The control works in this curriculum are typically divided into four variants (levels of difficulty) and cover the following key topics for Grade 10:

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

. This prevents "extraneous solutions" that could lead to a grade deduction.

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

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