1. Let's start by understanding that your request covers multiple units with formulas, questions, answers, and a test. 2. Since this is a broad request, I will provide a structured approach for one unit as an example: Algebra - Quadratic Equations. 3. Formulas: - Standard form: $ax^2 + bx + c = 0$ - Quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ - Discriminant: $\Delta = b^2 - 4ac$ 4. Example question: Solve $2x^2 - 4x - 6 = 0$. 5. Solution steps: 1. Identify coefficients: $a=2$, $b=-4$, $c=-6$. 2. Calculate discriminant: $\Delta = (-4)^2 - 4 \times 2 \times (-6) = 16 + 48 = 64$. 3. Apply quadratic formula: $$x = \frac{-(-4) \pm \sqrt{64}}{2 \times 2} = \frac{4 \pm 8}{4}$$ 4. Calculate roots: - $x_1 = \frac{4 + 8}{4} = \frac{12}{4} = 3$ - $x_2 = \frac{4 - 8}{4} = \frac{-4}{4} = -1$ 6. Test question: Solve $x^2 + 6x + 5 = 0$ using the quadratic formula. 7. Answer for test question: - $a=1$, $b=6$, $c=5$ - $\Delta = 6^2 - 4 \times 1 \times 5 = 36 - 20 = 16$ - $$x = \frac{-6 \pm \sqrt{16}}{2} = \frac{-6 \pm 4}{2}$$ - Roots: - $x_1 = \frac{-6 + 4}{2} = \frac{-2}{2} = -1$ - $x_2 = \frac{-6 - 4}{2} = \frac{-10}{2} = -5$ This example shows how to learn a unit with formulas, example questions, solutions, and a test question. If you want, I can continue with other units similarly.