Class 10 Algebra MCQs Quiz

Class 10 Maths Algebra MCQs

In Class 10, algebra forms an essential part of your mathematics journey. To help you deepen your understanding and practice this subject, let's delve into some algebra-focused multiple-choice questions (MCQs) that you may encounter.

Solving Linear Equations

1. What is the solution to the linear equation (3x - 7 = 17)? a) (x = -2) b) (x = -0.857) c) (x = 5) d) (x = 2.286)

Answer: a) (x = -2)

Explanation: To solve (3x - 7 = 17), add 7 to both sides, resulting in (3x = 24 \to x = 8/3 \to x = -2) since (3) is negative and the solution must be the opposite sign.

2. The value of (x) that satisfies the equation (2x + 1 = 5x - 3) is a) (x = 2) b) (x = 4) c) (x = -1) d) (x = \frac{1}{2})

Answer: c) (x = -1)

Explanation: To solve (2x + 1 = 5x - 3), subtract (2x) from both sides, resulting in (3x = 2 \to x = 2/3 \to x = -1) since we are subtracting a positive number from both sides, and the solution must be the opposite sign.

Linear Inequalities

3. Which of the following inequalities is satisfied by the solution set of the equation (2x + 1 \geq -3x + 4)? a) (x \leq 2) b) (x \geq -1) c) (x \leq -0.5) d) (x \geq 0.5)

Answer: b) (x \geq -1)

Explanation: To solve (2x + 1 \geq -3x + 4), subtract (2x) from both sides, resulting in (3x \geq 5 \to x \geq 5/3 \to x \geq -1) since we are subtracting a positive number from both sides, and the solution must retain the inequality sign.

4. The solution set of the inequality (3x - 1 \leq 2x + 3) is a) ([-\infty, 2]) b) ([2, \infty)) c) ([-1, \infty)) d) ([-3/2, 1])

Answer: d) ([-3/2, 1])

Explanation: To solve (3x - 1 \leq 2x + 3), subtract (2x) from both sides, resulting in (-x \leq 4 \to x \leq -4 \to x \geq 3/2) since we are subtracting a negative number from both sides, and the solution must retain the inequality sign. Therefore, the solution set is all (x) values greater than or equal to (3/2) and less than or equal to 2, or ([3/2, 2]). However, since we are given a "(\leq)" inequality, the endpoint of 2 is excluded, leaving us with ([-3/2, 1]).

Quadratic Equations

5. The root of the quadratic equation (x^2 + 2x - 3 = 0) is a) (x = 1) b) (x = -3) c) (x = -1.5) d) (x = 2)

Answer: b) (x = -3)

Explanation: To find the roots of the quadratic equation (x^2 + 2x - 3 = 0), we can use the quadratic formula (x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}). In this case, (a = 1), (b = 2), and (c = -3). Plugging these values into the formula, we get (x = \frac{-2 \pm \sqrt{2^2 - 4(1)(-3)}}{2(1)} = \frac{-2 \pm \sqrt{4 + 12}}{2} = \frac{-2 \pm \sqrt{16}}{2} = \frac{-2 \pm 4}{2} = -3) or (\frac{-2 + 4}{2} = 1). However, since the question asks for roots, we choose (-3).

6. The graph of the quadratic equation (y = x^2 + 2x - 3) has a vertex at a) ((-2, 5)) b) ((3, -2)) c) ((-3, 2)) d) ((1, -1))

Answer: c) ((-3, 2))

Explanation: To find the vertex of a parabola in the form (y = ax^2 + bx + c), we can use the formula (x_{vertex} = -\frac{b}{2a}). In this case, (a = 1) and (b = 2), so (x_{vertex} = -\frac{2}{2(1)} = -1). To find the corresponding (y)-value, substitute (x = -1) into the equation, resulting in (y = (-1)^2 + 2(-1) - 3 = 1 - 2 - 3 = -2). Therefore, the vertex is at ((-1, -2)). However, since the equation is in the form (y = x^2 + 2x - 3), we need to shift the vertex one unit to the left, resulting in ((-3, 2)).

Simplifying Expressions

7. The expression (\frac{3(x + 4)}{x - 3