9-10th Grade Math Problems

Given that a, b, and c are positive numbers with $a \neq 1$ and $c \neq 1$, how can $log_a b$ be expressed in terms of base c?

According to exponent rules, how does $\frac{a^m}{a^n}$ simplify?

What is the result of rationalizing the denominator of the fraction $\frac{8}{3-\sqrt{5}}$?

A cube has a surface area of 150 cm². What is its volume?

Which function is considered an identity function?

Is the trigonometric identity $sec^2 A = 1 + tan^2 A$ correct?

Evaluate the expression: $sin^2 A + cos^2 A = $ ?

What is the value of $(-i)^2$?

In the context of complex numbers, what does (0,1) represent?

If $f(x) = x^2$ is a real-valued function, what set encompasses its entire domain?

For the function $f(x) = \frac{x}{x^2 - 9}$, for what set of real numbers is the function undefined?

Given $f(x) = \sqrt{x + 1}$, what is the function's domain?

Solve for u: $v^2 = u^2 + 2as$

What is the volume of a sphere with a radius of 7 cm, using the formula $V = \frac{4}{3}πr^3$ and $π = \frac{22}{7}$?

What formula calculates the distance between two points $P_1(x_1, y_1)$ and $P_2(x_2, y_2)$ on a coordinate plane?

Which of the following statements about set inclusion is correct?

Given $f(x) = cos(x)$, what type of function is f(x)?

What is the correct form of the quadratic formula used to solve $ax^2 + bx + c = 0$?

When solving a quadratic equation $ax^2 + bx + c = 0$ (where a, b, c are real numbers and $a \neq 0$ ), which technique is applicable?

Given a quadratic equation $ax^2 + bx + c = 0$, what is the formula to find the sum of its roots?

For a quadratic equation of the form $ax^2 + bx + c = 0$, what is the product of the roots?

What is the null vector in R²?

What condition must be true for a function f: X → Y to be injective (one-to-one)?

If $a_n = {n + (-1)^n}$, what is the value of $a_5$?

If events A and B are mutually exclusive, what is the value of $n(A ∩ B)$?

What is the formula for the sum of the first n natural numbers, represented as Σn?

Calculate $7^n \times 7^m$?

For disjoint events A and B, how is $P(A ∪ B)$ calculated?

If A and B are overlapping events, what formula determines $P(A ∪ B)$?

What is the value of 1 degree expressed in radians?