Before calculating, identify the fundamental theorem required. For example, if solving a trigonometric equation like , first use the Pythagorean identity to create a quadratic equation in terms of cosxcosine x Define the Domain (

When working with derivatives, use the power rule and the chain rule for composite functions. Example Solution: Logarithmic Equation Problem : Solve

: Equations, identities, and transformations of trigonometric expressions. Powers and Roots : Properties of -th degree roots and powers with rational exponents.

The expression inside the log must be positive:

: Solving equations and inequalities involving axa to the x-th power logaxlog base a of x

Based on the definition of a logarithm: Step 3: Solve for . Step 4: Check against domain. Since , the answer is valid. ✅ Final Answer The answer to the example problem is

The official guide for the control works (tests) based on the is titled "Algebra and the Beginnings of Mathematical Analysis. Diadactic Materials for Grade 10" by Potapov and Shevkin. These materials provide multiple versions of control works designed specifically for the Nikolskii curriculum [1]. Structure of the Control Works