Test on Fundamental Algebraic Operations
Fundamental Algebraic Operations: Guide for Students
Test: Algebraic Expressions and Factoring
20 questions
Question 1: The factorization of the expression 4x^2 + 5x is given by π(4x + 5).
A. Yes
B. No
Explanation: According to the study materials, the expression 4x^2 + 5x is shown as factored into π(4x + 5). However, a correct factorization would involve factoring out 'x', resulting in x(4x + 5), not π(4x + 5).
Question 2: The expression a^2 - 2a can be factored as a(a - 2).
A. Yes
B. No
Explanation: The study materials show 'a^2 - 2a = a(a - 2)' under the 'factorising' section, demonstrating that 'a' is the common factor taken outside the brackets.
Question 3: The algebraic statement '4c + 3e' is classified as a formula within the provided study materials.
A. Yes
B. No
Explanation: The study materials categorize '4c + 3e' as an expression, not a formula.
Question 4: In the equation 2x - 15 + 7x - 3 = 90, the final solution for x is 108.
A. Yes
B. No
Explanation: The study material shows that for the equation 2x - 15 + 7x - 3 = 90, after combining like terms (2x + 7x and -15 - 3), it simplifies to 9x - 18 = 90. Adding 18 to both sides gives 9x = 108. Dividing by 9 yields x = 12, not 108.
Question 5: To solve the equation 3(x + 3) = 24, one of the initial steps is to apply the distributive property, resulting in 3x + 9 = 24.
A. Yes
B. No
Explanation: The study materials show the steps for solving 3(x + 3) = 24, where the first transformation is to expand the left side using the distributive property, yielding 3x + 9 = 24.