Mini-Lecture 5.1 Exponents and Scientific Notation

Size: px
Start display at page:

Download "Mini-Lecture 5.1 Exponents and Scientific Notation"

Transcription

1 Mini-Lecture.1 Eponents and Scientific Notation Learning Objectives: 1. Use the product rule for eponents.. Evaluate epressions raised to the zero power.. Use the quotient rule for eponents.. Evaluate epressions raised to the negative nth power.. Convert between scientific notation and standard notation. 6. Key vocabulary: eponential epressions, scientific notation. Eamples: 1. Use the product rule to simplify each epression. 9 7 a) b) m m m c) ( 6 y)(6 y) d) ( ab)( ab). Evaluate or simplify each epression a) b) c) ( 10) d) 0 ( + 1). Use the quotient rule to simplify each epression y a) b) c) 7 y 6 1 y 9y d) 1 6abc 9 abc. Simplify and write using positive eponents only. a) b) ( ) c) y y 6 d) a e) f) 1ab g) a b yz yz h) (a b)( a b ). Write each number in scientific notation or in standard notation. a) 6,000 b) c).6 10 d) Teaching Notes: Students need a lot of repetition and practice in order to master these objectives. Students often move constants along with a variable that has a negative eponent. For eample, in d) a common answer is a - = 1/(a ). Refer students to the eponent rule charts and the Writing a Number in Scientific Notation chart in the tet. Answers: 1a) 18, b) m 17, c) -6y, d) 1a 6 b, a) 1, b) -1, c) 1, d) 1; a), b) -y y, c), d) -9ab c ; a) 1 b) 1 9, c) 1 9 y d) a ; e), f) a 6 b 10 ; g) 9 1 z, a) 6.10, b) , c) , d) 90,000 16, M- Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

2 Mini-Lecture. More Work with Eponents and Scientific Notation Learning Objectives: 1. Use the power rules for eponents.. Use all eponent rules and definitions to simplify eponential epressions.. Compute, using scientific notation.. Key vocabulary: eponential epression, scientific notation. Eamples: 1. Simplify using the product rules for eponents. Write each answer using positive eponents only. a) ( ) b) ( y ) c) y d) ( m ) e) ( yz ) f) y g) 0 ( y z ) h) ( y ). Simplify using eponent rules and definitions. Write each answer using positive eponents only. a) a b c 9 b) ( ) c) 6 n m d) 10 7 y y 0 e) ( y) f) ( by) g) 1 z 7y y z h) 8 ( y ) ( y ). Perform each indicated operation using the properties of eponents. Write each answer in scientific notation. 8 9 a) (.9 10 )( ) b) ( 10 6 ) c) 10 Teaching Notes: Some students are confused by when to add eponents versus when to multiply eponents. Encourage students to write the eponent rules on an inde card to view while doing homework. Refer students to the Summary of Rules for Eponents chart in the tet. Answers: 1a) 6, b) y 6, c) d) y 9 1, e) 6 8y 6 y, d) 1 1 1, f) 6 by, g) y 7z 1 m, e) y z 6, f) 0 y 10, g) y, h) 096y1 ; a) ab 18 c, h) 7 y ; a).910-1, b) , c) , b) -6 6, c) 1 0 m n, M- Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

3 Mini-Lecture. Polynomials and Polynomial Functions Learning Objectives: 1. Identify term, constant, polynomial, monomial, binomial, trinomial, and the degree of a term and of a polynomial.. Define polynomial functions.. Review combining like terms.. Add polynomials.. Subtract polynomials. 6. Recognize the graph of a polynomial function from the degree of the polynomial. 7. Key vocabulary: term, constant, polynomial, monomial, binomial, trinomial, degree. Eamples: 1. Find the degree of each polynomial, state how many terms it has, and indicate whether it s a monomial, binomial, or trinomial. a) b) 9 c) + d) y +. Define a polynomial function.. Simplify each polynomial by combining like terms. a) + b) 10y 8y c) y + y d) + 6 e) 9y + 8y + y f). Add the polynomials ( ) ( 6 7 ) a) ( y y ) (y 7) b). Subtract the polynomials a) y ( ) 6. Match each equation with its graph. 1 y + + 8y + c) b) c) ( ) ( ) y M y ( 7 ) + 1) ) ) a) y = 1 Teaching Notes: b) y = c) y = + Most students find these polynomial operations easy. Tell students that identifying the degree of a polynomial is important for later work with factoring and solving equations. Remind students that this section is a review of distributing and collecting like terms. Some students forget to distribute the minus sign when lining up vertically. Answers: 1a) 1,1 monomial, b),1,monomial, c),,binomial, d),,trinomial; a), b) y, c) y+, d) -9, e) y+y, f) 6y + ; a) -y +1, b) - -10, c) 1 --, a) , b) +7, c) ; 6a)graph ; b) graph 1; c) graph Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

4 Mini-Lecture. Multiplying Polynomials Learning Objectives: 1. Multiply two polynomials.. Multiply binomials.. Square binomials.. Multiply the sum and difference of two terms.. Multiply three or more polynomials. 6. Evaluate polynomial functions. 7. Key vocabulary: FOIL. Eamples: 1. Multiply. a) ( )( ) 10 b) ( 6a )( a ) c) (.1 y z ) ( 6 y z ) d) ( ) y( y + ) bz ( za + baz b) g) ( + )( + ) e) f). Multiply. a) ( ) ( ) + b) ( + )( + ) c) ( y ) ( 6y ) d) ( + 6)( + 6) e). Multiply. f) a) ( + ) b) ( c) ) ( + 7) y y 1 1 y y 6. Multiply. a) ( + )( ) b) ( y b) ( y + b) c) b. Multiply. ( + ) 1 b) ( y ) c) ( y)( + y)( + y) a) ( ) ( ) 1 d) ( ) 6. If f ( ) =, find the following. a) f ( a ) b) f ( c ) c) f ( a+ b) d) f( a ) Teaching Notes: Encourage students to multiply binomials with FOIL mentally whenever possible. This will make factoring easier for them in future sections. Many students distribute the eponent when squaring a binomial, even after repeated reminders to multiply the binomial by itself. Refer students to the Square of a Binomial and Product of the Sum and Difference of Two Terms charts in the tet. Answers: 1a) 8, b) -0a, c).6 y 7 z 11, d) 6-8, e) -1y -6y, f) -ab z -ab z +b z, g) + ++1; a) +-1, b) ++6; c) 8y -1y+6, d) +1+6; e) - y +y 1, f) 1y y+ ; a) ++; b) -8+16; c) +1+9; a) -; b) y -9b 1 ; c), d) 6-b+b ; a) , b) y -8y +y -y+16;c) - y-y -y ; 6a) a -a, b) c -c, c) a +ab+b -a-b, d) a -6a+8 Copyright 009 Pearson Education, Inc., M-7 publishing as Pearson Prentice Hall

5 Mini-Lecture. The Greatest Common Factor and Factoring by Grouping Learning Objectives: 1. Identify the GCF.. Factor out the GCF of a polynomial s term.. Factor polynomials by grouping.. Key vocabulary: greatest common factor (GCF). Eamples: 1. Find the greatest common factor of each list of monomials. a), b) 1, 0 c). Factor out the greatest common factor. 1, 0 d) 9 y,7y a) 16 1 b) c) z z d) e) 18ab 1ab+ 9ab 1ab f) ( y ) + ( y ). Factor each polynomial by grouping. a) y + y + + b) y 1 y + 6 c) y + 9 7y 6 d) y y 1 Mied Practice. Factor each polynomial. a) 16 1 b) 7y 18 + y c) 8abc 1abc 8ac+ 6a d) 9 y( z + ) ( z + ) e) y y 1 f) Teaching Notes: Remind students to check their factoring answers by multiplication. Some students need to rewrite the coefficients in problem in factored form in order to see the greatest common factor. Some students omit the 1 in the answer to Problem b). Many students are confused at first by factor by grouping problems where a negative sign must be factored out of the second grouping, as in problem b). Answers: 1a), b), c), d) 9y; a) (-), b) 8(+1), c) z(1-z ), d) (6+- ), e) ab(6a -+b-a), f) (y-)(+1); a) (+1)(y+), b) (y-6)(-), c) (y+9)(-7), d) (y-)(+7); Mied Practice. a) ( -), b) 9y(-y + ), c) a(ab c-6b c-c+), d) (9y-)(z+), e) (y-)(y+7), f) (+)( +1) Copyright 009 Pearson Education, M-8 Inc., publishing as Pearson Prentice Hall

6 Mini-Lecture.6 Factoring Trinomials Learning Objectives: 1. Factor trinomial of the form + b + c.. Factor trinomial of the form a + b + c a. Method 1 - Trial and Check b. Method - Grouping. Factor by substitution.. Key vocabulary: prime, perfect square trinomial. Eamples: 1. Factor each trinomial. a) + + b) c) 6+ 8 d) + e) f) 10 g) + 8 h) 18 i) j) y 6y + 8y k) +. Factor each trinomial. a) Trial and check method. a) y + 1y+9 b) c) d) e) f) y 7y 0y Factor the trinomials. b) Grouping method. g) 10 7 h) i) Use substitution to factor each trinomial completely. 6 a) 6 b) c) ( a+ ) + 7( a+ ) + 1 Teaching Notes: Some students can factor trinomials very quickly using the trial and check method. Some students become very frustrated with the trial and check method and appreciate seeing the grouping method because it provides a recipe that works for any non-prime polynomial. Remind students to always try to factor a GCF first. Refer to the end of section eercises for mied practice. Refer students to the Factoring a Trinomial of the Form the Form a + b + c by Grouping charts in the tet. M-9 a + b + c and Factoring a Trinomial of Answers: 1a) (+)(+1), b) (+)(+), c) (-)(-), d) (+)(-1), e) (-)(+1), f) (-)(+), g) (+6)(-), h) (-)(+), i) prime, j) y (-)(-), k) (-)(-1); a) (y+)(y+), b) (-)(-), c) (-)(+), d) (7+)(-), e) (-1)(+), f) y (-)(+); g) (-11)(+); h) (+)(+); i) (-11)(+1) a) ( -6)( +1), b) ( +)( -), c) (a+8)(a+7) Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

7 Mini-Lecture.7 Factoring by Special Products Learning Objectives: 1. Factor a perfect square trinomial.. Factor the difference of two squares.. Factor the sum or difference of two cubes. Eamples: 1. Factor completely or state the polynomial is prime. a) + + b) 1+ 6 c) d) 1+ 1 e). Factor completely. a) 9 b) y 10y y f) y 81 c) + 9y + 0y 1 z 16 ( ) d) + 6 e) 7 f) Factor completely. a) + 8 b) +1 c) y 7 d) 6 e) p + 8q f) y + 1y g) ab 7b h) y + 0 Mied practice. a) 6 b) c) 1000y 1 d) 6y + 9y e) f) ( ) Teaching Notes: Encourage students to always check if the first and last terms of a trinomial are perfect squares. If they are, then perfect square trinomial factoring may apply. Some students understand the difference of a square formula better if a) and b) are also done using trinomial factoring with a 0 middle term. Some students find the sum and difference of cubes formulas confusing at first and need to see many eamples. Remind students to factor out a GCF whenever possible. Answers: 1a) (+), b) (-6), c) (+1), d) (-), e) y (-1), f) prime; a) (+7)(-7), b) (y+9)(y-9), 1 1 c) + z z, d) (+11)(-), e) (+)(-), f) (++ )(+- ); a) (+)( -+), b) (+1)( -+1), c) (y-)(y +y+9), d) (-)(16++ ), e) (p+q)(p -pq+q ), f) y (+)( -+), g) b (a-)(a +a+9), h) (y+)(9y -1y+); Mied Practice: a) (8+)(8-), b) (+8), c) (10y-1)(100y +10y+1), d) (-y), e) (+7)(-7), f) (+11)(-) Copyright 009 Pearson Education, M-0 Inc., publishing as Pearson Prentice Hall

8 Mini-Lecture.8 Solving Equations by Factoring and Problem Solving Learning Objectives: 1. Solve polynomial equations by factoring.. Solve problems that can be modeled by polynomial equations.. Find the -intercept of a polynomial function.. Key vocabulary: polynomial equation, quadratic equation, standard form, zero-factor property. Eamples: 1. Solve each equation. a) = 0 b) = 0 c) + = 70 ( ) d) + = e) ( 8) = + f) 1 + = g) (+ ) ( 9) ( 1) = 0 h) = i) + 7 = 18 j) = 6 k) = +. Solve. a) One number eceeds another number by 6 and the product of the two numbers is 7. Find the numbers. b) A certain rectangle s length is feet longer than its width. If the area of the rectangle is 70 square feet, find its dimensions. c) One leg of a right triangle is 1 inches longer than the smaller leg, and the hypotenuse is 16 inches longer than the smaller leg. Find the lengths of the sides of the triangle.. Match each polynomial function with its graph. y y 1) ) ) g),,9, h) {-,0,}, i) {-9,0,}, j) {-8,0,8}, k) {-,-1,1}; a) 6 and 1, or, -1 and -6, b) 10 ft by 7 ft, c) 10 in, in, 6 in; a) graph ; b) graph ; c) graph 1 Copyright 009 Pearson Education, Inc., M-1 publishing as Pearson Prentice Hall - a) f ( ) = ( )( + ) b) f ( ) = ( 1)( + ) c) h ( ) = ( + )( ) Teaching Notes: Remind students to always put the equation in standard form before factoring. Some students try to use the zero-factor property before the equation is in standard form. For eample in c) : + = 70 ( + ) = 70 = 70, + = 70 etc. Many students find the applied problems difficult and need to see more eamples. Remind students to check whether their answers are reasonable for applied problems. Refer students to the Solving a Polynomial Equation by Factoring chart in the tet. Answers: 1a) {0}, b) {}, c) {0,-7}, d), ; a) {6,}, b),, c) {-10,7}, d),, e) {0}, f) {1,7}; y

9 Additional Eercises.1 Form I Name Date Simplify each epression. Write answers with positive eponents t t 9 y y... a a Write each number in scientific notation , Write each number in standard notation, without eponents Simplify. Assume that variables in the eponent represent nonzero integers and that, y, and z are not y a y a 1. b c 1. z z 7 n E-10 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

10 Additional Eercises.1 Form II Name Date Simplify each epression. Write answers with positive eponents ( + ) a b ab a 6a a Write each number in scientific notation ,900, Write each number in standard notation, without eponents Simplify. Assume that variables in the eponent represent nonzero integers and that, y, and z are not y y a+ 1. a a z z z t t1 t 1. E-10 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

11 Additional Eercises.1 Form III Name Date Simplify each epression. Write answers with positive eponents ( y )(6 y z ) y z y z y y 9... a a a. 6. zy 8z y 6. Write each number in scientific notation. 7.,896,600, ,800,000,000, Write each number in standard notation, without eponents Simplify. Assume that variables in the eponent represent nonzero integers and that, y, and z are not a+ 6 a y y nm k nm k z y z y b a c b a c E-10 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

12 Additional Eercises. Form I Name Date Simplify. Write each answer using positive eponents only. 1. ( ). ( ) y. ( y ).. 6. z z z 6. Perform each indicated operation. Write each answer in scientific notation. 7. ( 10 6 ) Simplify. Assume that variables in the eponent represent nonzero integers and that all other variables are not (y n ) b b y a a y Solve. Write the answer in scientific notation. 1. A certain computer can do a simple computation in 10 7 seconds. Epress how long it would take this computer to do this task 000 times. 1. E-106 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

13 Additional Eercises. Form II Name Date Simplify. Write each answer using positive eponents only. 1. ( ). ( 6 ). ( y z ). a b 6. ( y z 1 ) a 1 a b ab 6. Perform each indicated operation. Write each answer in scientific notation. 7. ( 10 )(.1 10 ) 8. (.9 10 )(1. 10 ) Simplify. Assume that variables in the eponent represent nonzero integers and that all other variables are not b ( ) a a a b b y7 y a a y y Solve. Write the answer in scientific notation. 1. To convert from square inches to square meters, multiply by The area of a square is 9 10 square inches. Convert this area to square meters. 1. E-107 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

14 Additional Eercises. Form III Name Date Simplify. Write each answer using positive eponents only. 1.. ( z y 8 ) y 7 6 y z y y y y (a 7 y 6 ) (10a y )(a y ) 6. Perform each indicated operation. Write each answer in scientific notation (6. 10 )( )(. 10 ) Simplify. Assume that variables in the eponent represent nonzero integers and that all other variables are not ( a 1 ) ( a+ ) 1 ( a ) y y a1 a a a y y a a a a Solve. Write the answer in scientific notation Find a cube s volume if each side is 0.07 meters long. E-108 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

15 Additional Eercises. Form I Find the degree of each polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of these Name Date Perform the indicated operations.. (y + ) + (y + 1) 6. (7 + ) ( + ) y y6 y (8y 7) + (y 6) + ( y ) 9. ( + ) + (7 6 ) 10. (1y y + 6) (1y 8y 1) If P() = and Q() =, find each function value. 11. P(0) 1. Q( ) 1. P( 1) 1. Q() 1. A ball dropped from a cliff that is 1 feet above the ground. Neglecting air resistance, the height of the ball in feet at any time t, in seconds, can be described by the polynomial function P(t) = 16t + 1. Find the height of the ball at t = seconds E-109 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

16 Additional Eercises. Form II Name Date Find the degree of each polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of these y y Perform the indicated operations.. (6y 11) + (6y ) 6. ( 9) + ( + ) y y + 1 y 9. (11y y + ) (9y 7y ) 10. Find the sum of 10yz + y and 10yz + y 7. If P() = + 7 and Q() = 8, find each function value. 11. P( ) 1. Q() 1. P() 1. Q( ) 1. A projectile is fired upward from the ground with an velocity of 0 feet per second. Neglecting air resistance, the height of the projectile in feet at any time t, in seconds, can be described by the polynomial function P(t) = 16t + 0t. Find the height at t = seconds E-110 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

17 Additional Eercises. Form III Name Date Find the degree of each polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of these y y. y + 7 y Perform the indicated operations.. (7 y 8y + ) + ( y + y ) 6. (19ab 1a b + b ) (0ab 8a b b) 7. ( y y + 7) ( y + y 8) 8. Subtract from the sum of 8 + and y y y y y y If P() = and Q() = 9 +, find each function value. 11. P() 1. Q() 1. P( ) 1. Q() An object is thrown upward with an initial velocity of feet per second from the rim of a canyon. The rim is 80 feet above the canyon floor. Neglecting air resistance, the height of the projectile in feet at any time t, in seconds, can be described by the polynomial function P(t) = 16t + t Find the height at t = 8 seconds. E-111 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

18 Additional Eercises. Form I Name Date Multiply. 1. (7y)( 6y). ( )( ). (6 7) 1... Use the FOIL order to multiply.. ( + )( ). (y )(y 6) 6. ( 7)( + ).. 6. Use special product methods to multiply. 7. ( + 7)( 7) 8. (y ) 9. [ + ( + )][ ( + )] Multiply. 10. ( )( + )( + 16) 11. (z + )(z )(z ) If f() = 1, find the following. 1. f(a + 1) 1. f(a + h) f(a) Multiply. Assume that variables represent positive integers. 1. ( n + )( n ) 1. ( n y m )( n + y m ) E-11 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

19 Additional Eercises. Form II Multiply. 1. (1a b)( ab ). ( ab)(a ya ). (a + )(a a + 6) Name Date 1... Use the FOIL order to multiply.. ( )( + 8). (y )(y 7) 6. ( z)( + z).. 6. Use special product methods to multiply. 7. ( + y)( y) 8. (z ) 9. [6 (b )][6 + (b )] Multiply. 10. ( 7)( + 7)( + 9) 11. ( ) If f() =, find the following. 1. f(y ) 1. f(a + h) f(a) Multiply. Assume that variables represent positive integers. 1. ( a y b )(y b a y) 1. ( n + y)( n y ) E-11 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

20 Additional Eercises. Form III Name Date Multiply. 1. ( y)( 6 + y y ). ( )( + 1). (y 7)(y + y +1) Use the FOIL order to multiply (y z)(y + 7z) y y 6. Use special product methods to multiply y y 8. [( ) + 1] 9. [ + ( + )][ ( + )] Multiply. 10. ( )( 1)( + ) ( )( + 10)( + ) If f() = +, find the following. 1. f(z + ) 1. f(a + h) f(a) Multiply. Assume that variables represent positive integers. 1. (y a b y)(y a b y) 1. ( y n+1 )(y n y n 1 ) E-11 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

21 Additional Eercises. Form I Name Date Find the GCF of each list of monomials. 1.,,. y, 1 y, 8y 1.. Factor out the GCF ( ) + ( ). y(y + ) (y + ) y + 1y + 1y Factor each polynomial by grouping y + y 10. ab 7a b Solve. 1. The material needed to manufacture a bo with two square ends is given by the polynomial + y, where is the length of the square ends and y is the length of the other sides. Factor this polynomial. 1. An object dropped from 6 above the ground has a height of 16t + 6 feet after t seconds. Factor this polynomial E-11 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

22 Additional Eercises. Form II Name Date Find the GCF of each list of monomials y, 18 y, y. 7 y, 8 y, 1 y Factor out the GCF.. 6a b 9ab. (y + 1) (y + 1). y y + 10 y a 1 + a 1a 7. y + 1y Factor each polynomial by grouping. 8. 8y 6y y y y y Solve. 1. The material needed to manufacture a bo whose opposite sides are identical is given by the polynomial y + yz + z, where, y, and z are the lengths of the different sides. Factor this polynomial in terms of the reciprocals of each length. 1. An object shot from the ground with an initial velocity of 80 feet per second has a height of 16t + 80t feet after t seconds. Factor this polynomial E-116 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

23 Additional Eercises. Form III Name Date Find the GCF of each list of monomials. 1. y z, 18 yz, 9y z. 8ab c, 1a b c, 16a b c 1.. Factor out the GCF.. ab (b + 7) (b + 7). 16a b a b + ab ab. 1 y 8 y + 7 y 7y 6. y z 6y z + y z m n m n m n Factor each polynomial by grouping z z y + y 10. mn mn n a y b + a y 6b 6a y b a y b 1. Solve a b a b a b a b 6 6 m n m n m n m n 1. A design for a spherical metal shell is needed. The shell has a thickness of t, so that its inner radius is r and its outer radius is R = r + t. The volume of the material used for the shell is given by the polynomial R r. Factor this polynomial. Then rewrite the polynomial in simplest form in terms of the inner radius r and thickness t. 1. A model rocket is fired from the floor of a canyon that is 6 feet the canyon edge. If the object has an initial upward velocity of 18 feet per second, it will have a height of 16t + 18t 6 feet with respect to the edge after t seconds. Factor this polynomial E-117 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

24 Additional Eercises.6 Form I Name Date Factor each trinomial Use substitution to factor each polynomial completely (11 + ) + 9(11 + ) (y ) 1(y ) Solve. 1. Find all positive and negative integers b such that + b + can be factored. 1. Find all positive and negative integers b such that + b + can be factored. 1. The volume V() of a bo in terms of its height is given by the function V() = 6. Factor this epression for V() E-118 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

25 Additional Eercises.6 Form II Name Date Factor each trinomial y 1y. y 16y + y y + 9y 0 Use substitution to factor each polynomial completely. Solve (a + 7) (a + 7) ( + 8) + 11( + 8) Find all positive and negative integers b such that + b 1 factors. 1. Find all positive and negative integers b such that + b + factors. 1. The volume V() of a bo in terms of its height is given by the function V() = 1. Factor this epression for V() E-119 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

26 Additional Eercises.6 Form III Name Date Factor each trinomial y + 8y. + y + 8y y 8 y Use substitution to factor each polynomial completely (a + ) (a + ) (a ) (a ) Solve. 1. Find all positive and negative integers b such that + b factors. 1. Find all positive and negative integers b such that + b 8 factors. 1. The volume V() of a bo in terms of its height is given by the function V() = 1. Factor this epression for V() E-10 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

27 Additional Eercises.7 Form I Name Date Factor the following y ( 1) y t b 8a y 1. ( + 1) 1. ab 1000a y E-11 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

28 Additional Eercises.7 Form II Name Date Factor the following y y + y. y 6. 81y ( ) y y 8. a b + 1b 9. y y 11. ( + ) 1. a 18a + 81 b y + y 1. m m + 6 n E-1 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

29 Additional Eercises.7 Form III Name Date Factor the following y + 8 y y y. 9y y 9 7. ( 1) y b a + 6b a + b 11. a y y y + y E-1 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

30 Additional Eercises.8 Form I Name Date Solve each equation. 1. ( )( 6) = 0. ( + )( ) = 0. 8 = 0. + = 6. y = 1y 6. + = = 0 8. y = 6y 9. z 8z + 16 = t t = t(7 + t) 11. = 1. ( + )( 7)( 9) = Solve. 1. One number eceeds another number by 6 and their product is 91. Find the numbers. 1. A rectangular floor has an area of square meters. The length of the floor is meters less than twice the width. What is the length and width of the floor? 1. A board is leaning against a wall. The top of the board is feet above the ground, and the bottom of the board is feet from the bottom of the wall. How long is the board? E-1 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

31 Additional Eercises.8 Form II Name Date Solve each equation. 1. ( 1)( + 9) = 0. ( 1)( + )( 6) = = 0. Solve = = t = 6t 8. (9 10) = 0 9. ( 1) = t (7t + ) = t = ( + ) = 7( ) 1. If the sum of two numbers is and their product is 8 9, find the numbers. 1. A gardener wants to put a uniform border of gravel around the outside of a 16-foot by 0-foot garden. Find how wide the border should be if she has enough gravel to cover square feet. 1. A 10-foot ladder is placed against a wall so the bottom of the ladder is 6 feet from the bottom of the wall. How high from the ground is the top of the ladder? E-1 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

32 Additional Eercises.8 Form III Name Date Solve each equation. 1. (7 + 8)( ) = 0. 6( + 11)( 9) = 0. ( + 8)( 6)( 11) = 0. y y 16 = (6 1)( + ) = (t + ) t = 6(t ) 9. 7y + 1y = z + 7z = z Solve. y y 0 1. The sum of the square of two consecutive even integers is 80. Find the integers. 1. A contractor is going to lay a concrete sidewalk around a park. The park dimensions within the sidewalk are 10 feet by 110 feet. How wide will the sidewalk be if the contractor has enough concrete to cover 196 square feet? 1. A support cable runs from the top of a radio transmission tower to the ground. The distance between the base of the tower and the place where the cable is anchored is 90 feet. If the cable is 10 feet long, how tall is the tower? E-16 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

33 Name: Instructor: Date: Section: Section.1 Eponents and Scientific Notation Objective: Calculate using scientific notation. Suggested Format: Small group format Time: 10 minutes Answer each of the following questions. You may wish to use a calculator. 1. Each side of a cube is.1 10 cm. Calculate the volume of the cube in cubic centimeters. Give your answer in scientific notation. 1. The distance light travels in one year is approimately miles. How far does light travel in weeks? Write your answer in scientific notation, rounded to three decimal places.. According to the Medical College of Wisconsin, the average American consumes 8 grams of fat in a single day. If the population of the U.S. is 01,19,97 people, what is the total number of fat grams consumed by Americans in a single day? Write your answer in scientific notation, rounded to three decimal places. A- 1 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

34 Name: Instructor: Date: Section: Section. More Work with Eponents and Scientific Notation Objective: Write epressions containing positive and negative eponents in simplified form. Suggested Format: Think and Pair Time: 1 minutes Work each problem as quickly as you can. Speed is the goal in this part. Simplify the following ( 6) ( ) +.. y y.. Evaluate 0. ( 7 ) 0 y when = and y =.. +. Now work the following problems at a steady speed you are comfortable with. Then confirm your results on both parts with your partner ( 6 y ) ( ) ( ) y ( y) ( ) Evaluate y when = 1 and y =. 10. A- 1 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

35 Name: Instructor: Date: Section: Chapter Test Form A Simplify each epression. Write with positive eponents. 1. ( )( )( 6) 1.. y y. ( ) ( 1 ab 8a b ). 1 a b.. Write in scientific notation: 6,000.. Write without eponents: Use scientific notation to find the quotient. 6. ( 0.06)( ) Perform the indicated operations. 7. ( 8) ( ) ( y + ) + ( y + ) y( + ) ( )( + ) ( ) ( 1)( ) ( )( + ) 1. T- 99 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

36 Name: Instructor: Date: Section: Chapter Test Form A cont d Factor each polynomial completely y y y y y 0. Solve each equation ( )( + 7) = ( + )( 1) = ( ) = 0.. The sum of twice a number and its square is.. Find the number.. One number eceeds another number by 9,. and their product is 11. Find the numbers. T- 100 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

37 Name: Instructor: Date: Section: Chapter Test Form B Simplify each epression. Write answers with positive eponents. ( ) ( ) 0 1 6a b ab 1. a b 1.. a a m 1 m m a. a. ( y )( 9 y ) 1.. Use scientific notation to find the quotient.. 8 (.8 10 )( ) Write in scientific notation Write without the eponents Perform the indicated operations. 7. ( y) + ( y) ( y ) Subtract 6 from ( a b)( a + b) y ( y)( + y) ( y) ( )( + ) 1. Factor each polynomial completely a b + 6a b T- 101 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

38 Name: Instructor: Date: Section: Chapter Test Form B cont d 1. m + n 0mn a ab + a 8b y Solve each equation. 0. ( )( + )( ) = = = 6.. = 1.. A ball is dropped from the top of a 76 foot. building. Its height h ( t) at time t seconds is given by h ( t) = 16t Determine how long it takes the ball to hit the ground.. One number eceeds another number by, and. their product is 66. Find the numbers. T- 10 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

39 Name: Instructor: Date: Section: Chapter Test Form C Simplify each epression. Write answers with positive eponents. ( ) ( ) 0 6 y 8 y 1. 1 y 1.. y. m+ 7. m m.. Use scientific notation to find the quotient.. 6 ( )( 10 ) Write in scientific notation Write without eponents Perform the indicated operations. 7. ( + 11) ( + 1) + ( 8) ( 7y)( + y) y ( y ) ( 7) ( 7)( + 7) 1. Factor each polynomial completely y z y T- 10 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

40 Name: Instructor: Date: Section: Chapter Test Form C cont d 1. + y + 0y m y Solve each equations. 0. ( )( 1) = = = ( ) = The length of a rectangle is meters less than. twice the width. Find the dimensions of the rectangle if its area is 8 square meters.. One number eceeds another number by 7.. Their product is 10. Find the numbers. T- 10 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

41 Name: Instructor: Date: Section: Chapter Test Form D Circle the correct answer. Simplify each epression. Write answers with positive eponents. 1. ( y) ( y ) 7y a. 1 76y b. 1 9y 9y c. d y 6. a a. 9a b. a c. 9a d. 1 9a. y z 6 y a. z 9 z b. 6 9 y 6 z c. 9 y z d. 6 y ( 1 ) 0 a. 7 b. 8 c. 0 d.. Use scientific notation to find the quotient. ( )(,000 ) a b c d Write in scientific notation a b.,60,000 c d. 6,000,000 Perform the indicated operations. 7. ( y + y ) + ( y y + ) a. y y b. 0 c. y + y d. y y y T- 10 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

42 Name: Instructor: Date: Section: Chapter Test Form D cont d 8. Subtract ( ) from ( 6 + 6) a b c d ( + )( 9) a b c d ( + y)( 6y) a. c. 1y y b. 1y y d. 1y y + y y 11. ( y) a. 9 + y 1y b. 9 y 1y c. 9 y d. 9 + y 1. ( 7)( + 7) a b c d ( )( + 6 ) a b c d Factor each polynomial completely a b + 0a b a. a b( b a) b. a b( b + a) c. ab ( 8a b + 10a ) d. a b( 8b + 10a) a. ( )( ) b. ( 6 )( +1) c. ( )( ) d. ( + )( ) T- 106 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

43 Name: Instructor: Date: Section: Chapter Test Form D cont d 16. m + 9m 1m a. ( m + )( m 1) b. m ( m + )( m 1) c. m ( m )( m + 1) d. m ( m ) 17. 0y + y a. ( + y) b. ( y) c. ( y) d. ( y)( + y) 18. 6a + ab + b a. ( a + b)( b a) b. ( a b)( a + b) c. ( a + b)( a b) d. ( a b)( a b) y a. ( 9y) b. ( 9y)( 9y) c. ( + 9y) d. ( + 9y)( 9y) Solve each equation. 0. ( + )( ) = 0 a., 0, b., 0, c., d., 1. 7 = 0 a. 1 1, b., c. 1 1, d., T- 107 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

44 Name: Instructor: Date: Section: Chapter Test Form D cont d. + 1 = 1 a. 0,, b., c.,0, d.,. A stone is dropped from a foot cliff. Its height h ( t) at time t seconds is given by h ( t) = 16t +. Determine how long it takes the stone to hit the ground. a.. sec b.. sec c. sec d. 6 sec. The sum of a number and its square is 0. Find the number a., 10 b. 10, c. 6, d., 6. A rectangular room with an area of 80 square feet has a width that is 6 feet more than the length. Find the dimensions of the room. a. 1 feet by 0 feet b. 0 feet by 6 feet c. 1 feet by 18 feet d. 16 feet by feet T- 108 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

45 Name: Instructor: Date: Section: Chapter Test Form E Circle the correct answer. Simplify each epression. Write answers with positive eponents. 1. a b( a b ) 1a a. b 6 a b. 8 6b a c. d. 9 b a b 8 7 y 9 y. y a. b. y y 18 0 c. y y 1 d. 17 a+ 1. a a. a b. a+ c. a+ d. a. ( a b ) 1 a a. 6 6b b a b c. a d. 6b 6 a 6b ( )( ) Use scientific notation to find the quotient. a. 10 b. 10 c. 10 d Use scientific notation to find the quotient ( 10 )( 0.00 ) a b c. 10 d Perform the indicated operations. 7. ( 7 ) + ( + ) ( 9 ) a. b. + c d. T- 109 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall + + 7

46 Name: Instructor: Date: Section: Chapter Test Form E cont d 8. ( y)( y z) a. 1 y z b. 1 y z c. 1 y z d. 8 y z 9. ( y)( + 6y) a. c. + y + 0y b. + 1y 0y d. y + 0y + y 0y 10. mn ( m )( m + ) a. c. m n 10mn b. m n + 6m n 0mn m n + 1m n 0mn d. m n + 6m 10n 11. ( 7 ) a b c d ( 8)( + 8) a b. 6 c. 9 6 d ( + )( + ) a b c. + 1 d Factor each polynomial completely a. ( + 9)( + ) b. ( + )( + ) c. ( + )( + 1) d. ( + 6)( + ) T- 110 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

47 Name: Instructor: Date: Section: Chapter Test Form E cont d y y a. y ( ) b. ( y y) c. y ( 8 7) d. y ( )( ) 16. 8m + 1m 1 a. ( m )( m + ) b. ( m + )( m ) c. ( m )( m + ) d. ( m )( m + ) 17. 9m mn + 9n a. ( n m 7 ) b. ( m 7n)( m + 7n) c. ( 9m 9n) d. ( m + 7n) y + y a. ( + y) b. ( + y) c. ( + y) d. ( + y)( + y) a. does not factor b. ( + 1) 16( + 1) c. ( 16)( + 1) d. ( + 1)( + )( ) Solve each equation. 0. ( )( ) = 0 a.,0, b. 0,, c.,, d.,, T- 111 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

48 Name: Instructor: Date: Section: Chapter Test Form E cont d = 0 a., b., c., d.,. 1 = 18 a. 1, 6 b. 1,, 6 c. 6, 11 d. 1, 0, 6. ( + )( ) = + 6 a., b., c., d., A stone is thrown upward from the top of the cliff, which is 86 feet high, with an initial velocity of 8 feet per second. Neglecting air resistance, the height h ( t) of the stone t h t = 16t + 8t +. seconds after it is thrown is given by ( ) 86. When will the stone hit the ground? a. 10 sec b. 9 sec c. 6 sec d. sec. Find the height of the stone when t =. a. 896 feet b. 800 feet c. 70 feet d. 16 feet T- 11 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

49 Name: Instructor: Date: Section: Chapter Test Form F Circle the correct answer. Simplify each epression. Write down with positive eponents. ( ) ( ) m n m n 1. 8m n a. 0 b. 8 18m n c. 1 m n d. m 1 n y. 1 y 1+ y a. 1 y b. y 1 c. y 9 d. 6 y ( )( ) Use scientific notation to find the quotient a b c d a. 8 b. 6 c. 11 d. 7 Perform the indicated operations.. Subtract ( ) from ( 6 8) + a b c d a. b. c. + d. + 1 T- 11 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

50 Name: Instructor: Date: Section: Chapter Test Form F cont d 7. m n ( m )( n 1) a. m n + 6m n b. c. 0 d. 9m n + 6m n m n m n 6m n + 6m n 8. ( 6 ) a b c d ( 8)( + 8) a. 9 6 b c d ( a + b)( a b) a. 1a b c. 1a + 7ab 10b d. 7ab 10 b. 11. ( )( 7 + ) 1a + ab 10b 1a ab + 10b a. 9 b c d Factor each polynomial completely y y a. y ( + y) b. y ( y) c. ( y + ) d. y ( + y) y + 98y a. ( 7y)( + 7y) b. ( + 7y ) c. 6( 7y) d. ( 7y) T- 11 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

51 Name: Instructor: Date: Section: Chapter Test Form F cont d y y 1. a. ( 8 7y)( + 7 y) b. ( 16 y)( + 7y) c. ( 8 y)( + 7y) d. ( 8 + y)( 7y) 1a 8b a. ( a b)( a + 0ab + b ) b. ( a b)( a + 10ab + b ) c. ( a b)( a + 10ab + b ) d. b ( a b)( a 10ab + b ) b + 19b 18b a. b ( b 6)( 8b + 1) b. ( b + 6)( 8b 1) c. b ( b 6)( 8b 1) d. ( b + 6)( 8b 1) y a. ( 7y)( + 7y) b. ( + 7y)( + + 7y) c. ( + 7y)( + 7y) d. ( + 7 y) 18. 6a b a. ( 16a b ) b. ( 16a + b )( a b)( a + b) c. ( a b) ( a + b) d. ( 16a + b )( 16a b ) Solve each equation ( + 7)( ) = 0 a. 7,0, b. 7, c.,0, d. 7,0, = 0 a., 10 b., c., d. 10, = a. 9 9, b., 9 c., d. 9, T- 11 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

52 Name: Instructor: Date: Section: Chapter Test Form F cont d. ( 8) = a., 1 b. 8, 1 c., 1 d., 8. 8 ( ) = 6 9 a., b., c., d.,. If the cost, C ( ), for manufacturing units of a certain product is given by ( ) = 0 + C, find the number of units manufactured at a cost of $60. a. 6 units b. 8 units c. 70 units d. 9 units. The product of two consecutive even integers is less than times the smaller one. What are the numbers? a., 6 b. 0, c., d. 6, 8 T- 116 Copyright 009 Pearson Education, Inc., publishing as Pearson Prentice Hall

Mini-Lecture 8.1 Solving Quadratic Equations by Completing the Square

Mini-Lecture 8.1 Solving Quadratic Equations by Completing the Square Mini-Lecture 8.1 Solving Quadratic Equations b Completing the Square Learning Objectives: 1. Use the square root propert to solve quadratic equations.. Solve quadratic equations b completing the square.

More information

Mini-Lecture 7.1 Radicals and Radical Functions

Mini-Lecture 7.1 Radicals and Radical Functions Mini-Lecture 7. Radicals and Radical Functions Learning Objectives:. Find square roots.. Approimate roots.. Find cube roots.. Find n th roots.. Find n a n when a is an real number. 6. Graph square and

More information

Divisibility Rules Algebra 9.0

Divisibility Rules Algebra 9.0 Name Period Divisibility Rules Algebra 9.0 A Prime Number is a whole number whose only factors are 1 and itself. To find all of the prime numbers between 1 and 100, complete the following eercise: 1. Cross

More information

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Chapter 7 Maintaining Mathematical Proficiency Simplify the expression. 1. 5x 6 + 3x. 3t + 7 3t 4 3. 8s 4 + 4s 6 5s 4. 9m + 3 + m 3 + 5m 5. 4 3p 7 3p 4 1 z 1 + 4 6. ( ) 7. 6( x + ) 4 8. 3( h + 4) 3( h

More information

8/15/2018, 8:31 PM. Assignment: Math 0410 Homework150bbbbtsiallnew123. Student: Date: Instructor: Alfredo Alvarez Course: Math 0410 Spring 2018

8/15/2018, 8:31 PM. Assignment: Math 0410 Homework150bbbbtsiallnew123. Student: Date: Instructor: Alfredo Alvarez Course: Math 0410 Spring 2018 of 3 8/15/018, 8:31 PM Student: Date: Instructor: Alfredo Alvarez Course: Math 0410 Spring 018 Assignment: Math 0410 Homework150bbbbtsiallnew13 1. Evaluate x y for the given replacement values. x=4and

More information

Mini Lecture 1.1 Introduction to Algebra: Variables and Mathematical Models

Mini Lecture 1.1 Introduction to Algebra: Variables and Mathematical Models Mini Lecture. Introduction to Algebra: Variables and Mathematical Models. Evaluate algebraic epressions.. Translate English phrases into algebraic epressions.. Determine whether a number is a solution

More information

150. a. Clear fractions in the following equation and write in. b. For the equation you wrote in part (a), compute. The Quadratic Formula

150. a. Clear fractions in the following equation and write in. b. For the equation you wrote in part (a), compute. The Quadratic Formula 75 CHAPTER Quadratic Equations and Functions Preview Eercises Eercises 8 50 will help you prepare for the material covered in the net section. 8. a. Solve by factoring: 8 + - 0. b. The quadratic equation

More information

UNIT 9 (Chapter 7 BI) Polynomials and Factoring Name:

UNIT 9 (Chapter 7 BI) Polynomials and Factoring Name: UNIT 9 (Chapter 7 BI) Polynomials and Factoring Name: The calendar and all assignments are subject to change. Students will be notified of any changes during class, so it is their responsibility to pay

More information

= 9 = x + 8 = = -5x 19. For today: 2.5 (Review) and. 4.4a (also review) Objectives:

= 9 = x + 8 = = -5x 19. For today: 2.5 (Review) and. 4.4a (also review) Objectives: Math 65 / Notes & Practice #1 / 20 points / Due. / Name: Home Work Practice: Simplify the following expressions by reducing the fractions: 16 = 4 = 8xy =? = 9 40 32 38x 64 16 Solve the following equations

More information

Secondary Math 2H Unit 3 Notes: Factoring and Solving Quadratics

Secondary Math 2H Unit 3 Notes: Factoring and Solving Quadratics Secondary Math H Unit 3 Notes: Factoring and Solving Quadratics 3.1 Factoring out the Greatest Common Factor (GCF) Factoring: The reverse of multiplying. It means figuring out what you would multiply together

More information

Algebra I Polynomials

Algebra I Polynomials Slide 1 / 217 Slide 2 / 217 Algebra I Polynomials 2014-04-24 www.njctl.org Slide 3 / 217 Table of Contents Definitions of Monomials, Polynomials and Degrees Adding and Subtracting Polynomials Multiplying

More information

Polynomials 370 UNIT 10 WORKING WITH POLYNOMIALS. The railcars are linked together.

Polynomials 370 UNIT 10 WORKING WITH POLYNOMIALS. The railcars are linked together. UNIT 10 Working with Polynomials The railcars are linked together. 370 UNIT 10 WORKING WITH POLYNOMIALS Just as a train is built from linking railcars together, a polynomial is built by bringing terms

More information

Algebra I Notes Unit Eleven: Polynomials

Algebra I Notes Unit Eleven: Polynomials Syllabus Objective: 9.1 The student will add, subtract, multiply, and factor polynomials connecting the arithmetic and algebraic processes. Teacher Note: A nice way to illustrate operations with polynomials

More information

Mini Lecture 9.1 Finding Roots

Mini Lecture 9.1 Finding Roots Mini Lecture 9. Finding Roots. Find square roots.. Evaluate models containing square roots.. Use a calculator to find decimal approimations for irrational square roots. 4. Find higher roots. Evaluat. a.

More information

LESSON 9.1 ROOTS AND RADICALS

LESSON 9.1 ROOTS AND RADICALS LESSON 9.1 ROOTS AND RADICALS LESSON 9.1 ROOTS AND RADICALS 67 OVERVIEW Here s what you ll learn in this lesson: Square Roots and Cube Roots a. Definition of square root and cube root b. Radicand, radical

More information

Lecture Guide. Math 90 - Intermediate Algebra. Stephen Toner. Intermediate Algebra, 3rd edition. Miller, O'Neill, & Hyde. Victor Valley College

Lecture Guide. Math 90 - Intermediate Algebra. Stephen Toner. Intermediate Algebra, 3rd edition. Miller, O'Neill, & Hyde. Victor Valley College Lecture Guide Math 90 - Intermediate Algebra to accompany Intermediate Algebra, 3rd edition Miller, O'Neill, & Hyde Prepared by Stephen Toner Victor Valley College Last updated: 4/17/16 5.1 Exponents &

More information

Algebra I. Polynomials.

Algebra I. Polynomials. 1 Algebra I Polynomials 2015 11 02 www.njctl.org 2 Table of Contents Definitions of Monomials, Polynomials and Degrees Adding and Subtracting Polynomials Multiplying a Polynomial by a Monomial Multiplying

More information

Mini Lecture 1.1 Introduction to Algebra: Variables and Mathematical Models

Mini Lecture 1.1 Introduction to Algebra: Variables and Mathematical Models Mini Lecture. Introduction to Algebra: Variables and Mathematical Models. Evaluate algebraic epressions.. Translate English phrases into algebraic epressions.. Determine whether a number is a solution

More information

Polynomials and Factoring

Polynomials and Factoring 7.6 Polynomials and Factoring Basic Terminology A term, or monomial, is defined to be a number, a variable, or a product of numbers and variables. A polynomial is a term or a finite sum or difference of

More information

Instructor: Richard Getso Course: Math 200.P10 TR 1:00 PM Spring 2016 (Getso)

Instructor: Richard Getso Course: Math 200.P10 TR 1:00 PM Spring 2016 (Getso) 1/8/016 Practice Test 1 (Chapter 11) Richard Getso Student: Richard Getso Date: 1/8/16 Instructor: Richard Getso Course: Math 00.P10 TR 1:00 PM Spring 016 (Getso) Assignment: Practice Test 1 (Chapter 11)

More information

5.1, 5.2, 5.3 Properites of Exponents last revised 6/7/2014. c = Properites of Exponents. *Simplify each of the following:

5.1, 5.2, 5.3 Properites of Exponents last revised 6/7/2014. c = Properites of Exponents. *Simplify each of the following: 48 5.1, 5.2, 5.3 Properites of Exponents last revised 6/7/2014 Properites of Exponents 1. x a x b = x a+b *Simplify each of the following: a. x 4 x 8 = b. x 5 x 7 x = 2. xa xb = xa b c. 5 6 5 11 = d. x14

More information

Algebra II Chapter 5: Polynomials and Polynomial Functions Part 1

Algebra II Chapter 5: Polynomials and Polynomial Functions Part 1 Algebra II Chapter 5: Polynomials and Polynomial Functions Part 1 Chapter 5 Lesson 1 Use Properties of Exponents Vocabulary Learn these! Love these! Know these! 1 Example 1: Evaluate Numerical Expressions

More information

Appendix A A318. Appendix A.1 (page A8) Vocabulary Check (page A8) Answers to All Exercises and Tests. x (c) Bounded

Appendix A A318. Appendix A.1 (page A8) Vocabulary Check (page A8) Answers to All Exercises and Tests. x (c) Bounded A Answers to All Eercises and Tests Appendi A Appendi A. (page A) Vocabulary Check (page A). rational. irrational. absolute value. composite. prime. variables; constants. terms. coefficient 9. Zero-Factor

More information

Algebra Final Exam Review Packet

Algebra Final Exam Review Packet Algebra 1 00 Final Eam Review Packet UNIT 1 EXPONENTS / RADICALS Eponents Degree of a monomial: Add the degrees of all the in the monomial together. o Eample - Find the degree of 5 7 yz Degree of a polynomial:

More information

Additional Exercises 7.1 Form I The Greatest Common Factor and Factoring by Grouping

Additional Exercises 7.1 Form I The Greatest Common Factor and Factoring by Grouping Additional Exercises 7.1 Form I The Greatest Common Factor and Factoring by Grouping Find the greatest common factor of each list of monomials. 1. 10x and 15 x 1.. 3 1y and 8y. 3. 16 a 3 a, 4 and 4 3a

More information

Summer Prep Packet for students entering Algebra 2

Summer Prep Packet for students entering Algebra 2 Summer Prep Packet for students entering Algebra The following skills and concepts included in this packet are vital for your success in Algebra. The Mt. Hebron Math Department encourages all students

More information

Algebra I Part B. Help Pages & Who Knows

Algebra I Part B. Help Pages & Who Knows Algebra I Part B & Who Knows 83 Vocabulary General Absolute Value the distance between a number,, and zero on a number line; written as. Eample: 5 = 5 reads The absolute value of 5 is 5. -7 = 7 reads The

More information

University of Colorado at Colorado Springs Math 090 Fundamentals of College Algebra

University of Colorado at Colorado Springs Math 090 Fundamentals of College Algebra University of Colorado at Colorado Springs Math 090 Fundamentals of College Algebra Table of Contents Chapter The Algebra of Polynomials Chapter Factoring 7 Chapter 3 Fractions Chapter 4 Eponents and Radicals

More information

8.2 Solving Quadratic Equations by the Quadratic Formula

8.2 Solving Quadratic Equations by the Quadratic Formula Section 8. Solving Quadratic Equations by the Quadratic Formula 85 8. Solving Quadratic Equations by the Quadratic Formula S Solve Quadratic Equations by Using the Quadratic Formula. Determine the Number

More information

Solving and Graphing Polynomials

Solving and Graphing Polynomials UNIT 9 Solving and Graphing Polynomials You can see laminar and turbulent fl ow in a fountain. Copyright 009, K1 Inc. All rights reserved. This material may not be reproduced in whole or in part, including

More information

Chapter 10. Section 10.1 = 2(27) Practice Problems. The value of 2y + y 6 when y = 3 is 57. The height of the object at 1 second is 514 feet.

Chapter 10. Section 10.1 = 2(27) Practice Problems. The value of 2y + y 6 when y = 3 is 57. The height of the object at 1 second is 514 feet. Chapter 0 Section 0. Practice Problems. (+ + ( ( + ( ( + (. ( + ( + 0. ( z.z+ + (z.z+. z + z.z.z+ +. z.z+.. +. +... ( + ( + ( + ( ( + ( ( +. (b+ (b 0 (b+ + ( b+ 0 b b+ + 0 b +. ( + + ( + ( + + + ( + +

More information

Unit 3. Expressions and Equations. 118 Jordan School District

Unit 3. Expressions and Equations. 118 Jordan School District Unit 3 Epressions and Equations 118 Unit 3 Cluster 1 (A.SSE.): Interpret the Structure of Epressions Cluster 1: Interpret the structure of epressions 3.1. Recognize functions that are quadratic in nature

More information

STANDARDS OF LEARNING CONTENT REVIEW NOTES. ALGEBRA I Part II. 2 nd Nine Weeks,

STANDARDS OF LEARNING CONTENT REVIEW NOTES. ALGEBRA I Part II. 2 nd Nine Weeks, STANDARDS OF LEARNING CONTENT REVIEW NOTES ALGEBRA I Part II 2 nd Nine Weeks, 2016-2017 1 OVERVIEW Algebra I Content Review Notes are designed by the High School Mathematics Steering Committee as a resource

More information

Due for this week. Slide 2. Copyright 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Due for this week. Slide 2. Copyright 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley MTH 09 Week 3 Due for this week Homework 3 (on MyMathLab via the Materials Link) The fifth night after class at 11:59pm. Read Chapter 6.6, 8.4 and 11.1-11.5 Do the MyMathLab Self-Check for week 3. Learning

More information

Algebra Review C H A P T E R. To solve an algebraic equation with one variable, find the value of the unknown variable.

Algebra Review C H A P T E R. To solve an algebraic equation with one variable, find the value of the unknown variable. C H A P T E R 6 Algebra Review This chapter reviews key skills and concepts of algebra that you need to know for the SAT. Throughout the chapter are sample questions in the style of SAT questions. Each

More information

Intermediate Algebra 100A Final Exam Review Fall 2007

Intermediate Algebra 100A Final Exam Review Fall 2007 1 Basic Concepts 1. Sets and Other Basic Concepts Words/Concepts to Know: roster form, set builder notation, union, intersection, real numbers, natural numbers, whole numbers, integers, rational numbers,

More information

Mini-Lecture 6.1 Rational Functions and Multiplying and Dividing Rational Expressions

Mini-Lecture 6.1 Rational Functions and Multiplying and Dividing Rational Expressions Learning Objectives: Mini-Lecture 6. Rational Functions and Multiplying and Dividing Rational Epressions. Find the domain of a rational function.. Simplify rational epressions.. Multiply rational epressions.

More information

LATE AND ABSENT HOMEWORK IS ACCEPTED UP TO THE TIME OF THE CHAPTER TEST ON

LATE AND ABSENT HOMEWORK IS ACCEPTED UP TO THE TIME OF THE CHAPTER TEST ON Trig/Math Anal Name No LATE AND ABSENT HOMEWORK IS ACCEPTED UP TO THE TIME OF THE CHAPTER TEST ON HW NO. SECTIONS ASSIGNMENT DUE FS-1 4-4 Practice Set A #1-57 eoo 4-5 Practice Set B #1-45 eoo, 57, 59 FS-

More information

2 P a g e. Essential Questions:

2 P a g e. Essential Questions: NC Math 1 Unit 5 Quadratic Functions Main Concepts Study Guide & Vocabulary Classifying, Adding, & Subtracting Polynomials Multiplying Polynomials Factoring Polynomials Review of Multiplying and Factoring

More information

Multiplication of Polynomials

Multiplication of Polynomials Summary 391 Chapter 5 SUMMARY Section 5.1 A polynomial in x is defined by a finite sum of terms of the form ax n, where a is a real number and n is a whole number. a is the coefficient of the term. n is

More information

Multiplying Monomials

Multiplying Monomials 320 Chapter 5 Polynomials Eample 1 Multiplying Monomials Multiply the monomials. a. 13 2 y 7 215 3 y2 b. 1 3 4 y 3 21 2 6 yz 8 2 a. 13 2 y 7 215 3 y2 13 521 2 3 21y 7 y2 15 5 y 8 Group coefficients and

More information

SECTION P.5. Factoring Polynomials. Objectives. Critical Thinking Exercises. Technology Exercises

SECTION P.5. Factoring Polynomials. Objectives. Critical Thinking Exercises. Technology Exercises BLITMCPB.QXP.0599_48-74 2/0/02 0:4 AM Page 48 48 Chapter P Prerequisites: Fundamental Concepts of Algebra Technology Eercises 98. The common cold is caused by a rhinovirus. The polynomial -0.75 4 + + 5

More information

Review: Properties of Exponents (Allow students to come up with these on their own.) m n m n. a a a. n n n m. a a a. a b a

Review: Properties of Exponents (Allow students to come up with these on their own.) m n m n. a a a. n n n m. a a a. a b a Algebra II Notes Unit Si: Polynomials Syllabus Objectives: 6. The student will simplify polynomial epressions. Review: Properties of Eponents (Allow students to come up with these on their own.) Let a

More information

Algebra II Notes Polynomial Functions Unit Introduction to Polynomials. Math Background

Algebra II Notes Polynomial Functions Unit Introduction to Polynomials. Math Background Introduction to Polynomials Math Background Previously, you Identified the components in an algebraic epression Factored quadratic epressions using special patterns, grouping method and the ac method Worked

More information

Algebra 2/Trig Apps: Chapter 5 Quadratics Packet

Algebra 2/Trig Apps: Chapter 5 Quadratics Packet Algebra /Trig Apps: Chapter 5 Quadratics Packet In this unit we will: Determine what the parameters a, h, and k do in the vertex form of a quadratic equation Determine the properties (vertex, axis of symmetry,

More information

NIT #7 CORE ALGE COMMON IALS

NIT #7 CORE ALGE COMMON IALS UN NIT #7 ANSWER KEY POLYNOMIALS Lesson #1 Introduction too Polynomials Lesson # Multiplying Polynomials Lesson # Factoring Polynomials Lesson # Factoring Based on Conjugate Pairs Lesson #5 Factoring Trinomials

More information

Lesson 10.1 Polynomials

Lesson 10.1 Polynomials Lesson 10.1 Polynomials Objectives Classify polynomials. Use algebra tiles to add polynomials. Add and subtract polynomials. A contractor is buying paint to cover the interior of two cubical storage tanks.

More information

1 of 32 4/24/2018, 11:38 AM

1 of 32 4/24/2018, 11:38 AM 1 of 3 4/4/018, 11:38 AM Student: Date: Instructor: Alfredo Alvarez Course: Math 0410 Spring 018 Assignment: Math 0410 Homework149aleks 1 Insert < or > between the pair of integers to make the statement

More information

Radical Expressions, Equations, and Functions

Radical Expressions, Equations, and Functions Radical Expressions, Equations, and Functions 0 Real-World Application An observation deck near the top of the Sears Tower in Chicago is 353 ft high. How far can a tourist see to the horizon from this

More information

Bishop Kelley High School Summer Math Program Course: Algebra 2 A

Bishop Kelley High School Summer Math Program Course: Algebra 2 A 06 07 Bishop Kelley High School Summer Math Program Course: Algebra A NAME: DIRECTIONS: Show all work in packet!!! The first 6 pages of this packet provide eamples as to how to work some of the problems

More information

Review for Mastery. Integer Exponents. Zero Exponents Negative Exponents Negative Exponents in the Denominator. Definition.

Review for Mastery. Integer Exponents. Zero Exponents Negative Exponents Negative Exponents in the Denominator. Definition. LESSON 6- Review for Mastery Integer Exponents Remember that means 8. The base is, the exponent is positive. Exponents can also be 0 or negative. Zero Exponents Negative Exponents Negative Exponents in

More information

UNIT 2 FACTORING. M2 Ch 11 all

UNIT 2 FACTORING. M2 Ch 11 all UNIT 2 FACTORING M2 Ch 11 all 2.1 Polynomials Objective I will be able to put polynomials in standard form and identify their degree and type. I will be able to add and subtract polynomials. Vocabulary

More information

Activity 1 Multiply Binomials. Activity 2 Multiply Binomials. You can use algebra tiles to find the product of two binomials.

Activity 1 Multiply Binomials. Activity 2 Multiply Binomials. You can use algebra tiles to find the product of two binomials. Algebra Lab Multiplying Polynomials You can use algebra tiles to find the product of two binomials. Virginia SOL A..b The student will perform operations on polynomials, including adding, subtracting,

More information

When factoring, we ALWAYS start with the (unless it s 1).

When factoring, we ALWAYS start with the (unless it s 1). Math 100 Elementary Algebra Sec 5.1: The Greatest Common Factor and Factor By Grouping (FBG) Recall: In the product XY, X and Y are factors. Defn In an expression, any factor that is common to each term

More information

5.3. Polynomials and Polynomial Functions

5.3. Polynomials and Polynomial Functions 5.3 Polynomials and Polynomial Functions Polynomial Vocabulary Term a number or a product of a number and variables raised to powers Coefficient numerical factor of a term Constant term which is only a

More information

A2T. Rational Expressions/Equations. Name: Teacher: Pd:

A2T. Rational Expressions/Equations. Name: Teacher: Pd: AT Packet #1: Rational Epressions/Equations Name: Teacher: Pd: Table of Contents o Day 1: SWBAT: Review Operations with Polynomials Pgs: 1-3 HW: Pages -3 in Packet o Day : SWBAT: Factor using the Greatest

More information

Chapter 4 Test, Form 2A

Chapter 4 Test, Form 2A NME TE PERIO SORE hapter Test, orm Write the letter for the correct answer in the blank at the right of each question.. What is the slope-intercept form of the equation of a line with a slope of 5 and

More information

Bishop Kelley High School Summer Math Program Course: Algebra 2 A

Bishop Kelley High School Summer Math Program Course: Algebra 2 A 015 016 Bishop Kelley High School Summer Math Program Course: Algebra A NAME: DIRECTIONS: Show all work in packet!!! The first 16 pages of this packet provide eamples as to how to work some of the problems

More information

review for math TSI 182 practice aafm m

review for math TSI 182 practice aafm m Eam TSI 182 Name review for math TSI 182 practice 01704041700aafm042430m www.alvarezmathhelp.com MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplif.

More information

Precalculus Notes: Unit P Prerequisite Skills

Precalculus Notes: Unit P Prerequisite Skills Syllabus Objective Note: Because this unit contains all prerequisite skills that were taught in courses prior to precalculus, there will not be any syllabus objectives listed. Teaching this unit within

More information

x (vertex is halfway between the x-intercepts)

x (vertex is halfway between the x-intercepts) Big Idea: A quadratic equation in the form a b c 0 has a related function f ( ) a b c. The zeros of the function are the -intercepts of its graph. These -values are the solutions or roots of the related

More information

Quadratic Graphs and Their Properties

Quadratic Graphs and Their Properties - Think About a Plan Quadratic Graphs and Their Properties Physics In a physics class demonstration, a ball is dropped from the roof of a building, feet above the ground. The height h (in feet) of the

More information

EXPONENT REVIEW!!! Concept Byte (Review): Properties of Exponents. Property of Exponents: Product of Powers. x m x n = x m + n

EXPONENT REVIEW!!! Concept Byte (Review): Properties of Exponents. Property of Exponents: Product of Powers. x m x n = x m + n Algebra B: Chapter 6 Notes 1 EXPONENT REVIEW!!! Concept Byte (Review): Properties of Eponents Recall from Algebra 1, the Properties (Rules) of Eponents. Property of Eponents: Product of Powers m n = m

More information

Chapter 8 Class Notes 8-A1 (Lessons 8-1&8-2) Monomials and Factoring p Prime Factorization: a whole number expressed as the of factors.

Chapter 8 Class Notes 8-A1 (Lessons 8-1&8-2) Monomials and Factoring p Prime Factorization: a whole number expressed as the of factors. Chapter 8 Class Notes Alg. 1H 8-A1 (Lessons 8-1&8-) Monomials and Factoring p. 40-4 Prime Factorization: a whole number epressed as the of factors. Tree Method: Ladder Method: Factored Form of a Monomial:

More information

COUNCIL ROCK HIGH SCHOOL MATHEMATICS. A Note Guideline of Algebraic Concepts. Designed to assist students in A Summer Review of Algebra

COUNCIL ROCK HIGH SCHOOL MATHEMATICS. A Note Guideline of Algebraic Concepts. Designed to assist students in A Summer Review of Algebra COUNCIL ROCK HIGH SCHOOL MATHEMATICS A Note Guideline of Algebraic Concepts Designed to assist students in A Summer Review of Algebra [A teacher prepared compilation of the 7 Algebraic concepts deemed

More information

review for math TSI 55 practice aafm m

review for math TSI 55 practice aafm m Eam TSI Name review for math TSI practice 01704041700aafm042430m www.alvarezmathhelp.com MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the

More information

5. 2. The solution set is 7 6 i, 7 x. Since b = 20, add

5. 2. The solution set is 7 6 i, 7 x. Since b = 20, add Chapter : Quadratic Equations and Functions Chapter Review Eercises... 5 8 6 8 The solution set is 8, 8. 5 5 5 5 5 5 The solution set is 5,5. Rationalize the denominator. 6 The solution set is. 8 8 9 6

More information

Module 2, Section 2 Solving Equations

Module 2, Section 2 Solving Equations Principles of Mathematics Section, Introduction 03 Introduction Module, Section Solving Equations In this section, you will learn to solve quadratic equations graphically, by factoring, and by applying

More information

Quadratic Functions. Key Terms. Slide 1 / 200. Slide 2 / 200. Slide 3 / 200. Table of Contents

Quadratic Functions. Key Terms. Slide 1 / 200. Slide 2 / 200. Slide 3 / 200. Table of Contents Slide 1 / 200 Quadratic Functions Table of Contents Key Terms Identify Quadratic Functions Explain Characteristics of Quadratic Functions Solve Quadratic Equations by Graphing Solve Quadratic Equations

More information

Quadratic Functions. Key Terms. Slide 2 / 200. Slide 1 / 200. Slide 3 / 200. Slide 4 / 200. Slide 6 / 200. Slide 5 / 200.

Quadratic Functions. Key Terms. Slide 2 / 200. Slide 1 / 200. Slide 3 / 200. Slide 4 / 200. Slide 6 / 200. Slide 5 / 200. Slide 1 / 200 Quadratic Functions Slide 2 / 200 Table of Contents Key Terms Identify Quadratic Functions Explain Characteristics of Quadratic Functions Solve Quadratic Equations by Graphing Solve Quadratic

More information

Slide 1 / 200. Quadratic Functions

Slide 1 / 200. Quadratic Functions Slide 1 / 200 Quadratic Functions Key Terms Slide 2 / 200 Table of Contents Identify Quadratic Functions Explain Characteristics of Quadratic Functions Solve Quadratic Equations by Graphing Solve Quadratic

More information

Additional Exercises 10.1 Form I Solving Quadratic Equations by the Square Root Property

Additional Exercises 10.1 Form I Solving Quadratic Equations by the Square Root Property Additional Exercises 10.1 Form I Solving Quadratic Equations by the Square Root Property Solve the quadratic equation by the square root property. If possible, simplify radicals or rationalize denominators.

More information

MATH 110: FINAL EXAM REVIEW

MATH 110: FINAL EXAM REVIEW MATH 0: FINAL EXAM REVIEW Can you solve linear equations algebraically and check your answer on a graphing calculator? (.) () y y= y + = 7 + 8 ( ) ( ) ( ) ( ) y+ 7 7 y = 9 (d) ( ) ( ) 6 = + + Can you set

More information

Words to Review. Give an example of the vocabulary word. Numerical expression. Variable. Evaluate a variable expression. Variable expression

Words to Review. Give an example of the vocabulary word. Numerical expression. Variable. Evaluate a variable expression. Variable expression 1 Words to Review Give an example of the vocabulary word. Numerical expression 5 12 Variable x Variable expression 3x 1 Verbal model Distance Rate p Time Evaluate a variable expression Evaluate the expression

More information

ACCUPLACER MATH 0310

ACCUPLACER MATH 0310 The University of Teas at El Paso Tutoring and Learning Center ACCUPLACER MATH 00 http://www.academics.utep.edu/tlc MATH 00 Page Linear Equations Linear Equations Eercises 5 Linear Equations Answer to

More information

( ) Chapter 7 ( ) ( ) ( ) ( ) Exercise Set The greatest common factor is x + 3.

( ) Chapter 7 ( ) ( ) ( ) ( ) Exercise Set The greatest common factor is x + 3. Chapter 7 Exercise Set 7.1 1. A prime number is an integer greater than 1 that has exactly two factors, itself and 1. 3. To factor an expression means to write the expression as the product of factors.

More information

Using the Laws of Exponents to Simplify Rational Exponents

Using the Laws of Exponents to Simplify Rational Exponents 6. Explain Radicals and Rational Exponents - Notes Main Ideas/ Questions Essential Question: How do you simplify expressions with rational exponents? Notes/Examples What You Will Learn Evaluate and simplify

More information

Collecting Like Terms

Collecting Like Terms MPM1D Unit 2: Algebra Lesson 5 Learning goal: how to simplify algebraic expressions by collecting like terms. Date: Collecting Like Terms WARM-UP Example 1: Simplify each expression using exponent laws.

More information

Math 101 Study Session Spring 2016 Test 4 Chapter 10, Chapter 11 Chapter 12 Section 1, and Chapter 12 Section 2

Math 101 Study Session Spring 2016 Test 4 Chapter 10, Chapter 11 Chapter 12 Section 1, and Chapter 12 Section 2 Math 101 Study Session Spring 2016 Test 4 Chapter 10, Chapter 11 Chapter 12 Section 1, and Chapter 12 Section 2 April 11, 2016 Chapter 10 Section 1: Addition and Subtraction of Polynomials A monomial is

More information

6.2 Multiplying Polynomials

6.2 Multiplying Polynomials Locker LESSON 6. Multiplying Polynomials PAGE 7 BEGINS HERE Name Class Date 6. Multiplying Polynomials Essential Question: How do you multiply polynomials, and what type of epression is the result? Common

More information

Math Analysis/Honors Math Analysis Summer Assignment

Math Analysis/Honors Math Analysis Summer Assignment Math Analysis/Honors Math Analysis Summer Assignment To be successful in Math Analysis or Honors Math Analysis, a full understanding of the topics listed below is required prior to the school year. To

More information

Equations Quadratic in Form NOT AVAILABLE FOR ELECTRONIC VIEWING. B x = 0 u = x 1 3

Equations Quadratic in Form NOT AVAILABLE FOR ELECTRONIC VIEWING. B x = 0 u = x 1 3 SECTION.4 Equations Quadratic in Form 785 In Eercises, without solving the equation, determine the number and type of solutions... In Eercises 3 4, write a quadratic equation in standard form with the

More information

x 2 + x + x 2 x 3 b. x 7 Factor the GCF from each expression Not all may be possible. 1. Find two numbers that sum to 8 and have a product of 12

x 2 + x + x 2 x 3 b. x 7 Factor the GCF from each expression Not all may be possible. 1. Find two numbers that sum to 8 and have a product of 12 Factor the GCF from each expression 4 5 1. 15x 3x. 16x 4 Name: a. b. 4 7 3 6 5 3. 18x y 36x y 4x y 5 4. 3x x 3 x 3 c. d. Not all may be possible. 1. Find two numbers that sum to 8 and have a product of

More information

ALGEBRA I SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 2 27? 1. (7.2) What is the value of (A) 1 9 (B) 1 3 (C) 9 (D) 3

ALGEBRA I SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 2 27? 1. (7.2) What is the value of (A) 1 9 (B) 1 3 (C) 9 (D) 3 014-015 SEMESTER EXAMS SEMESTER 1. (7.) What is the value of 1 3 7? (A) 1 9 (B) 1 3 (C) 9 (D) 3. (7.3) The graph shows an eponential function. What is the equation of the function? (A) y 3 (B) y 3 (C)

More information

Basic ALGEBRA 2 SUMMER PACKET

Basic ALGEBRA 2 SUMMER PACKET Name Basic ALGEBRA SUMMER PACKET This packet contains Algebra I topics that you have learned before and should be familiar with coming into Algebra II. We will use these concepts on a regular basis throughout

More information

Name Class Date. Multiplying Two Binomials Using Algebra Tiles

Name Class Date. Multiplying Two Binomials Using Algebra Tiles Name Class Date Multiplying Polynomials Going Deeper Essential question: How do you multiply polynomials? 6-5 A monomial is a number, a variable, or the product of a number and one or more variables raised

More information

Algebra I. Exponents and Polynomials. Name

Algebra I. Exponents and Polynomials. Name Algebra I Exponents and Polynomials Name 1 2 UNIT SELF-TEST QUESTIONS The Unit Organizer #6 2 LAST UNIT /Experience NAME 4 BIGGER PICTURE DATE Operations with Numbers and Variables 1 CURRENT CURRENT UNIT

More information

Looking Ahead to Chapter 10

Looking Ahead to Chapter 10 Looking Ahead to Chapter Focus In Chapter, you will learn about polynomials, including how to add, subtract, multiply, and divide polynomials. You will also learn about polynomial and rational functions.

More information

Mini-Lecture 2.1 Simplifying Algebraic Expressions

Mini-Lecture 2.1 Simplifying Algebraic Expressions Copyright 01 Pearson Education, Inc. Mini-Lecture.1 Simplifying Algebraic Expressions 1. Identify terms, like terms, and unlike terms.. Combine like terms.. Use the distributive property to remove parentheses.

More information

Quadratic Expressions and Equations

Quadratic Expressions and Equations Unit 5 Quadratic Expressions and Equations 1/9/2017 2/8/2017 Name: By the end of this unit, you will be able to Add, subtract, and multiply polynomials Solve equations involving the products of monomials

More information

Chapter 5: Exponents and Polynomials

Chapter 5: Exponents and Polynomials Chapter 5: Exponents and Polynomials 5.1 Multiplication with Exponents and Scientific Notation 5.2 Division with Exponents 5.3 Operations with Monomials 5.4 Addition and Subtraction of Polynomials 5.5

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Math 2 Stud Guide-Chapters 8 and 9 Name Date: Time: MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find all square roots of the number. ) 600 9,

More information

Ready To Go On? Skills Intervention 7-1 Integer Exponents

Ready To Go On? Skills Intervention 7-1 Integer Exponents 7A Evaluating Expressions with Zero and Negative Exponents Zero Exponent: Any nonzero number raised to the zero power is. 4 0 Ready To Go On? Skills Intervention 7-1 Integer Exponents Negative Exponent:

More information

Pre-Algebra 2. Unit 9. Polynomials Name Period

Pre-Algebra 2. Unit 9. Polynomials Name Period Pre-Algebra Unit 9 Polynomials Name Period 9.1A Add, Subtract, and Multiplying Polynomials (non-complex) Explain Add the following polynomials: 1) ( ) ( ) ) ( ) ( ) Subtract the following polynomials:

More information

9.1. Solving Quadratic Equations. Investigation: Rocket Science CONDENSED LESSON

9.1. Solving Quadratic Equations. Investigation: Rocket Science CONDENSED LESSON CONDENSED LESSON 9.1 Solving Quadratic Equations In this lesson you will look at quadratic functions that model projectile motion use tables and graphs to approimate solutions to quadratic equations solve

More information

a = B. Examples: 1. Simplify the following expressions using the multiplication rule

a = B. Examples: 1. Simplify the following expressions using the multiplication rule Section. Monomials Objectives:. Multiply and divide monomials.. Simplify epressions involving powers of monomials.. Use epressions in scientific notation. I. Negative Eponents and Eponents of Zero A. Rules.

More information

Prerequisites. Copyright Cengage Learning. All rights reserved.

Prerequisites. Copyright Cengage Learning. All rights reserved. Prerequisites P Copyright Cengage Learning. All rights reserved. P.4 FACTORING POLYNOMIALS Copyright Cengage Learning. All rights reserved. What You Should Learn Remove common factors from polynomials.

More information

Section 1.1. Chapter 1. Quadratics. Parabolas. Example. Example. ( ) = ax 2 + bx + c -2-1

Section 1.1. Chapter 1. Quadratics. Parabolas. Example. Example. ( ) = ax 2 + bx + c -2-1 Chapter 1 Quadratic Functions and Factoring Section 1.1 Graph Quadratic Functions in Standard Form Quadratics The polynomial form of a quadratic function is: f x The graph of a quadratic function is a

More information

A.5. Solving Equations. Equations and Solutions of Equations. Linear Equations in One Variable. What you should learn. Why you should learn it

A.5. Solving Equations. Equations and Solutions of Equations. Linear Equations in One Variable. What you should learn. Why you should learn it A46 Appendi A Review of Fundamental Concepts of Algebra A.5 Solving Equations What you should learn Identify different types of equations. Solve linear equations in one variable and equations that lead

More information