Algebra 2 Ch Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Transcription

1 Name: lass: ate: I: lgebra 2 h. 8. Multiple hoice Identify the choice that best completes the statement or answers the question.. istance varies directly as time because as time increases, the distance traveled increases proportionally. The speed of sound in air is about 335 feet per secon How long would it take for sound to travel,725 feet? 35 sec 30 sec 45 sec 40 sec 2. Given: y varies inversely as, and y 4 when 4. Write and graph the inverse variation function. y y 4 y y 6

2 Name: I: 3. etermine whether the data set represents a direct variation, an inverse variation, or neither. y irect variation Inverse variation Neither 4. Simplify Identify any -values for which the epression is undefine The epression is undefined at 4. 5 The epression is undefined at 2 and The epression is undefined at 2 and The epression is undefined at Multiply 8 4 y 2 6. ivide 5 3 9y2 z 6 3z 3 4y 4. ssume that all epressions are define 6 4 yz z y 8 z 9 y y 2 z 3 2 y 25. ssume that all epressions are define 9 3y 25 9y 0 5y 8 5 y 8 7. Solve heck your answer There is no solution because the original equation is undefined at 5. 2

3 Name: I: 8. dd ()( 7) + 6 ( 7)() Subtract Identify any -values for which the epression is undefine 6 4 The epression is undefined at 4 and ( 4) ( ) The epression is undefined at 4 and The epression is undefined at 4 and 4. 6 The epression is undefined at 4 and 4. 3

4 Name: I: Graph the function. 0. y 4 Simplify the rational epression

5 Name: I: Multiply. 3. q q q + 4 4q q 2 q q 2q 4q q 2q + 8 4q + 20q 2 4q () 6 7( 4) 6 y 2 9 2y 5y y + 3 5(y + 3) 2 (y + 3) 2 () 2 ( 4) 42 2 ( 4) 2 () 42 2 y 3 2 5(y 3) 2 ivide s 2 2s s 2 + 3s 0 s 5 s + 5 s 2 s s 5 s s s s 2 s 2 5s dd or subtract

6 Name: I: ( + 2)( 4) + 8 ( + 2)( 4) ( + 2)( 4) 2. Factor the trinomial a 2 + 4a ( a + 4) ( a + ) ( a + 6) ( a + 8) ( a + ) ( a + 48) ( a 8) ( a 6) 22. Factor ( + 3) ( 2 + 2) ( + 2) ( + 3) ( + 2) ( 2 3) ( + 2) ( 2 + 3) 23. Let 5, y 8, and y 2 5. Let y vary inversely as. Find Simplify the rational epression Multiply. Simplify your answer ivide. Simplify your answer m m 8 8m 8 m 8 (8m) mm ( 8) 27. ivide. 8 m m 8 8 m 2 + 0m + 24 m + 4 m + 6 m 6 m 4 m + 4 6

7 I: lgebra 2 h. 8. nswer Section MULTIPLE HOIE. NS: r 335 ft per sec Find the constant of variation r. d 335t Write the direct variation function., t Substitute. t 35 Solve. It would take 35 seconds for sound to travel,725 feet. orrect! Use the direct variation equation d rt. Set up a proportion and solve. First, write the direct variation function. Then, substitute the given values and solve. PTS: IF: asic REF: Page 570 OJ: 8-.2 Solving irect Variation Problems ST: 2.0.G TOP: 8- Variation Functions NT: c

8 I: 2. NS: y k y varies inversely as. 4 k 4 Substitute the given values. 6 k Solve for k. y 6 Write the variation function. Make a table of values to graph y 6. Use both positive and negative values. y Undefined Inverse variation equations are in the form y k/. This equation does not have the correct constant of variation. To find k, use y and substitute the given - and y-values. This equation does not have the correct constant of variation. To find k, use y k and substitute the given - and y-values. orrect! PTS: IF: verage REF: Page 57 OJ: 8-.4 Writing and Graphing Inverse Variation ST: 2.0.G TOP: 8- Variation Functions KEY: inverse variation relationship graph NT: 2.5..e 2

9 I: 3. NS: In inverse variation, the product of the two quantities is constant. y y In direct variation, the ratio of the two quantities is constant. y y This data set represents an inverse variation. If the ratio of each y pair is the same, the relationship is a direct variation. If the product of each y pair is the same, the relationship is an inverse variation. orrect! PTS: IF: asic REF: Page 572 OJ: 8-.6 Identifying irect and Inverse Variation NT: 2.5..e ST: 2.0.G TOP: 8- Variation Functions KEY: inverse variation relationship 4. NS: ( ) ( + 5)( 2) ()( 2) 5 Factor from the numerator and reorder the terms. Factor the numerator and denominator. ivide the common factors and simplify. The epression is undefined at those -values, 2 and 4, that make the original denominator 0. Look at the original epression to find the values that make it undefine orrect! on't forget to redistribute the. on't forget to redistribute the. Look at the original epression to find the values that make it undefine PTS: IF: verage REF: Page 578 OJ: Simplifying by Factoring - NT: c ST: 2.2. TOP: 8-2 Multiplying and ividing Rational Epressions 3

10 I: 5. NS: rrange the epressions so like terms are together: 8 9( 4 )(y 2 y 2 )z z 3 y 4. Multiply the numerators and denominators, remembering to add eponents when multiplying: 72 5 y 4 z 6 2z 3 y 4. ivide, remembering to subtract eponents: 6 5 y 0 z 3. Since y 0, this epression simplifies to 6 5 z 3. variable raised to the 0 power simplifies to. When dividing powers with the same base, subtract the eponents. orrect! Multiply, then simplify. PTS: IF: asic REF: Page 578 OJ: Multiplying Rational Epressions NT: c ST: 2.2. TOP: 8-2 Multiplying and ividing Rational Epressions 6. NS: y 25 3y y 3y 9 25 y8 5 Rewrite as multiplication by the reciprocal. Simplify by canceling common factors. orrect! To divide by a fraction, you multiply by its reciprocal. To divide by a fraction, you multiply by its reciprocal. Multiply the first fraction by the reciprocal of the second fraction. PTS: IF: asic REF: Page 579 OJ: ividing Rational Epressions NT: c ST: 2.2. TOP: 8-2 Multiplying and ividing Rational Epressions 4

11 I: 7. NS: Note that 5. 5 ( 5) ( + 6) Factor The factor ( 5) cancels. 5 ecause the left side of the original equation is undefined when 5, there is no solution. Is the original equation defined for this value of? Factor the numerator and cancel common factors before solving for. Is the original equation defined for this value of? Factor the numerator and cancel common factors before solving for. Is the original equation defined for this value of? orrect! PTS: IF: verage REF: Page 579 OJ: Solving Simple Rational Equations NT: c ST: 2.0. TOP: 8-2 Multiplying and ividing Rational Epressions 8. NS: Factor the denominators. The L is ()( 7). 7 ()( 7) Ê ˆ Ê ˆ + Multiply by Ë Á 7 ()( 7) Ë Á ()( 7) ()( 7) ()( 7) ( + 5)( 7) ()( 7) + 5 dd the numerators. Factor the numerator. ivide the common factor. Find a common denominator before adding the fractions. This is the first fraction rewritten with the common denominator. dd this to the second fraction. Find a common denominator before adding the fractions. orrect! PTS: IF: verage REF: Page 584 OJ: dding Rational Epressions NT: c ST: 2.2. TOP: 8-3 dding and Subtracting Rational Epressions 5

12 I: 9. NS: ( 4) ( ) ( 4) ( ) + 6 Ê 4 ˆ Ë Á ( + 6) ( 4) ( 4) ( ) 2 2 Ê 48 2 ˆ Ë Á ( 4) ( ) ( 4) ( ) ( 4) ( ) ( 6) ( ) ( 4) ( ) 6 4 Factor the denominators. The L is ( 4) ( ), so multiply + 6 by 4 4. Subtract the numerators. Multiply the binomials in the numerator. istribute the negative sign. Write the numerator in standard form. Factor the numerator, and divide out common factors. The epression is undefined at 4 and 4 because these values of make the factors ( 4) and ( ) equal 0. orrect! heck your distribution of the negative sign. id you factor the numerator and divide out common factors correctly? id you factor the numerator and divide out common factors correctly? PTS: IF: verage REF: Page 585 OJ: Subtracting Rational Epressions NT: c ST: 2.2. TOP: 8-3 dding and Subtracting Rational Epressions 0. NS: PTS: IF: L2 REF: 2- Graphing Rational Functions OJ: 2-. Graphing Rational Functions NT: P J..6 P J.2.2 P J.2.3 TOP: 2- Eample KEY: rational function constant of variation inverse variation. NS: PTS: IF: L2 REF: 2-2 Simplifying Rational Functions OJ: 2-2. Simplifying Rational Epressions NT: NEP c P J..5 P J..6 TOP: 2-2 Eample 2 2. NS: PTS: IF: L2 REF: 2-2 Simplifying Rational Functions OJ: 2-2. Simplifying Rational Epressions NT: NEP c P J..5 P J..6 TOP: 2-2 Eample 2 6

13 I: 3. NS: PTS: IF: L3 REF: 2-3 Multiplying and ividing Rational Epressions OJ: 2-3. Multiplying Rational Epressions NT: NEP b NEP c P J..5 TOP: 2-3 Eample 4. NS: PTS: IF: L2 REF: 2-3 Multiplying and ividing Rational Epressions OJ: 2-3. Multiplying Rational Epressions NT: NEP b NEP c P J..5 TOP: 2-3 Eample 2 5. NS: PTS: IF: L3 REF: 2-3 Multiplying and ividing Rational Epressions OJ: 2-3. Multiplying Rational Epressions NT: NEP b NEP c P J..5 TOP: 2-3 Eample 2 6. NS: PTS: IF: L2 REF: 2-3 Multiplying and ividing Rational Epressions OJ: ividing Rational Epressions NT: NEP b NEP c P J..5 TOP: 2-3 Eample 4 7. NS: PTS: IF: L2 REF: 2-3 Multiplying and ividing Rational Epressions OJ: ividing Rational Epressions NT: NEP b NEP c P J..5 TOP: 2-3 Eample 4 8. NS: PTS: IF: L2 REF: 2-5 dding and Subtracting Rational Epressions OJ: 2-5. dding and Subtracting Rational Epressions With Like enominators NT: NEP 2005 N5b NEP b NEP c P J..5 TOP: 2-5 Eample 9. NS: PTS: IF: L3 REF: 2-5 dding and Subtracting Rational Epressions OJ: 2-5. dding and Subtracting Rational Epressions With Like enominators NT: NEP 2005 N5b NEP b NEP c P J..5 TOP: 2-5 Eample NS: PTS: IF: L2 REF: 2-5 dding and Subtracting Rational Epressions OJ: dding and Subtracting Rational Epressions With Unlike enominators NT: NEP 2005 N5b NEP b NEP c P J..5 TOP: 2-5 Eample 4 7

14 I: 2. NS: a 2 + 4a + 48 ( a +?) ( a +?) Look for the factors of 48 whose sum is 4. ( a + 6) ( a + 8) The factors are 6 and 8. Look for factors whose product is the trinomial's last term. Use the FOIL method to check your answer. orrect! Use the FOIL method to check your answer. PTS: IF: asic REF: Page 54 OJ: Factoring ^2 + b + c When c is Positive NT: d TOP: 8-3 Factoring ^2 + b + c 22. NS: Since a 2, the coefficients of the First terms must be factors of 2. Since c 6, the Last terms must be factors of 6. Since b 7, the Outer and Inner products must add up to 7. The sum of the products of the outer and inner terms should be 7. It may be helpful to make a table to check all the factors of 2 and all the factors of 6. Then check the products of the outer and inner terms to see if the sum is 7. You reversed the second terms in the parentheses. When b is negative, the factors of c are both negative. When b is positive, the factors of c are both positive. The coefficient of the -term in the second binomial cannot be. heck your answer. orrect! PTS: IF: asic REF: Page 549 OJ: Factoring a^2 + b + c When c is Positive NT: d TOP: 8-4 Factoring a^2 + b + c 23. NS: y 2 y 2 Write the Product Rule for Inverse Variation Substitute 5 for, 8 for y, and 5 for y Simplify and solve for 2. ivide both sides of the equation by the same number, not subtract. The Product Rule for Inverse Variation states that ()(y) (2)(y2). The Product Rule for Inverse Variation states that ()(y) (2)(y2). orrect! PTS: IF: asic REF: Page 853 OJ: 2-.4 Using the Product Rule NT: 2.5..e ST:.. TOP: 2- Inverse Variation 8

15 I: 24. NS: ( 3)( 2) Factor the numerator and denominator. 3 ( 3)( 2) ivide out the common factors. 2 Simplify. Factor the denominator. ivide out common factors. orrect! Factor the denominator. ivide out common factors. Factor the denominator. ivide out common factors. PTS: IF: asic REF: Page 867 OJ: Simplifying Rational Epressions with Trinomials NT: c ST:.4. TOP: 2-3 Simplifying Rational Epressions 25. NS: ( + 2)( 3) ( + ) 2( 3) ( + 2)( + 2) ( + ) 2 ( + 2) + 2 Factor the numerator and denominator. Simplify. Multiply the remaining factors. orrect! Factor the numerator and denominator and divide out the common factors. Factor the numerator and denominator and divide out the common factors. Factor the numerator and denominator and divide out the common factors. PTS: IF: verage REF: Page 879 OJ: Multiplying Rational Epressions ontaining Polynomials NT: c ST:.4. TOP: 2-4 Multiplying and ividing Rational Epressions 9

16 I: 26. NS: m m 8 8m m 8m m 8 (8m) mm ( 8) 8 m 8 Write as multiplication by the reciprocal. Multiply the numerators and the denominators. ivide out common factors. Simplify. orrect! ivide out common factors, and simplify. First, write as multiplication by the reciprocal. Then, multiply the numerators and the denominators. Write as multiplication by the reciprocal first. PTS: IF: asic REF: Page 880 OJ: ividing by Rational Epressions and Polynomials NT: c ST:.4. TOP: 2-4 Multiplying and ividing Rational Epressions 27. NS: m 2 + 0m + 24 m + 4 ( m + 4) ( m + 6) Factor the numerator. m + 4 m + 6 ivide out the common factors. Simplify. orrect! First, factor the numerator. Then, divide out the common factors and simplify. heck the signs. First, factor the numerator. Then, divide out the common factors and simplify. PTS: IF: asic REF: Page 894 OJ: ivide a Polynomial by a inomial ST:.4. TOP: 2-6 ividing Polynomials NT: c 0