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Section 10.2 Worksheets

PDF Version of these Worksheets

Worksheet Worksheet 1
A4US

1.

Consider the expression \((x + 2)(x - 5)\text{.}\) Describe the "big picture" perspective of the expression and put boxes around the terms as appropriate.

2.

Consider the expression \(x + 2(x - 5)\text{.}\) Describe the "big picture" perspective of the expression and put boxes around the terms as appropriate.

3.

Determine whether you think the following equation is valid. Explain your reasoning.

\begin{equation*} \sin(x + y) = \sin(x) + \sin(y) \end{equation*}

4.

Solve the equation \(x \ln(2) + 3 = -4\text{.}\) Do it once using a substitution for then do it without a that substitution. Use a complete presentation both times.

Worksheet Worksheet 2
A4US

1.

Consider the expression \(2x(x - 3) + 4\text{.}\) Describe the "big picture" perspective of the expression and put boxes around the terms as appropriate.

2.

Evaluate the expression \(2x(x - 3) - 5\) when \(x = 2\text{.}\) Use a complete presentation.

3.

Check the presentation for errors. If you find one, circle it and describe the mistake in words.

\begin{equation*} \begin{aligned} 3x + f(4) \amp = f(10) \\ 3x + 4 \amp = 10 \amp \eqnspacer \amp \text{Cancel out the $f$} \\ 3x \amp = 6 \amp \amp \text{Subtract $4$ from both sides} \\ x \amp = 2 \amp \amp \text{Divide both sides by $3$} \end{aligned} \end{equation*}

4.

Check the presentation for errors. If you find one, circle it and describe the mistake in words.

\begin{equation*} \begin{aligned} \exp(x) + 3 \amp = 8 \\ \exp(x) \amp = 5 \amp \eqnspacer \amp \text{Subtract $3$ from both sides} \\ x \amp = \frac{5}{\exp} \amp \amp \text{Divide both sides by $\exp$} \\ \end{aligned} \end{equation*}

Worksheet Worksheet 3
A4US

1.

Consider the expression \((x + 1)^2 - (x - 1)^2\text{.}\) Describe the "big picture" perspective of the expression and put boxes around the terms as appropriate.

2.

Check the presentation for errors. If you find one, circle it and describe the mistake in words.

\begin{equation*} \begin{aligned} (x + 4)^2 - (x - 3)^2 \amp = (x^2 + 16) - (x^2 - 9) \amp \eqnspacer \amp \text{Distribute the square} \\ \amp = x^2 - x^2 + 16 + 9 \amp \amp \text{Rearrange the terms} \\ \amp = 25 \amp \amp \text{Combine like terms} \end{aligned} \end{equation*}

3.

Simplify the expression \((x + 1)^2 - (x - 1)^2\) using a complete presentation.

4.

Solve the equation \(2 \tan(x) - 5 = -3\) for Do it once using a substitution for then do it without that substitution. Use a complete presentation both times.

Worksheet Worksheet 4
A4US

1.

Check the presentation for errors. If you find one, circle it and describe the mistake in words.

\begin{equation*} \begin{aligned} 6 \exp(2) \amp = 10 \\ x \amp = \frac{10}{\exp(2)} \amp \eqnspacer \amp \text{Divide both sides by $\exp(2)$} \\ x \amp = \frac{5}{\exp(1)} \amp \amp \text{Reduce} \end{aligned} \end{equation*}

2.

Solve the equation \(ax + b = c\) for the variable using a complete presentation.

3.

Check the presentation for errors. If you find one, circle it and describe the mistake in words.

\begin{equation*} \begin{aligned} x \log(5) \amp = \log(7) \\ x \amp = \frac{\log(7)}{\log(5)} \amp \eqnspacer \amp \text{Divide both sides by $\log(5)$} \\ x \amp = \frac{7}{5} \amp \amp \text{Cancel out the $\log$} \end{aligned} \end{equation*}

4.

Solve the equation \(2 \log(x) = \log(x) + 5\) for Do it once using a substitution for then do it without that substitution. Use a complete presentation both times.

Worksheet Worksheet 5
A4US

1.

Solve the equation \(ax + b = cx + d\) for the variable using a complete presentation.

2.

Solve the equation \(x\sin(1) + \cos(2) = x \ln(3) - f(4)\text{.}\) Use a complete presentation.

3.

Solve the equation \(3\ln(x) + \ln(4) = 8\) for Use a complete presentation.

4.

Solve the equation \(3x + \log(6) = \exp(3)\text{.}\) Use a complete presentation.