Chapter 1 Test PC11 A2 - Version 2024Eshorter PDF

**LO 1: Demonstrate an understanding of how to classify real numbers and evaluate square and cube roots without technology.** **Self-Assessment (circle one):** I feel that for this outcome I am: Proficient Developing Emerging 1. Evaluate each radical, if possible. Write each answer as a fraction...

**LO 1: Demonstrate an understanding of how to classify real numbers and evaluate square and cube roots without technology.** **Self-Assessment (circle one):** I feel that for this outcome I am: Proficient Developing Emerging 1. Evaluate each radical, if possible. Write each answer as a fraction in lowest terms. +-----------------------------------+-----------------------------------+ | b. [\$\\sqrt\[3\]{- | c\) [\$- | | \\frac{24}{81}}\$]{.math | \\sqrt{\\frac{48}{75}}\$]{.math | |.inline} |.inline} | +===================================+===================================+ | a. [\$\\sqrt\[3\]{- | | | 0.000000125}\$]{.math | | |.inline} | | +-----------------------------------+-----------------------------------+ 2. Estimate the following to 1 decimal place. You must show your thinking! ----------------------------------------------------------------------------------------------- **LO 2:** *Demonstrate an understanding of how to convert between mixed and entire radicals.* ----------------------------------------------------------------------------------------------- **Self-Assessment (circle one):** I feel that for this outcome I am: Proficient Developing Emerging 3. Write each radical as a mixed radical in simplest terms. +-----------------------------------+-----------------------------------+ | a. [\$\\sqrt{384}\$]{.math | b. [\$- | |.inline} | \\sqrt\[4\]{2560}\$]{.math | | |.inline} | +-----------------------------------+-----------------------------------+ 4. Write each radical as an entire radical in simplest terms. +-----------------------------------+-----------------------------------+ | a. [\$- 4\\sqrt{6}\$]{.math | b. [\$- 2\\sqrt\[5\]{- | |.inline} | 6}\$]{.math.inline} | +-----------------------------------+-----------------------------------+ -------------------------------------------------------------------------------------- **L.O. 3: Demonstrate an understanding of powers with positive rational exponents.** -------------------------------------------------------------------------------------- **Self-Assessment (circle one):** I feel that for this outcome I am: Proficient Developing Emerging 5. Write each power as a radical, then evaluate. +-----------------------------------+-----------------------------------+ | a. [\$\\left( 0.1296 | b\) [\${- \\left( \\frac{6}{48} | | \\right)\^{\\frac{3}{4}}\$]{. | \\right)}\^{\\frac{2}{3}}\$]{.mat | | math | h | |.inline} |.inline} | +===================================+===================================+ | | c\) [\$\\left( \\frac{486}{64} | | | \\right)\^{0.2}\$]{.math | | |.inline} | +-----------------------------------+-----------------------------------+ 6. Write the radical as a power with a rational exponent. ----------------------------------------------------------------------------- \ [\$\$\\left( \\sqrt\[4\]{\\frac{1}{36}} \\right)\^{3}\$\$]{.math.display}\ ----------------------------------------------------------------------------- -------------------------------------------------------------------------------------- **L.O. 4: Demonstrate an understanding of powers with negative rational exponents.** -------------------------------------------------------------------------------------- **Self-Assessment (circle one):** I feel that for this outcome I am: Proficient Developing Emerging 7. Write the power with a positive rational exponent. ------------------------------------------------------------------------------ \ [\$\$- \\left( \\frac{5}{7} \\right)\^{- \\frac{7}{2}}\$\$]{.math.display}\ ------------------------------------------------------------------------------ 8. Evaluate each power without using a calculator. +-----------------------------------+-----------------------------------+ | b. [\$\\left( 81 \\right)\^{- | | | \\frac{3}{4}}\$]{.math | | |.inline} | | +===================================+===================================+ | a. [\$- \\left( 32 \\right)\^{- | c\) [\$\\left( \\frac{100}{36} | | \\frac{4}{5}}\$]{.math | \\right)\^{- | |.inline} | \\frac{3}{2}}\$]{.math.inline} | +-----------------------------------+-----------------------------------+ ----------------------------------------------------------------------------------------------------------------------------------- **L.O. 5: Apply the exponent laws and order of operations to evaluate numerical expressions and simplify algebraic expressions.** ----------------------------------------------------------------------------------------------------------------------------------- **Self-Assessment (circle one):** I feel that for this outcome I am: Proficient Developing Emerging 9. Evaluate each expression without using a calculator. Write the answer as an integer or a fraction in lowest terms. ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ [\$\\left\\lbrack \\left( - \\frac{3}{5} \\right)\^{- 1} \\right\\rbrack\^{\\frac{1}{3}} \\div \\left\\lbrack \\left( - \\frac{3}{5} \\right)\^{2} \\right\\rbrack\^{\\frac{1}{3}}\$]{.math.inline} ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 10. Simplify the following expression. Write each expression with positive rational exponents. --------------------------------------------------------------------------------------------------------------------- [\$\\left( \\frac{3x\^{- 2}y\^{\\frac{1}{4}}}{81xy\^{- \\frac{11}{4}}} \\right)\^{- \\frac{1}{3}}\$]{.math.inline} ---------------------------------------------------------------------------------------------------------------------