Transcript Jeopardy
Jeopardy Fun with Radicals More Fun with Radicals Exciting Extra Exciting Exponents Exponents Scientific Pot Luck Q $100 Q $100 Q $100 Q $100 Q $100 Q $200 Q $200 Q $200 Q $200 Q $200 Q $300 Q $300 Q $300 Q $300 Q $300 Q $400 Q $400 Q $400 Q $400 Q $400 Q $500 Q $500 Q $500 Q $500 Q $500 Final Jeopardy $100 Question Fun with Radicals What is the simplified answer for 6 2 6 $100 Answer Fun with Radicals 2 6 2 Add the coefficient of like radicals $200 Question Fun with Radicals What is the simplified answer for 5 3 9 3 $200 Answer Fun with Radicals 4 3 Subtract coefficient of like radicals $300 Question Fun with Radicals What is the simplified answer for 5 7 $300 Answer Fun with Radicals 35 Multiply the radicands and simplify if possible $400 Question Fun with Radicals What is the simplified answer for 7 3 $400 Answer Fun with Radicals 21 3 Multiply by the “special 1” simplify if possible 3 3 , then $500 Question Fun with Radicals Graph the point 5 on the number line. $500 Answer Fun with Radicals 1 2 3 4 5 Is between 4 and 9 , so it’s square root is between the square roots of those numbers, 2 and 3 $100 Question More Fun with Radicals Solve 121 $100 Answer More Fun with Radicals 11 We are looking for the positive square root of the perfect square, 121 $200 Question More Fun with Radicals Estimate the 227 $200 Answer More Fun with Radicals About 15.2 It falls between the perfect squares 225 and 256, so it’s square root is between 15 and 16. Since 227 is closest to 225, it’s square root is also closer to 15 than 16. $300 Question More Fun with Radicals Identify each of the radicals as rational or irrational 45 10 49 100 $300 Answer More Fun with Radicals 45 10 49 100 Irrational, They are not perfect squares so cannot simplify to a number that can be a fraction Rational They are perfect squares so simplify to the integers 7 and 10. Both 7 and 10 can be written as fractions. $400 Question More Fun with Radicals Simplify 5 10 $400 Answer More Fun with Radicals 50 25 2 25 2 5 2 Multiply the radicands, then simplify by finding perfect square factors. $500 Question More Fun with Radicals Combine 4 3 6 3 $500 Answer More Fun with Radicals 2 3 Since we have like radicands, we can subtract the coefficients $100 Question Exciting Exponents Simplify 1 3 $100 Answer Exciting Exponents 1 3 The negative exponent is simplified by moving it’s base to the other side of the fraction bar and making it a positive exponent. We put a 1 in the numerator as a place holder. $200 Question Exciting Exponents Evaluate 3 3 2 4 $200 Answer Exciting Exponents 1. Make the exponents “happy” by moving their bases to the other side of the fraction bar. 2. Simplify by multiplying the base by itself according to the exponent 42 33 4 4 16 3 3 3 27 $300 Question Exciting Exponents Evaluate 2 3 3 3 $300 Answer Exciting Exponents 1. Same base so we can Subtract the exponent. ( 2 3) 3 3 3 1 Remember, any number to the first power is always itself. $400 Question Exciting Exponents Evaluate 6 10 8 6 $400 Answer Exciting Exponents 1. Same base so we can add the exponents. ( 10 8) 6 6 2 2. Now we must simplify; get rid of that negative exponent. Move the base to the other side of the fraction bar and make the exponent positive “happy”. 1 62 3. Finally, multiply the base by itself to finish simplifying. 1 1 6 6 36 $500 Question Exciting Exponents Evaluate 3 1 2 4 $500 Answer Exciting Exponents 1. Simplify the negative exponent by moving its base to the other side of the fraction bar and make the exponent positive. Remember, 21 = 2. 3 1 4 2 2. Now, find common denominators and add the fractions. 3 2 5 1 1 4 4 4 4 $100 Question Extra Exciting Exponents What is the simplified answer for 5 6 1 8x y z $100 Answer Extra Exciting Exponents Move bases with negative exponents to the other side of the fraction bar and make the exponents positive, “happy”. Bases with positive exponents stay where they are!! 5 6 1 8x y z 6 8y 5 1 x z $200 Question Extra Exciting Exponents What is the simplified answer for 5 24 x y 3 6x 1 $200 Answer Extra Exciting Exponents 24 4 1. The fraction 6 reduces to 1 2. Move bases with negative exponents to the other side of the fraction bar and make the exponents positive, “happy”. Bases with positive exponents stay where they are!! 5 4x y 1x 3 1 4 x3 6 x5 y1 x3 2 x 3. Subtract exponents for x 5 so we have to move that x base to the other side of the fraction bar for our final answer. 4 2 x y $300 Question Extra Exciting Exponents What is… 6 When x=2 ? ( x5) $300 Answer Extra Exciting Exponents 1. Substitute 2 for the variable x and simplify the exponent. 6 (2 5) 6 3 2. Now we have a negative exponent so we have to move its base to the other side of the fraction bar and make the exponent positive. 1 63 3. Multiply the base 6 by itself 3 times. 1 1 6 6 6 216 $400 Question Extra Exciting Exponents Simplify 3 4 4 (4 ) $400 Answer Extra Exciting Exponents Remember, parentheses are another way of saying multiply. 1. Bases are the same, so we can add the exponents. 4 ( 3 4) 4 1 2. Since any number to the power of 1 is itself, the answer is… 4 $500 Question Extra Exciting Exponents Simplify the Expressions (1) 1 2 1 0 8 5 5 7 7 $500 Answer Extra Exciting Exponents (1) 1 1 1 1 1 2 1 1 1 2 1 5 5 0 7 7 (7 7) 5 8 1 5 1 0 $100 Question Scientific Pot Luck Simplify 5 10 $100 Answer Scientific Pot Luck Step 1 – simplify the fraction Now that we simplified the fraction, we multiply by the “special 1” 5 5 1 1 10 2 10 2 1 2 2 2 2 2 $200 Question Scientific Pot Luck What is 8.6 x 10-3 in standard notation? $200 Answer Scientific Pot Luck Move the decimal to the left 3 spaces (exponent tells you how far to move and which direction) 8.6 x 10-3 0.0086 $300 Question Scientific Pot Luck What is the product of 80,000 and 90 written in scientific notation $300 Answer Scientific Pot Luck Move the decimal to the left until just 1 digit is to it’s left. Your exponent will be the number of decimal hops. 7 2 0 0 0 0 0= 7.2 x 106 $400 Question Scientific Pot Luck Simplify the quotient and write the answer in scientific notation (9 x 107) (3 x 104) $400 Answer Scientific Pot Luck Subtract exponents 7-4=3 (9 x 107) (3 x 104) Divide 9 3 = 3 (3 x 103) $500 Question Scientific Pot Luck How much greater is 9.4 x 103 than 7.5 x 10-2 $500 Answer Scientific Pot Luck 2 methods to solve. 1. Adjust one of the numbers so the exponents are the same. Remember LARS when moving the decimal and changing the exponent. 2. Change both numbers to standard notation. Subtract. Then, change the difference back to scientific notation. (I find this one easier unless the exponents are extremely big.) 9400.000 - 3. Adjust to scientific notation .075 9399.925 9.39925 x 103 Final Jeopardy How are you going to study for the math test tonight? Final Jeopardy Answer 1. Review notes and practice problems from the unit. 2. Work out all the problems from the study guide and check my answers to the key I now know is correct.