mathematics beginner 10 sample questions

Algebraic Expressions MCQ Practice Test

Mathematical phrases with variables

Q1. Given the algebraic expression 3(x^2 + 2x - 3) - 2(x^2 - 4x - 7), what is the resulting expression after combining like terms?

Explanation: Distribute: 3(x^2 + 2x - 3) = 3x^2 + 6x - 9 and -2(x^2 - 4x - 7) = -2x^2 + 8x + 14. Combine like terms: (3-2)x^2 + (6+8)x + (-9+14) = x^2 + 14x + 5.

Q2. If x² - 3x + 1 = 0, what is the value of x + 1/x?

Explanation: Divide the equation by x (x ≠ 0): x - 3 + 1/x = 0, so x + 1/x = 3 — true for both roots, since the equation was built so the expression is single-valued. The old stem paired x² + 5x - 6 = 0 (roots 1 and -6, giving 2 or -37/6) with options that matched neither, and its LaTeX was broken.

Q3. If f(x) = sqrt(16x^2 + 9), what is the value of f(-1)?

Explanation: Substitute x = -1: f(-1) = sqrt(16(-1)^2 + 9) = sqrt(16 + 9) = sqrt(25) = 5. Because the radical symbol denotes the principal (non-negative) root, the value is 5, not -5.

Q4. Given the algebraic expression −2x² + 5x + 3, what is the value of the coefficient of the linear term?

Explanation: In the given expression −2x² + 5x + 3, the linear term is 5x. The coefficient of a term is the numerical value multiplied by the variable. In this case, the coefficient of the linear term is 5.

Q5. If x² + 2x − 6 = 0, what is the value of (x + 1)²?

Explanation: (x + 1)² = x² + 2x + 1 = (x² + 2x − 6) + 7 = 0 + 7 = 7.

Q6. Given the expression 2(x² + 2x) + 3(x² + 2x) − 2(x − 3), what is the result after combining like terms?

Explanation: Distribute first: 2(x² + 2x) = 2x² + 4x and 3(x² + 2x) = 3x² + 6x, while −2(x − 3) = −2x + 6. Grouping like terms: (2x² + 3x²) + (4x + 6x − 2x) + 6 = 5x² + 8x + 6.

Q7. What is the simplified form of the algebraic expression ⚑(3x² + 2x) - 2(2x² + 3x) + x²?

Explanation: To simplify the expression, we need to distribute the coefficients inside the parentheses, then combine like terms. Distributing the coefficients, we get: 3x² + 2x - 4x² - 6x + x². Combining like terms, we get: -4x² + 3x² + 2x - 6x + x² = x² - 7x

Q8. If x² + 6x + 11 = (x + a)² + b, what are the values of a and b?

Explanation: (x + 3)² = x² + 6x + 9, so x² + 6x + 11 = (x + 3)² + 2 — that is, a = 3 and b = 2. The old stem equated the square root of a quadratic with a completed square, which is algebraically impossible, and its equations did not resolve.

Q9. What is the simplified form of the expression (x² + 2x − 3) + 2(x² − 4x + 2)?

Explanation: Expanding: x² + 2x − 3 + 2x² − 8x + 4 = 3x² − 6x + 1. The old stem carried a stray '✎' glyph in place of a coefficient, and none of the old options matched the true simplification.

Q10. What are the roots of x² + 5x + 6 = 0?

Explanation: Factoring: (x + 2)(x + 3) = 0, so x = −2 or x = −3.

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Algebraic Expressions MCQ Practice Test | Mind Hustle