Algebra and Coordinate Geometry Practice Quiz (5 questions)

1. Which statements describe quadratic factorisation?

A. A three-term quadratic is factorised by taking the square root of each term separately.

B. A difference of two squares is factorised by adding its square roots.

C. A difference of two squares can be written as a product of conjugate factors.

D. Some three-term quadratic expressions can be expressed as products of linear factors.

E. Quadratic factorisation requires every term to contain the same variable factor.

Answer: (C), (D)

Explanation

A difference of squares factors into conjugate factors, and suitable three-term quadratics factor into linear factors. Taking square roots term by term, adding the roots, or requiring a common variable factor are not general factorisation rules.

2. When working with powers, which statements are valid?

A. Index rules also cover raising a power to another power.

B. Index rules cover multiplication and division of powers with suitable bases.

C. Fractional indices are included in the rules for manipulating powers.

D. Negative indices are included in the rules for manipulating powers.

E. Fractional indices are outside the scope of power index rules.

Answer: (A), (B), (C), (D)

Explanation

Index rules apply to operations with powers, including multiplication, division, and powers raised to powers; they also cover negative and fractional indices. The claim excluding fractional indices is incorrect.

3. Algebraic fractions can be combined by:

A. Combining their numerators while retaining an appropriate shared denominator.

B. Adding fractions after expressing them with a common denominator.

C. Adding denominators directly while leaving both numerators unchanged.

D. Rewriting fractions before combining them when their denominators differ.

E. Subtracting fractions after expressing them with a common denominator.

Answer: (A), (B), (D), (E)

Explanation

Algebraic fractions can be added and subtracted, typically after rewriting them over a common denominator. Adding the denominators directly while preserving the numerators does not perform either operation correctly.

4. Which statements describe simplification of algebraic fractions?

A. Terms joined by addition can be cancelled across the fraction bar.

B. Common factors may be cancelled whether found in one expression or both.

C. A factor shared by numerator and denominator can reduce the fraction.

D. A common factor in the numerator and denominator can be cancelled.

E. Simplification may cancel a shared factor appearing in both expressions.

Answer: (B), (C), (D), (E)

Explanation

Simplification works by cancelling factors common to the numerator and denominator, and the shared factor may occur in either or both expressions. Individual terms joined by addition are not factors and cannot be cancelled across the fraction bar.

5. Which operation can be performed with algebraic fractions?

A. Algebraic fractions can be multiplied by combining their fractional factors.

B. Multiplying algebraic fractions requires finding a common denominator first.

C. Multiplying two algebraic fractions requires adding their numerators.

D. Dividing algebraic fractions is carried out by multiplying their denominators.

E. Dividing algebraic fractions is performed by subtracting their denominators.

Answer: (A)

Explanation

Algebraic fractions can be multiplied, combining the fractions as a product. Adding numerators, subtracting denominators, requiring a common denominator for multiplication, or multiplying denominators as the division rule are not the stated operations.