Chapter 1: Number Systems

Q1. Express 0.375 as a fraction in the simplest form.

Q3. Simplify: $$(\sqrt{8} + \sqrt{18}) – (\sqrt{2} + \sqrt{50})$$

Q5. Rationalize the denominator of the expression: $$\frac{5}{2 + \sqrt{3}}$$

Chapter 2: Polynomials

Q1. Find the zeros of the polynomial: $$3x^2 – 6x + 2$$

Q2. Divide $$2x^3 – 9x^2 + 5x – 6$$ by $$x – 3$$ and verify the division.

Q4. Factorize: $$x^3 – 27x$$ = $$x(x^2 – 27)$$ = $$x(x – 3\sqrt{3})(x + 3\sqrt{3})$$

Q5. Prove that $$(x – 2)$$ is a factor of $$2x^3 – 5x^2 – 4x + 8$$

Chapter 5: Heron’s Formula

Q5. Find the area of an equilateral triangle with side $10$ cm using Heron’s formula.

Chapter 6: Statistics

Q2. The following table shows the distribution of weights (in kg) of students in a school:

Draw a histogram representing the given data with the discontinuous class intervals and convert them into continuous form for constructing a frequency polygon.