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Exam 12: What Is Algebra

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Question 21

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Calculate the sum and product of the pairs of polynomials. A) $4 x ^ { 2 } + {}^{-} 7 x + 3 \text { and } 3 x + 5$ B) $5 x + {}^{-} 6 \text { and } {}^{-} 3 x + 7$

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A) The sum is , and the produc...

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Question 22

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Make a drawing of a balance for the equation $4 x + 5 = 5 x + 3$ . Solve the equation by showing actions with the balance, one step at a time.

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Question 23

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For each situation, write an equation using a variable. Then solve the equation to answer the question. A) Krista has 4 more T-shirts than Leeann has, and Marika has 2 fewer T-shirts than Leeann has. The three students have 20 T-shirts in all. How many T-shirts does each have? B) The entry fee at the fair is $5, and ride tickets cost 75¢ each. Pat spent $19.25 in all, for entry and ride tickets. How many ride tickets did Pat buy?

What is the difference between an arithmetic sequence and a geometric sequence?

Two students have been looking for a function rule for the data below. n | f(n) 1 3 2 5 3 8 4 12 Akeena: "I got f(n) = $\frac { 1 } { 2 }$ n(n +1) + 2." Bea: "Yes, but my mom worked a long time on it and said f(n) = $\frac { 1 } { 2 }$ n(n + 1) + 2 + (n - 1)(n - 2)(n - 3)(n - 4). Let's ask the teacher." How would you respond to the two students?

Give the first four numbers of each of the following sequences. A) An arithmetic sequence with first term 19 and difference 20 B) A geometric sequence with first term 1.2 and ratio 3

Use $a ^ { m } \cdot a ^ { n } = a ^ { m + n }$ to justify defining $a ^ { \frac { 1 } { 2 } }$ = $\sqrt{a}$

Find a likely function rule for each of the following. Show your work. A) $\begin{array} { | l | l | } \hline x & f ( x ) \\\hline 2 & 15 \\\hline 3 & 19 \\\hline 4 & 23 \\\hline 5 & 27 \\\hline \ldots & \ldots \\\hline\end{array}$ f(x)= B) $\begin{array} { | l | l | } \hline x & y \\\hline 1 & 14 \\\hline 2 & 11 \\\hline 3 & 8 \\\hline 4 & 5 \\\hline \ldots & \ldots \\\hline\end{array}$ y= C) $\begin{array} { | l | l | } \hline x & g ( x ) \\\hline 4 & 29 \\\hline 3 & 21 \\\hline 1 & 5 \\\hline 2 & 13 \\\hline \ldots & \ldots \\\hline\end{array}$ g(x)= D) $\begin{array} { | l | l | } \hline x & y \\\hline 0 & 5 \\\hline 1 & 6 \\\hline 2 & 9 \\\hline 3 & 14 \\\hline 4 & 21 \\\hline \ldots & \ldots \\\hline\end{array}$ y=