Chapter 1 Prerequisites
Chapter 1 Practice Test
Chapter Practice Test
For the following exercises, identify the number as rational, irrational, whole, or natural. Choose the most descriptive answer.
- [latex]-13[/latex]
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rational
- [latex]\sqrt{2}[/latex]
For the following exercises, evaluate the equations.
- [latex]2\left(x+3\right)-12=18[/latex]
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[latex]x=12[/latex]
- [latex]y{\left(3+3\right)}^{2}-26=10[/latex]
- Write the number in standard notation:[latex]3.1415\,×\,{10}^{6}[/latex]
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3,141,500
- Write the number in scientific notation: 0.0000000212.
For the following exercises, simplify the expression.
- [latex]-2\cdot {\left(2+3\cdot 2\right)}^{2}+144[/latex]
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[latex]16[/latex]
- [latex]4\left(x+3\right)-\left(6x+2\right)[/latex]
- [latex]{3}^{5}\cdot {3}^{-3}[/latex]
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9
- [latex]{\left(\frac{2}{3}\right)}^{3}[/latex]
- [latex]\frac{8{x}^{3}}{{\left(2x\right)}^{2}}[/latex]
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[latex]2x[/latex]
- [latex]\left(16{y}^{0}\right)2{y}^{-2}[/latex]
- [latex]\sqrt{441}[/latex]
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21
- [latex]\sqrt{490}[/latex]
- [latex]\sqrt{\frac{9x}{16}}[/latex]
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[latex]\frac{3\sqrt{x}}{4}[/latex]
- [latex]\frac{\sqrt{121{b}^{2}}}{1+\sqrt{b}}[/latex]
- [latex]6\sqrt{24}+7\sqrt{54}-12\sqrt{6}[/latex]
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[latex]21\sqrt{6}[/latex]
- [latex]\frac{\sqrt[3]{-8}}{\sqrt[4]{625}}[/latex]
- [latex]\left(13{q}^{3}+2{q}^{2}-3\right)-\left(6{q}^{2}+5q-3\right)[/latex]
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[latex]13{q}^{3}-4{q}^{2}-5q[/latex]
- [latex]\left(6{p}^{2}+2p+1\right)+\left(9{p}^{2}-1\right)[/latex]
- [latex]\left(n-2\right)\left({n}^{2}-4n+4\right)[/latex]
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[latex]{n}^{3}-6{n}^{2}+12n-8[/latex]
- [latex]\left(a-2b\right)\left(2a+b\right)[/latex]
For the following exercises, factor the polynomial.
- [latex]16{x}^{2}-81[/latex]
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[latex]\left(4x+9\right)\left(4x-9\right)[/latex]
- [latex]{y}^{2}+12y+36[/latex]
- [latex]27{c}^{3}-1331[/latex]
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[latex]\left(3c-11\right)\left(9{c}^{2}+33c+121\right)[/latex]
- [latex]3x{\left(x-6\right)}^{-\frac{1}{4}}+2{\left(x-6\right)}^{\frac{3}{4}}[/latex]
For the following exercises, simplify the expression.
- [latex]\frac{2{z}^{2}+7z+3}{{z}^{2}-9}\cdot \frac{4{z}^{2}-15z+9}{4{z}^{2}-1}[/latex]
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[latex]\frac{4z-3}{2z-1}[/latex]
- [latex]\frac{x}{y}+\frac{2}{x}[/latex]
- [latex]\frac{\frac{a}{2b}-\frac{2b}{9a}}{\frac{3a-2b}{6a}}[/latex]
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[latex]\frac{3a+2b}{3b}[/latex]