵ ⇒ x = 5.
• Q26: Curved surface area = πrl = (22/7) × 7 × 10 = 220 cm².
• Q27: Adding both equations: 2x = 14 ⇒ x = 7. Substituting back: 7 + y = 10 ⇒ y = 3.
• Q28: Discriminant D = b² − 4ac = 16 − 16 = 0. Since D = 0, the equation has two equal (real and coincident) roots.
• Q29: Let the number be 100. After +25%: 125. After −20%: 125 × 0.8 = 100. Net change = 0% (no overall change).
• Q30: Diagonal = √(8² + 6²) = √(64 + 36) = √100 = 10 cm.

Tips for Maths Practice

• ✓Paste questions from a single chapter (e.g. Trigonometry) for focused topic practice.
• ✓Set difficulty to Tough for JEE, competitive exam, or board-level problems.
• ✓Use the timer to simulate real exam conditions and improve speed.
• ✓Read the step-by-step explanation after every question — even the ones you got right.
• ✓Use 'Retry Weak Areas' after each test to drill only the questions you missed.

The full maths ladder, class by class

Same subject, every level — from foundational arithmetic to senior-secondary calculus.

• Class 6 Math practice test— step-by-step solved problems
• Class 8 Math practice test— step-by-step solved problems
• Class 9 Math practice test— step-by-step solved problems
• Class 10 Math practice test— step-by-step solved problems
• Class 11 Math practice test— step-by-step solved problems
• Class 12 Math practice test— step-by-step solved problems

Frequently Asked Questions