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### 2001-C: Symbolic Algebra 1

• Topic Cluster: Pure Mathematics
• Topic: Algebra
• Objective: Solve algebraic equations with one or two steps to find a symbolic answer.
• Content:
• Level: 2

Symbols like $$x$$, $$y$$, and $$z$$ can be manipulated just like numbers can. You can add, subtract, multiply, or divide both sides of an equation by a symbol. To Solve for a variable means that you have only that variable on one side of the equation.

For example, let's say that I have an equation like this: $$Z = X Y^2 + Y^3 X + (Y - X) XY$$ This equation would be referred to as "$$Z$$ in terms of $$X$$ and $$Y$$".

Imagine you have $$Z = \text{some long function that includes } X \text{ and } Y.$$ Imagine that you are able to manipulate the equation so that instead, it looks like this: $$Y = \text{some long function that includes } Z \text{ and } X.$$ This is called "Solving for $$Y$$ in terms of $$X$$ and $$Z$$."

1. Solve for $$B$$:
$$A = B C$$
2. Solve for $$E$$:
$$D = E + F$$
3. Solve for $$G$$:
$$H = G - I$$
4. Solve for $$N$$:
$$M = \frac{N}{O}$$
5. Solve for $$Q$$:
$$P = 5 Q$$
6. Solve for $$L$$:
$$J = K - L$$
7. Solve for $$R$$:
$$\frac{S}{R} = T$$
8. Solve for $$m$$:
$$E = mgh$$
9. Solve for $$h$$:
$$E = mgh$$
10. Solve for $$m$$:
$$E = \frac{1}{2} m v^2$$
11. Solve for $$v$$. Note that there are two solutions.
$$E = \frac{1}{2} m v^2$$
12. Solve for $$F_1$$:
$$F_1 - F_2 = m a$$
13. Solve for $$a$$:
$$F_1 - F_2 = ma$$
14. Solve for $$v_i$$:
$$v_f = v_i + at$$
15. Solve for $$a$$:
$$v_f = v_i + at$$
16. Solve for $$t$$:
$$v_f = v_i + at$$
17. Solve for $$v$$. Note that there are two solutions.
$$a = \pm \frac{v^2}{r}$$
18. Solve for $$r$$:
$$a = \frac{v^2}{r}$$
19. Solve for $$m_1$$:
$$F = \frac{G m_1 m_2}{r^2}$$
20. Solve for $$m_2$$:
$$F = \frac{G m_1 m_2}{r^2}$$
21. Solve for $$r$$. Note that there are two solutions :
$$F = \frac{G m_1 m_2}{r^2}$$

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