| Topic | Problem | Solution |
|---|---|---|
| None | \( 2 \quad 5 \) points An atom of uranium-235 (of… | Since momentum is conserved, we have \( m_{\text{Th}}v_{\text{Th}} = m_{\text{He}}v_{\text{He}} \). |
| None | find the zeros of \( 3 x^{2}+13 x-10=0 \) | \( \Delta = b^{2} - 4 a c \) |
| None | \( 7^{3 x-6}+100=101 \) | \( 7^{3 x-6} = 1 \) |
| None | If the central angle whose measure \( 110^{\circ}… | \( \text{Central angle} = 110^{\circ} \) |
| None | \( 0 \div 9= \) \( \frac{0}{6}= \) | \( \frac{0}{9}=0 \) |
| None | A bag with 8 marbles has 4 fed -marbles, 3 bluo f… | 1. Calculate total number of marbles: 4 red + 3 blue + 1 yellow = 8 |
| None | Solve and graph the solution: \[ |3 x+4| \geq 13 … | 1. \( 3x + 4 \geq 13 \) or \( 3x + 4 \leq -13 \) |
| None | Write the number in standard (decimal) notation: … | \( 9.73 \times 10^{-2} \) |
| None | Write the number in scientific notation: \[ 0.091… | \(0.0913 = 9.13 \times 10^{-2}\) |
| None | \( \int(\sqrt[3]{x} \cdot \sqrt[2]{x}) x d x \) | \( = \int(x^{\frac{1}{3}} \cdot x^{\frac{1}{2}}) dx \) |
| None | A number \( b \) is at most 18 . | \(b \leq 18\) |
| None | If a \( 15 \mathrm{~kg} \) ball takes 54 seconds … | 1. \( t = 54 \mathrm{~s} \) |
| None | Roll two dice virtually (by calculator: [APP] 10.… | Roll the two dice virtually for \( n \) times, where \( n = 36, 50, 100, 1000, 10000 \). Record the… |
| None | Find the equation of the tangent line to \( g(x)=… | \(g'(x)=3x^{2}\) |
| None | A particle moves according to the equation \( x=1… | \(v(t) = \frac{dx}{dt} = 144t^{8}\) |
| None | The position of a particle moving along \( x \) a… | \(x(t) = t^3 + 8t^2 + 35\) |
| None | [2] \( \int\left(4 \sqrt{x}+\frac{8}{\sqrt{x}}\ri… | \(\int\left(4 \sqrt{x}+\frac{8}{\sqrt{x}}\right) dx = \int(4x^{\frac{1}{2}}+8x^{-\frac{1}{2}}) dx\) |
| None | Find the surface area of the surface generated by… | \int_{0}^{1} 2\pi y \sqrt{1+{\left( \frac{dy}{dx} \right)}^2} dx |
| None | \( { }_{7}^{14} \mathrm{~N} \) How many neutrons … | \(N - Z\) |
| None | \( { }_{6}^{13} C \) What is the atomic mass of t… | \({ }_{6}^{13}C\) |
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