GenMath Grade 11 Exam (GMAT2111)
AMA OED ANSWERLogarithmic Expressions
Question 1: Evaluate the logarithmic expression: 3 log9 x^2 = 6 log9 x
Question 2: Evaluate the logarithmic expression: (log3 2)(log3 4) = log3 8
Question 3: Evaluate the logarithmic expression: 3(log9 x)^2 = 6 log9 x
Question 4: Find the value of each logarithmic expression: log7 (7^3 · 7^8) and log7 7^3 + log7 7^8
Question 5: Without using a calculator, find the value of the logarithmic expression: log1/2 16
Question 6: Evaluate the logarithmic expression: (log3 2)(log3 4) = log3 6
Question 7: Find the value of each logarithmic expression: log7 7^5 and 5 · log7 7
Question 8: Evaluate the logarithmic expression: (log3 2)(log3 4) = log3 8
Question 9: Find the value of each logarithmic expression: log3 (27 · 81) and log3 27 + log3 81
Question 11: Without using a calculator, find the value of the logarithmic expression: log9 729
Question 12: Without using a calculator, find the value of the logarithmic expression: log7 1
Question 13: Evaluate the logarithmic expression: log3 2x^2 = 2 log3 2x
Question 14: Without using a calculator, find the value of the logarithmic expression: log2 32
Question 19: Without using a calculator, find the value of the logarithmic expression: log5 5
Question 21: Evaluate the logarithmic expression: log 2^2 = (log 2)^2
Question 22: Find the value of each logarithmic expression: log7 (49/7) and log7 49 - log7 7
Question 24: Find the value of each logarithmic expression: log2 (2^4/2^10) and log2 2 - log2 2^10
Question 25: Evaluate the logarithmic expression: log3 2x^2 = log3 2 + 2 log3 x
Exponential Expressions
Question 15: Simplify the given expression and find the value of x: 2^4 = x
Question 16: Simplify the given expression and find the value of x: 4^3 = x
One-to-One and Inverse Functions
Question 10: The set A = {(-4, 4), (-3, 2), (-2, 1), (0, -1), (1, -3), (2, -5)} of ordered pairs form a function. Find the inverse of this function.
Question 17: The relation pairing a real number to its square is a one-to-one function.
Question 18: Fill in the table that represents the inverse of the function defined by: x = -4, -3, -2, -1, 0, 1, 2, 3, 4; y = -9, -7, -5, -3, -1, 1, 3, 5, 7.
Question 23: The relation pairing an SSS member to his/her SSS number is a one-to-one function.
Stocks and Bonds
Question 20: Tell whether the following is a characteristic of stocks or bonds: (a) A form of equity financing or raising money by allowing investors to be part owners of the company. (b) A form of debt financing, or raising money by borrowing from investors.
Frequently Asked Questions
What are the properties of logarithms used in solving these expressions?
The key logarithm properties include: Product Rule (log_b (xy) = log_b x + log_b y), Quotient Rule (log_b (x/y) = log_b x - log_b y), Power Rule (log_b (x^n) = n log_b x), and Change of Base (log_b x = log_k x / log_k b). These properties simplify complex logarithmic expressions.
What is a one-to-one function?
A one-to-one (injective) function is a function where each element in the domain maps to a unique element in the codomain, and no two different inputs produce the same output. It passes the horizontal line test, and its inverse is also a function.
How do you find the inverse of a function defined by ordered pairs?
To find the inverse of a function defined by ordered pairs, swap the x and y coordinates of each pair. For example, if the function has a pair (a, b), the inverse has the pair (b, a). Ensure the resulting relation is a function (each input has exactly one output).
What is the difference between stocks and bonds?
Stocks represent equity financing, where investors become part owners of a company and may receive dividends. Bonds represent debt financing, where investors lend money to the issuer and receive periodic interest payments (coupons) until the bond matures.
Why is the relation pairing a real number to its square not a one-to-one function?
The relation y = x^2 is not one-to-one because different inputs can produce the same output (e.g., x = 2 and x = -2 both yield y = 4). This violates the requirement that each input maps to a unique output, failing the horizontal line test.