Key Topics Practice

A tour across six important Class 10 areas: Real Numbers, Quadratic Equations, Introduction to Trigonometry, Pair of Linear Equations, Arithmetic Progressions, and Coordinate Geometry. We’ll work through these together on the board.

1Real Numbers

Question 1

Use Euclid’s Division Algorithm to find the HCF of 4052 and 12576.

Question 2

Prove that √3 is an irrational number.

2Quadratic Equations

Question 3

Solve the quadratic equation 2x² − 5x + 3 = 0 by factorisation.

Question 4

For the equation 3x² − 4x + 1 = 0:

(a) Find the discriminant and state the nature of the roots.
(b) Solve the equation using the quadratic formula.

3Introduction to Trigonometry

Question 5

In a right triangle, if sin A = 3/5, find the values of cos A and tan A.

Question 6

Evaluate: 2 tan²45° + cos²30° − sin²60°

4Pair of Linear Equations in Two Variables

Question 7

Solve for x and y using the substitution method: x + y = 14 and x − y = 4.

Question 8

Solve for x and y using the elimination method: 3x + 2y = 11 and 2x + 3y = 4.

5Arithmetic Progressions

Question 9

Find the 10th term of the AP: 2, 7, 12, 17, …

Question 10

Find the sum of the first 15 terms of the AP: 3, 7, 11, …

6Coordinate Geometry

Question 11

Find the distance between the points (3, 4) and (7, 1).

Question 12

Find the coordinates of the point which divides the line segment joining (2, 3) and (7, 8) internally in the ratio 2 : 3.