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Study Guides > Mathematics for the Liberal Arts

F1.04: Exercises

Part I.

As you work through these, make a page of notes of anything you need to remember about how to use your calculator.
  1. Evaluate each.
    1. [latex]3+4[/latex]
    2. [latex]7-12[/latex]
    3. [latex]12\div4[/latex]
    4. [latex]8\cdot3[/latex]
    5. [latex]\sqrt{36}[/latex]
    1. Find [latex]{{2}^{4}}[/latex]
    2. Find [latex]{{3}^{0.7}}[/latex]
    3. Find [latex]\sqrt[5]{32}={{32}^{{}^{1}\!\!\diagup\!\!{}_{5}\;}}[/latex]
    4. Find [latex]\sqrt[6]{79}={{79}^{{}^{1}\!\!\diagup\!\!{}_{6}\;}}[/latex]
    1. Find [latex]\pi[/latex].
    2. Find [latex]2\pi[/latex]
    3. Evaluate the area of a circle with radius 2: [latex]A=\pi{{r}^{2}}[/latex].
  4. Use a calculator to evaluate each.
    1. [latex]8-6[/latex]
    2. [latex]-6+8[/latex]
  5. Evaluate each of these expressions.
    1. [latex]{{3}^{2x}}[/latex], where [latex]x=3[/latex]
    2. [latex]\sqrt{4x+13}[/latex], where [latex]x=3[/latex]
  6. Evaluate this expression:    [latex]\frac{{{x}^{2}}-6x}{4x+2}[/latex], where [latex]x=3[/latex]
  7. Use a calculator to multiply 8,000,000 by 60,000.
  8. A sofa is priced at $887 in the furniture store. The sales tax is 8.25%.
    1. Estimate the total amount you’ll have to pay with both the cost and the tax.
    2. Use your calculator to compute the total amount you’ll have to pay.
    3. Is your calculator answer close to your estimate?

Part II.

For any problems for which the answers are not whole numbers, round to three decimal places. That will enable you to check the problems without the results being too confusing.   For the algebra problems, use the calculator as needed, including in checking the results.
  1. Evaluate [latex]{{3}^{4}}[/latex]using your calculator’s exponent key and then check it by multiplying by hand.
  2. Evaluate [latex]{{4}^{3}}[/latex]using your calculator’s exponent key and then check it by multiplying by hand.
  3. Evaluate each.
    1. [latex]{{(1.06)}^{22}}[/latex]
    2. [latex]\sqrt[4]{217}={{217}^{{}^{1}\!\!\diagup\!\!{}_{4}\;}}[/latex]
  4. Evaluate each.
    1. [latex]{{(2.13)}^{9}}[/latex]
    2. [latex]\sqrt[7]{383}={{383}^{{}^{1}\!\!\diagup\!\!{}_{7}\;}}[/latex]
  5. Use the [latex]\pi[/latex] key on your calculator when evaluating [latex]3+8\pi[/latex].       Check your work by estimating [latex]\pi[/latex] as 3 and working it in your head.
  6. Use the [latex]\pi[/latex] key on your calculator when evaluating [latex]12\pi-7[/latex].       Check your work by estimating [latex]\pi[/latex] as 3 and working it in your head.
  7. Use your calculator to evaluate [latex]73-37[/latex]and then use the negative number key as part of evaluating [latex]-37+73[/latex]. Check your work by doing it by hand.
  8. Use your calculator to evaluate [latex]24-35[/latex]and then use the negative number key as part of evaluating [latex]-35+24[/latex]. Check your work by doing it by hand.
  9. Evaluate each of these expressions:
    1. [latex]{{3}^{2x}}[/latex], where [latex]x=3[/latex]
    2. [latex]\frac{{{x}^{2}}-6x}{4x+2}[/latex], where [latex]x=3[/latex]
  10. Evaluate each of these expressions:
    1. [latex]{{2}^{x+3}}[/latex], where [latex]x=4[/latex]
    2. [latex]\frac{3x+15}{5{{x}^{2}}-11}[/latex], where [latex]x=4[/latex]
  11. Use your calculator to multiply 2,700,000 by 1,138.3 . Write what your calculator shows and then the answer in standard number notation, not scientific notation. Check your work by estimating the first number as about 3,000,000 and the second number as about 1000. Multiply those by hand and see if this estimate is close to your calculator’s answer.
  12. Use your calculator to multiply 9,701.3 by 81,200,000. Write what your calculator shows and then the answer in standard number notation, not scientific notation. Check your work by estimating the first number as about 10,000 and the second number as about 80,000,000. Multiply those by hand and see if this estimate is close to your calculator’s answer.
  13. The price of a car is $24,871 and the tax due on this is 9.3%. Find the total of the price and tax. First estimate it, explaining how you are estimating, and then use a calculator to compute it.
  14. The price of a car is $40,373 and the tax due on this is 4.6%. Find the total of the price and tax. First estimate it, explaining how you are estimating, and then use a calculator to compute it.
Work the following problems and check your work as we learned in Topic A. Use a calculator to do the arithmetic easily in the solution of the problem and in checking your answer.
  1. Simplify [latex]-12(x-2)[/latex]
  2. Simplify [latex]7(3m-8)[/latex]
  3. Solve [latex]32y-15=81[/latex]
  4. Solve [latex]19=3-7t[/latex]
  5. Solve [latex]6(3m-11)=32[/latex]
  6. Solve [latex]9(2q-7)=12[/latex]
  1. Solve [latex]\frac{12}{m}=\frac{5}{2}[/latex]
  2. Solve[latex]\frac{8}{17}=\frac{t}{9}[/latex]
  3. Solve [latex]\frac{18}{11}=\frac{38}{w}[/latex]
  4. Solve [latex]\frac{1.12}{7.2}=\frac{v}{96}[/latex]
  5. Solve [latex]\frac{m}{72}=0.6482[/latex]
  6. Solve [latex]\frac{18}{r}=0.938[/latex]
  1. Solve for y: [latex]y-7=3(x-5)[/latex]
  2. Solve for y: [latex]y-9=13(x-7)[/latex]
  3. 37.   Solve for y: [latex]y-2=0.12(x-10)[/latex]
  4. Solve for y: [latex]y-10=-1.42(x-20)[/latex]
  5. 39.                  Solve for y: [latex]y-1.12=-0.063(x-12.72)[/latex]
 

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  • Mathematics for Modeling. Authored by: Mary Parker and Hunter Ellinger. License: CC BY: Attribution.