Test on Fundamental Mathematics Concepts

Question 1: The product of two negative integers results in a positive integer.

A. Ano

B. Ne

Explanation: According to the rules for multiplication and division, a negative integer multiplied by a negative integer equals a positive integer.

Question 2: When applying an exponent to a fraction, the exponent only applies to the numerator.

A. Ano

B. Ne

Explanation: The rule for exponents with fractions states that (a/b)^n = a^n/b^n, meaning the exponent applies to both the numerator and the denominator.

Question 3: The product of two exponents with the same base, such as x^a imes x^b, simplifies to x^{a+b}.

A. Ano

B. Ne

Explanation: The study materials provide two rules for the product of exponents with the same base: the 'PRODUCT RULE' states x^a imes x^b = x^{(a imes b)}, and the 'EXPONENT RULE' states x^a imes x^b = x^{(a-b)}. Neither of these rules indicates that the product simplifies to x^{a+b}.

Question 4: Which of the following expressions is equivalent to 7(2y - 4)?

A. 14y - 4

B. 7(2y) - 4

C. 14y - 28

D. 9y - 28

Explanation: To simplify the expression 7(2y - 4), apply the Distributive Law. Multiply the term outside the parentheses by each term inside: 7 times 2y equals 14y, and 7 times -4 equals -28. Therefore, 7(2y - 4) simplifies to 14y - 28.

Question 5: What is the solution for x in the equation 2(x - 3) = x + 1?

A. x = 7

B. x = -5

C. x = 5

D. x = -7

Explanation: To solve the equation 2(x - 3) = x + 1, first apply the distributive law to the left side: 2 times x minus 2 times 3 equals 2x - 6. The equation becomes 2x - 6 = x + 1. Next, to get the variable alone, subtract x from both sides: 2x - x - 6 = x - x + 1, which simplifies to x - 6 = 1. Finally, add 6 to both sides: x - 6 + 6 = 1 + 6, resulting in x = 7.