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Name: _____________________ Algebra 1: Final Review Packet

(Homework is listed by date assigned; homework is due the following class period)

HW# Date In-Class Homework

39

T 6/10

Final Review

Multiple Choice Practice Final Exit Quiz

HW39: HW39 Worksheet #1-22 all (pgs 17-21 in this packet) Correct Homework Online Turn in your textbook

40

W

6/11

Final Review

Multiple Choice Practice Final Exit Quiz

HW40: HW40 Worksheet #23-53 (pgs 11-16 in this packet) Correct Homework Online Turn in your textbook

41

Th 6/12

F

6/13

Final Exam

Finals Schedule: Thursday 6/12

Period 1 8:00 – 10:00 Period 2 10:25 – 12:25 Friday 6/13

Period 3 8:00 – 10:00 Period 4 10:25 – 12:25

Please bring the following to class for your Final Exam:

This completed and corrected packet

(Notes #39-40 and HW #39-40)

Pencils, eraser Your Algebra Textbook Earned extra credit points Something quiet to do in case you finish your final

early.

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Algebra 1 Final Exam Information: 50 Multiple choice questions covering Chapters 1-10 & supplemental unit Solving:

linear equations (Chp1-2) proportions (Chp 2) linear inequalities (Chp 3) absolute value equations (Chp 3) systems of equations by substitution & elimination/addition methods (Chp 6) quadratic equations (Chp 9) radical equations (Chp 10)

Graphing: Linear functions (Chp 5) Quadratic functions (Chp 9)

Lines: (Chp 5) Finding slope Finding x- and y-intercepts Writing equation of a line given slope and y-intercept Writing equation of a line given two points Writing equation of a line given an equation of a line parallel to it & a point on the line

Exponents: (Chp 7) Multiplying terms, including terms in scientific notation Raising terms to a power (positive power, negative power, zero power), including terms in scientific

notation Simplifying terms in a fraction Raising a term to the zero power Raising terms to a negative power Raising a power to a power, including terms in scientific notation Converting terms to and from standard form and scientific notation

Polynomials: (Chp 8) Put in standard form Add, subtract Multiply (including FOIL) Divide (factor numerator and denominator of a fraction before simplifying) Factor by GCF and/or X Box methods

Quadratics: (Chp 9) Find the vertex State whether it is opening up or down Compare its width to y = x2 Find the domain and range Find the axis of symmetry Solve by quadratic formula Using the determinant to find the number of real solutions of a quadratic

Radicals (roots) (Chp 10) Add, subtract Multiply (including FOIL) Divide (rationalize the denominator, both when the denominator is a mon

Sequences: (Supplemental unit) Identifying a sequence as arithmetic or geometric Finding the recursive and explicit rules for arithmetic or geometric sequences Interpreting word problems – writing equations, identifying the meaning of domain/range.

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Final Exam Review Notes Day 39 Linear Functions (Writing equations, finding slope, finding intercepts) Equations of Lines:

Start with slope: m = ________ Parallel means _________ slope Perpendicular means ______________, _______________ slope Plug in m and point (x, y) into _____________ Solve for b Plug m and b into ___________ Covert to standard form, if necessary

Slope-Intercept Form Standard Form X & Y Intercepts 1.) Find the slope of the line passing through the pair of points: (-4, 7) and (2, 9) 2.) Write the equation in slope-intercept form. State the slope (m) and y-intercept (b)

12

3x y

3.) Write the equation in standard form and find the x and y intercepts.

36

4y x

4.) Write the equation of the line with slope of 2

7 and y-intercept 4 in standard form.

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5.) Write the equation of the line with slope -4 and passing through the point (6, -1) in standard form.

6.) Write the equation of the line passing through the points (-3, 2) and (1, 4) in slope-intercept form

7.) Write the equation of the line parallel to y = -2x + 3 and passing through the point (4, -1) in standard form.

8.) Graph the line: 2 3 10x y

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9

-8

-7

-6-5

-4

-3-2

-1

12

3

45

6

7

89

10y

Solving Systems of Equations Method 1: Substitution (A) Solve 1 equation for a variable (B) Substitute the expression that the variable is equal to into the OTHER equation (C) Solve for the first variable. (D) Substitute the value you just found into one of the equations and solve for the 2nd variable (E) Write your answer as an ordered pair.

Method 2: Elimination/Addition (A) Choose a variable that you want to cancel out. (B) Multiply one or both equations by numbers to get the coefficient of that variable to be the same number but with opposite signs (C) Add the equations to eliminate the variable (D) Solve for your first variable (E) Substitute the value you just found into one of the equations & solve for the 2nd variable. (F) Write your answer as an ordered pair.

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9.) Solve for a and b using the substitution method

2 4

3 4 15

a b

a b

10.) Solve for x and y by using the addition/elimination method: 2 5 3

3 6 9

x y

x y

Exponent Rules

Get rid of negative exponents first by moving the variables with negative exponents to the OTHER side of the fraction and making the exponent positive.

When you see an exponent outside of parenthesis, rewrite the term in the parenthesis the same number of times as the exponent says.

Zero Exponent Rule: 0 1a When terms are being multiplied...ADD the exponents When terms are being divided…SUBTRACT/CANCEL the exponents

Examples: Simplify each expression as much as possible. Leave only positive exponents in your answer!!

11.)

34 2

74

12

x y

x y

12.) 5 3 4

2 7 6 918 6

12 9

x y xy

x y x y

6

13.) 8 2 36x y z

14.) 00 3 6 0 24 5 3x y x y xy

15.) Solve the proportion:

x 2

14

x

10

16.) a) convert to scientific notation: 0.00000781 b) convert to standard notation: 3.1 x 105 c) multiply; leave your answer in scientific notation: (-7.3 x 10-4)(9.1 x 108)

17.) Leave each answer in standard form:

a) Subtract the polynomials: (2x3 5x2 3x) (x3 8x2 11) b) Multiply the polynomials: (4x2 x 6)(2x 3) c) Simplify:

3 2

3

4 12 3

4 12

m m m

m m

18.) Factor each expression completely:

a) 22 32x

b) 2 23 15 18a ab b c) 3x2 + 6x – 105

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Final Exam Review Notes Day 40

Absolute Value:

Isolate the | | Write 2 equations Check both answers by plugging both values back into original equation

Solve each absolute value equation: 1.) 2 5 11p 2.) 3 5 6r

Solve each quadratic by factoring: 3.) 6x2 = 18x 4.) 23 2 21x x Radicals Simplify ALL radicals at the start AND end of the problem! Add/Subtract Multiply Divide (fractions with radicals) 1.) Simplify all radicals 2.) If the # under the radicals is the same, then add or subtract the coefficients (numbers in front) but leave the radicals the same

1.) Multiply the outside numbers together. This gives you your new outside number. 2.) Multiply the inside numbers together. This gives you your new inside number. 3.) Simplify all radicals again.

1.) Simplify all radicals. 2.) Multiply the numerator & denominator by the radical that is in the bottom of the fraction. 3.) Simplify all radicals. 4.) Simplify/reduce the coefficients in the fraction.

Examples: Simplify each expression completely.

5.) 288 50

6.) 32 5 8

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7.) 3 72 8 50

8.) 2 12 5 24

9.) 27 5

10.) 3

8

11.) 6

5 3 12.)

6

3 2

Sequences: Arithmetic Sequences

(add/subtract with each term) Geometric Sequence

(multiply/divide with each term) Recursive Formula: 1( ) ( )f n f n d

( )f n = nth term

( 1)f n = value of the previous term d = common difference Explicit Formula:

( )f x mx b m = common difference (d)

b = value of the 0th term

Recursive Formula: 1( ) ( )f n f n r

( )f n = nth term

( 1)f n = value of the previous term r = common difference Explicit Formula

( ) xf x a b a = value of the 0th term b = common ratio

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13.) Consider the sequence: 11, 8, 5, 2, -1, . . . a) Is it arithmetic or geometric: b) What is the 0th term? c) What is the common difference/ratio? d) Write a recursive rule e) Write an explicit rule:

14.) Consider the sequence:

18, 4, 2, 1, , . . .

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a) Is it arithmetic or geometric: b) What is the 0th term? c) What is the common difference/ratio? d) Write a recursive rule e) Write an explicit rule:

Solving Radical Equations:

(A) Get the radical alone (B) Square both sides (C) Solve for the variable. If the equation is a quadratic (contains an x2) then set the equation

to 0 and solve by factoring. (D) Check your solutions by substituting them into the original equation.

For 15-16, solve and check your solution(s):

15.) 4 2 5x 16.) 3 2 4x x

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Important Parts of Quadratic Functions Standard Form:

2y ax bx c

Vertex: a point (___, ___) x-coordinate:

2

bx

a

y-coordinate: plug the value you got for x into original equation

Direction of opening: *find a* If a is positive, the parabola opens up and the vertex is a minimum. If a is negative, the parabola opens down and the vertex is a maximum.

Width: *find a and make it positive* If =1, the graph is the same width as y = x2

If <1, the graph is wider than y = x2

If > 1, the graph is narrower than y = x2

Without graphing, find the information for each parabola:

17.) 2( ) 2 8 3f x x x Vertex: ________ Axis of Symmetry: _________ Direction of opening? _______ Max or Min? _______ Wider, narrower, or same width as y = x2 ? ______ Domain:__________ Range: ____________

18.) 23( ) 6 5

2f x x x

Vertex: ________ Axis of Symmetry: _________ Direction of opening? _______ Max or Min? _______ Wider, narrower, or same width as y = x2 ? ______ Domain:__________ Range: ____________

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HW #40: 25-63 all Please show all of your work and corrections! For #25-29, simplify each expression:

25.) 24 53a b 26.) 2 5

6 3

12

8

d f

d f

27.) 8 9 57 4m n mn

28.) 23 2 3 58 3 6x y xy x y 29.) 5 3 0

4 8 7

80

14

r s t

r s t

Solve and graph: **When necessary, re-write your answer as a sandwich.** 30.) 1 3 or 2 6x x

31.) 5 2 1 7x

32.) 3 1 5 and 2 1x x

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Solve:

33.) 2 4x 34.) 2 3 1 5x

For #35-36, describe each parabola: 35.) h(x)=‐2x2+12x–17 Vertex:________ Direction of opening? _______ Max or min?________ Width compared to y = x2 ? _______ Axis of symmetry: ________ Domain: ________ Range: ________

36.) g(x)=‐2x2+8x–5 Vertex:________ Direction of opening? _______ Max or min?________ Width compared to y = x2 ? _______ Axis of symmetry: ________ Domain: ________ Range: ________

For #37-38, solve and check your solutions. 37.) 5 7 5x Check(s):

38.) 4 3x x Check(s):

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39.) Consider the sequence: -8, -5, -2, 1, . . . a) Is it arithmetic or geometric: b) What is the 0th term? c) What is the common difference/ratio? d) Write a recursive rule e) Write an explicit rule:

40.) Consider the sequence: -1, 4, -16, 64, . . . a) Is it arithmetic or geometric: b) What is the 0th term? c) What is the common difference/ratio? d) Write a recursive rule e) Write an explicit rule:

41.) Solve by factoring: 4x2 = 10x

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For #42-51, simplify:

42.) 649a 43.)

6 520x y

44.) 2 60 45.) 2 6 8

46.) 2 7 32 6a b ab 47.) 3

5

48.) 2 3 5 2 3 3 2 49.) 8

3 7

50.) 2 20 6 45

51.) 3 18 2 8

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52.) Find the missing side of the right triangle

x

106

For #53-55, solve for x. Show your check.

53.) 2 1 5x 54.) 3 3 12x

55.) 3 3 1x x (Hint: be sure to use FOIL on the left side!) For #56-59, factor completely: 56.) p3 – 9p2 + 8p

57.) w3 – 2w2 – 9w + 18

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58.) 2k2 – 7k – 4

59.) 2x3 – 14x2 – 16x

For #60-63, solve each equation: 60.) 23 6 0m m 61.) 22 7 5c c 62.) 2 24 20 10 3 4x x x 63.) 3 210 24 0x x x

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HW#39: 1-24 all Name: Please show all of your work and corrections! 1.) Solve for x:

7 3 2 1 4 5 2 1x x x 2.) Solve for x and graph on a number line: 5 1 8 11x x

3.) Graph: 2x – y = 6

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9

-8

-7

-6

-5

-4

-3-2

-1

1

2

3

45

6

7

8

9

10

y

4.) Graph the line by finding the x and y

intercepts: 2 4x y

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9

-8

-7

-6-5

-4

-3

-2

-1

1

2

3

45

6

7

8

9

10

y

18

5.) Graph using the slope and y-intercept: 2x – 3y = -6

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

45

6

7

8

9

10

y

6.) Graph these two lines on the same graph to the right. Find the slope of each line. a) x = -5 slope = _____ b) y = 6 slope = _____

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

10

y

7.) Write the formula for slope. Then use this formula to find the slope of the line passing through the pair of points: a) slope = __________ b) (-2, -3) and (1, -7)

8.) Find the equation of the line passing through the given point with the given slope: m = -4 (-5, 7)

9.) Find the equation of the line passing through the pair of points: (-1, 1) and (1, 2)

10.) Find the equation of the line parallel to 1

53

y x

and passing through

(3, -2)

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11.) Solve the proportion:

3

8 9

x x

12.) Simplify; leave all answers in positive exponents.

a) 3 5 2 7 08 4x y z xy z b) 24 8 33x y z c) 24 3 3

5

3 6

2

x y xz

z y

13.) Factor completely: a) 6y2 – 7y – 5 b) x3 + 5x2 – 4x – 20 c) 3x2 – 3x – 6

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14.) Leave each answer in standard form: a) Subtract the polynomials: b) Multiply the polynomials:

3 2 3 2(5 2 7 ) ( 2 3 15)x x x x x

2(3 2 1)( 5)x x x c) Simplify:

2

2

2 10 12

6 8

m m

m m

Solve by graphing.

15.) 3 5

2 3 8

y x

y x

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

10y

Solve by substitution.

16.) 2 3

2 9

y x

x y

Solve by the addition method.

17.) 2 3 12

3 4 1

x y

x y

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For #18-19, write each number in scientific notation: 18.) 34,000,000 19.) 0.0002089 For #20-21, write each number in standard form: 20.) -4.56 x 106 21.) 2.01 x 10-4 For #22-24, evaluate and write each answer in scientific notation:

22.) 3 72.1 x 10 5.0 x 10 23.) 243.4 x 10 24.) 6

2

2.7 x 10

3.0 x 10