entire acf 92 workbook - bloomfield...

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A. Fisher

Acf 92 workbook

TABLE OF CONTENTS: Math History Activity ……………………………………. p. 2 – 3 Simplify Expressions with Integers ……………………… p. 4 Simplify Expressions with Fractions …………………….. p. 5 Simplify Expressions with Decimals …………………….. p. 6 Laws of Exponents Notes ………………………………... p. 7 – 9 Laws of Exponents Classwork Problems ………………... p. 10 – 13 Laws of Exponents Homework Exercises ……………….. p. 14 – 15 Cartesian Coordinate System Notes ……………………... p. 16 – 25 Cartesian Coordinate System Classwork Problems ……... p. 26 – 30 Cartesian Coordinate System Homework Exercises …….. p. 31 – 33 Blank Graph Paper ………………………………………. P. 34 Answers ………………………………………………….. p. 35 – 42

MATH HISTORY ACTIVITY

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CONTACT INFORMATION: NAME:______________________________________ phone number: ______________________________________________________________ e-mail address you check most frequently (write clearly) ____________________________________________________________________________ DIRECTIONS: Answer these questions as best you can. Reflect on some of them before you write your explanation. 1) How many semesters have you completed at Bloomfield College? ______________________________________________________________________________ 2) How many courses are you taking this semester? What are they? ______________________________________________________________________________ ______________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ 3) Are you working this semester? How many hours per week? Have you outlined a plan so that you know how to manage your time between your work responsibilities and your studies? _____________________________________________________________________________ _____________________________________________________________________________ 4) Do you have a child or relative which you are responsible to take care of? Have you outlined a plan so that you know how to manage your time between your personal responsibilities and your studies? _____________________________________________________________________________ _____________________________________________________________________________ 5) What was the last math course you took? How many years ago? ______________________________________________________________________________ 6) How do you rate your math ability? Give some examples.

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_____________________________________________________________________________ _____________________________________________________________________________ 7) What do you feel are your strengths in a math class? Give some examples. _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ 8) What do you feel are your weaknesses in a math class? Give some examples. _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ 9) What do you think you will do differently in this math course in comparison to what you did for past math courses? _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ 10) List the resources that are available to you so that you may succeed in this course. _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________

SIMPLIFY EXPRESSIONS WITH INTEGERS Go to section 7.3 in textbook (p.209 – 211) for notes & examples

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Simplify each algebraic expression. 1) 5x – 3x + 2x + 12x – 18x 2) 6y + 3y – 8y + 15y – 21y – 11y 3) 7a + 16b – 2b + 6a – 14a + 5b 4) 22m – 8n + 4n – 7 – 2m + 1 – 9n 5) 5x2 – 4y2 + 33xy – y2 – 8xy + 22x2 6) 7x2 – 7y2 + 10xy – 3y2 – 19xy + 12x2 7) 11m + 3(3 + 11m) 8) 12a + 7(5 + 10a) 9) 3(6x + y) – 18x + 9y 10) 5(3x – 2y) + 15x + 40y 11) 21 – 9(a – 5) 12) 44 – 5(2b – 4) 13) 10(3a – 7b) + 20(b – a) 14) 5(x – 5y) - 8(y – x) 15) 9x – 4x + 7x + 15x – 23x 16) 7y + 5y – 2y + 21y – 40y – 25y 17) 6a + 34b – 6b + 6a – 12a + 9b 18) 14m – 7n + 3n – 9 – 4m + 5 – 6n 19) x2 – 9y2 + 13xy – y2 – 7xy + 10x2 20) 8x2 – 4y2 + 21xy – 2y2 – 41xy + 12x2 21) 12m + 3(8 + 10m) 22) 15a + 8(9 + 11a) 23) 9(2x + y) – 18x + 9y 24) 6(4x – 7y) + 25x + 50y 25) 64 – 4(a – 1) 26) 12 – 5(4b – 6) 27) 20(3a – 7b) + 10(b – a) 28) 3(x – 8y) - 9(y – x)

SIMPLIFY EXPRESSIONS WITH FRACTIONS Go to section 7.3 in textbook (p.209 – 211) for notes & examples

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Simplify each algebraic expression.

1) 2)

3) 4)

5) 6)

7) 8)

9) 10)

11) 12)

13) 14)

15) 16)

17) 18)

19) 20)

SIMPLIFY EXPRESSIONS WITH DECIMALS Go to section 7.3 in textbook (p.209 – 211) for notes & examples

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Simplify each algebraic expression. 1) 0.2x + 0.8x – 0.5x – 0.7x 2) 1.3a – 2.4b – 4.5a + 5.2b – 6.7b + 1.5a 3) -21.7 – 14.25x + 3.5y – 11.1x + 3.06y – 1 4) 0.01m – 0.02n + 0.001m – 0.002 – 0.01m 5) 0.5(12x – 6y + 4) – 0.25(16x + 4y – 20) 6) 0.1(2.5a + 3.5b – 4.5c) + 0.01(12a – 15b + 10c)

7) 8) 0.9(20m – 10n – 90) – 0.03(100m + 200n – 300)

9) 10) 5x + 0.08y – 1.4z +

11) 0.6y + 0.5y – 0.3y – 0.9y 12) 4.6x – 4.4y – 9.1y + 1.3x – 8.8y + 5.5x 13) -14.3 – 10.75x + 2.7y – 20.2x + 5.06y – 1 14) 0.04m – 0.08n + 0.004m – 0.008 – 0.04m 15) 0.25(12x – 4y + 28) – 0.5(16x + 4y – 20) 16) 0.01(2.5a + 3.5b – 4.5c) + 0.1(12a – 15b + 10c)

17) 18) 0.7(20m – 10n) – 0.03(100m + 200n – 300)

19) 20) 0.3x + 0.09y – 2.6z +

LAWS OF EXPONENTS NOTES

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The following laws of exponents are for multiplying and dividing monomials.

PRODUCT RULE:

am · an = am+n (when multiplying like bases, add the powers) Examples: 1) x4 · x5 = x4+5 = x9 2) 55 · 58 = 55+8 = 513 3) a7 · a · a12 = a7+1+12 = a20 4) (3x6)(2x4) = (3·2)x6+4= 6x10 5) (4m8n2)(-2mn4)(5m4n3) = (4·-2·5)(m8+1+4)(n2+4+3) = -40m13n9

POWER RULE: (ambm)n = amnbmn (when taking a monomial to a power, multiply the powers including the coefficient’s) Examples: 1) (a4b3)2 = a4·2b3·2 = a8b6 2) (3m2n5)4 = 31·4m2·4n5·4 = 34 m8 n20 = 81 m8 n20 3) (-2xy7z2)5 = (-2)5x5y35z10 = -32x5y35z10 4) (6a9b6)2 = 62a18b12 = 36a18b12 (-c4d2)5 (-1)5c20d10 -c20d10 QUOTIENT RULE: am = am - n (when dividing with like bases, subtract the powers) an (Note: it is always the numerator's power minus the denominator's power) Examples: 1) x6 = x6 – 4 = x2 2) m5n7 = m5-4n7-10 = mn-3 x 4 m4n10 3) 8a3b7 = 8 a3 - (-5)b7-9 = 2 a8n-2 4a-5b9 4 ZERO POWER RULE:

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a0 = 1 (any term to the zero power is one) Examples: 1) (m5 n7)0 = 1 2) (4m8n2)(-2mn4)0 = (4m8n2)(1) = 4m8n2 3) (-4)0 = 1

****It is improper to leave negative powers in your final answer. All final answers should be written with positive powers. Therefore, you will need the following property. **** NEGATIVE POWER RULE: a-n = 1 and 1 = an (take the reciprocal of only the variable that is to the negative power) an a-n Examples: 1) 3x-4 = 3 · 1 = 3 2) -5m-8n2 = -5y5n2 x4 x4 x10y-5 m8x10 NOTE: Apply the negative power rule to only negative POWERS. EXAMPLES: Simplify the following expressions. Write the final answers without negative exponents. Simplify means to combine like terms using the laws of exponents. Also, you may work with negative powers as you are simplifying within the problem. You just cannot leave negative powers in the final answer. 1) 12-4(128) = 12-4+8 =124 (product rule) or = 1 • 128 (negative power rule) 124 = 128 - 4 = 124 (quotient rule) 2) (5a4b6)(12abc)0(-2a2bc5) = (5a4b6) (1) (-2a2bc5) (zero power rule) -10a6b7c5 (product rule) 3) -42m6n-3p5 = -7m6-11 n-3-(-5) p5-5 (quotient rule) 6m11n-5p5 = -7m-5n2p0 = -7n2 (negative power and zero power rule) m5 4) (-3ab6 )5 = (-3)5a5b30 (power rule) (-a5b2)7 (-1)7a35b14

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= -243a5b30 -1a35b14 = 243a5-35b30-14 (quotient rule) = 243a-30b16 = 243b16 (negative power rule) a30 5) 2m7n3 • (3mp8)3 = 2m7n3 • 27m3p24 (power rule)

(3n5p-3)2 2mn6 9n5p-6 2mn6

= 54m10n3p24 (product rule in numerator & denominator) 18mn11p-6 = 3 m10-1n3-11 p24 - (-6) (quotient rule) = 3m9n-8p30 = 3m9p30 (negative power rule) n8 6) (7xy)(-x4y3)5(2x5y6)-2 = (7xy)(-15x20y15)(2-2x -10y -12) (power rule) = (7xy)(-x20y15)(x -10y -12) (negative power rule)

22 = -7 x1+20-10 y1+15-12 (product rule) 4 = -7 x11 y4 4

7) (2)-5 = (need to apply the negative power rule first before you can multiply)

= or

= is the final answer.

LAWS OF EXPONENTS CLASSWORK PROBLEMS

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Simplify. Use the Product Rule. 1) 105 · 108 2) 43 · 49 · 410 3) 915 · 9 · 90

4) (-5)7 · (-5)4 · (-5)2 5) (-21)3 · (-21)15 · (-21)21 6)

7) 8) (xy)3 · (xy)7 · (xy)9 9) (4abc)5 · (4abc)11 · (4abc)19

10) (x + y)5 · (x + y)3 11) (2a – 3b)4 · (2a – 3b)5 12) (m – 2n)13 · (m – 2n) 13) x3 · x5 · x8 14) 2x9 · 2x4 · 2x 15) (x4y7) · (x3y9) 16) (3xy5z) · (2x2yz4) 17) (-5x3y12) · (2x7y10) 18) (3a5b)(-5a6b7c8)(-abc)

19) (9m3n2)(-2m5n7)(3m3n9) 20) 21)

Simplify. Use the Quotient Rule. 22) 512 ÷ 54 23) 217 ÷ 27 24) (-3)25 ÷ (-3)10

25) 26) 27)

28) x15 ÷ x10 29) y7 ÷ y4 30) (xy)18 ÷ (xy)17

31) 32) 33)

34) 35) 36)

37) 38) 39)

Simplify. Use the Power Rule.

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40) (a5b7)3 41) (x9y10z11)7 42) (2x4)3 43) (3x5y3z)4 44) (6a9b21c4)3 45) (-5x8y7)2 46) (-a10b12c14)11 47) (-3x2y5)5 48) (-2m11n21p3)4

49) 50) 51)

52)

53)

54)

55)

56)

57)

58)

59)

60)

Simplify. Use the Negative Power Rule. Final answers must have positive powers only. 61) 2-3 62) 3-2 63) (-5)-2

64) (-2)-5 65)

66)

67)

68)

69)

70) x-5 71) x-3y-2 72) x-10y6 73) 2x-9 74) -3x-8 75) 4x-11y-12 76) -5x-3y-5 77) -7x8y2 78) -10x-9y4z-1

79)

80)

81)

12

82)

83)

84)

85)

86)

87)

88)

89)

90)

Simplify. Write final answers with positive powers. 91) (x3y7)(x9y10) 92) (2x11y12)(-3x4y5) 93) (4x8y)(3xy)(2x2y6) 94) (-7a10b3)(-a4b2c5)(-3a2b4c7) 95) (5x3)(5x3)(5x3) 96) 5(4x5y7)(-2x12y0) 97) (x8)2 · (x3)5 98) (2x7)3 · (3x12)3 99) (x7y5)6 · (x4y9)3 100) (-2xy)4 · (-9xy)0 · (-x2y4)3 101) (5x5y3z2)2 · (-3x8y9z3)3 · (x6y7z8)4

102)

103)

104)

105)

106)

107)

108)

109)

110)

111)

112)

113)

Simplify. Write final answers with positive powers.

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114)

115)

116)

117)

118)

119)

120)

121)

122)

123)

124)

125)

126)

127)

128)

129)

130)

131)

132)

133)

134)

135)

136)

137)

138)

139)

140)

141)

142)

143)

144)

145)

LAWS OF EXPONENTS HOMEWORK EXERCISES

Simplify. Use the Product Rule.

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1) 34 · 39 2) 67 · 6 · 615 3) (-8)3 · (-8)5 · (-8)7

4)

5) (2x + y)7 · (2x + y)3 6) x5 · x7 · x9

7) (2x4y9)(5x3y2)(3x2y5) 8) (-3m3n2p4)(-m5n7p9)(-3mnp) 9)

Simplify. Use the Quotient Rule.

10) 1016 ÷ 1013 11) (-2)8 ÷ (-2)2 12)

13) x7 ÷ x 14) 15) 16)

Simplify. Use the Power Rule. 17) (x3y5z6)2 18) (4x6y7z8)5 19) (-5x8y7)2 20) (-xy2z3)15

21) 22)

23)

24)

25)

Simplify. Use the Negative Power Rule. Final answers must have positive powers only.

26) 3-3 27) (-2)-5 28)

29)

30)

31)

32)

Simplify. Use the Negative Power Rule. Final answers must have positive powers only.

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33) a-3b-2 34) a-7b9 35) 3x-5y-2 36) -8a-4b4c-1

37)

38)

39)

40)

Simplify. Write final answers with positive powers. 41) (4x9y5)(-xy)(2x2y6) 42) -2(3x3)(4x3)(5x3) 43) (4x8)2 · (2x4)4 44) (x7y5)6 · (x4y9)3 45) (5x5y3z2)2 · (-3x8y9z3)0 · (x6y7z8)4

46)

47)

48)

49)

50)

51)

52)

53)

54)

55)

56)

CARTESIAN COORDINATE SYSTEM NOTES

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René Descartes, (1596-1650), a French philosopher and mathematician, invented the Cartesian Coordinate System linking algebra and geometry. The Coordinate System is a tool to represent algebraic equations as a graph. The Coordinate System has two perpendicular number lines called the axes; the horizontal line is the x-axis and the vertical line is the y-axis. The two axes meet at the point called the origin.

The two axes divide the plane into four regions referred to as quadrants; they are numbered as Roman Numerals starting with the top right region and going counter-clockwise.

PLOT AND IDENTIFY POINTS

NOTE: When the axes are not numbered it is understood to increase by one.

Consider point A (see figure 2). Point A has the coordinates (5, 4). The point is plotted starting at the origin, (0,0). Move 5 units to the right on the x-axis (the first coordinate in the pair) and then, move 4 units up on the y-axis (the second coordinate in the pair).

(x, y) can be referred to as ordered pair, point, or coordinates. The first coordinate in the ordered pair is always “x”, and the second coordinate is always “y”.

A

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Practice: a) Find the coordinates of each point. b) Identify which quadrant each point lies in.

1) point A 2) point B 3) point C 4) point D 5) point E 6) point F 7) point G

B

A

F

D E

C

Answers: 1) A (2, 2) in Quadrant I 2) B (-3, 6) in Quadrant II 3) C (-4, -5) in Quadrant III 4) D (7, -2) in Quadrant IV 5) E (0, -3) lies on the y-axis (not in Quadrant) 6) F (3, 0) lies on the x-axis (not in a Quadrant)

NOTE: Quadrant I: coordinates are always (+, +) Quadrant II: coordinates are always (–, +) Quadrant III: coordinates are always (–,–) Quadrant IV: coordinates are always (+,–)

If a point lies on an axis, then it is referred to as lying on the respective axis.

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SOLUTIONS OF LINEAR EQUATIONS WITH TWO VARIABLES

Ax + By = C (A, B, C are real numbers; x, y are variables) is a linear equation with two variables.

Example: x – 2y = 8

The solutions to the equation are ordered pairs (x, y) in which the coordinate values are substituted into the equation making a true statement.

Example: Determine if the following ordered pairs are solutions to the equation, x – 2y = 8.

a) (0, – 4) b) (-2, -5) c) (6, 1)

Solution: a) Substitute 0 for x and – 4 for y into the equation: ? 0 – 2(-4) = 8 0 + 8 8 = 8 true statement; therefore (0, – 4) is a solution to x – 2y = 8

b) Substitute -2 for x and –5 for y into the equation: ? -2 – 2(-5) = 8 -2 + 10 8 = 8 true statement; therefore (-2, –5) is a solution to x – 2y = 8

c) Substitute 6 for x and 1 for y into the equation: ? 6 – 2(1) = 8 6 – 2 4 ≠ 8 false statement; therefore (6, 1) is not a solution to x – 2y = 8

GRAPH LINEAR EQUATIONS WITH TWO VARIABLES Ax + By = C and y = mx + b are both linear equations with two variables. Ax + By = C is referred to as a linear equation in standard form. y = mx + b is referred to as a linear equation in slope-intercept form.

Both forms of the equations are linear and the graph will be a straight line. To Graph a Linear Equation

• Choose at least 3 real numbers for one coordinate. • Substitute the values into the equation to find the other coordinate. (more than 3 values may need to

be chosen when graphing other non-linear equations)The ordered pairs (x, y) are solutions to the equations.

• Plot the points and draw a straight line through the points.

NOTE: Every point (x, y) on the line is a solution to the equation.

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Example 1: Graph the linear equation: 2x + y = 1

Solution: If the directions state the equation is linear, then the graph must be a straight line.

step 1) 3 values for x were chosen; let x = -3, 0, 2 (note: any real # may be chosen) step 2) The values were substituted into the equation and solved for y. The ordered pair (x, y) was formed.

x (chosen)

2x + y = 1 y Ordered pair

– 3

2(-3) + y = 1 -6 + y = 1 y = 7

7

A (-3, 7)

0

2(0) + y = 1 0 + y = 1 y = 1

1

B (0, 1)

2

2(2) + y = 1 4 + y = 1 y = -3

-3

C (2, -3)

step 3) Plot each point and draw a line through the points. Include the arrows when drawing the line. This step gives a complete representation of the linear equation.

A

B

C

Note: If a straight line is not created when connecting the points, then an error was made. Check if the points were plotted correctly or check the calculations.

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Example 2: Graph the linear equation: y = –3x + 4


step 1) 3 values for x were chosen; let x = -1, 0, 3 (note: any real # may be chosen.) step 2) The values were substituted into the equation and solved for y. The ordered pair (x, y) was formed.

x (chosen)

y = –3x + 4 y Ordered pair

– 1

y = –3(–1) + 4 y = 4 + 4 y = 8

8

A (-1, 8)

0

y = –3(0) + 4 y = 0 + 4 y = 4

4

B (0, 4)

3

y = –3(3) + 4 y = –9 + 4

y = –5

-5

C (3, –5)


A

B

C

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Example 3: Graph the linear equation: ½ x – 2y = 5


step 1) 3 values for x were chosen; let x = -2, 0, 6 (multiples of 2 were chosen for the values of x so that computation with fractions would be easier.) step 2) The values were substituted into the equation and solved for y. The ordered pair (x, y) was formed.

x (chosen)

½ x – 2y = 5 y Ordered pair

– 2

½ (– 2) – 2y = 5 -1 – 1 – 2y = 5 – 2y = 6

-3

A (-2, -3)

0

½ (0) – 2y = 5 0 – 2y = 5 – 2y = 5 y = -5/2

B (0, -2 ½ )

6

½ (6) – 2y = 5 3 – 2y = 5 – 2y = 2

y = -1

-1

C (6, –1)


Note: It is possible for coordinates to be fractions or decimals.

B C

A

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Example 4: Graph the linear equation: y = x


step 1) 3 values for x were chosen; let x = -3, 0, 4 (note: any real # may be chosen) step 2) The values were substituted into the equation and solved for y. The ordered pair (x, y) was formed.

x (chosen)

y = x y Ordered pair

– 3

y = –3 y = -3

-3

A (-3, -3)

0

y = 0 y = 0

0

B (0, 0)

4

y = 4 y = 4

4

C (4, 4)

step 3) Plot each point and draw a line through the points. Include the arrows.

C

B

A

GRAPH OF LINEAR EQUATIONS OF HORIZONTAL & VERTICAL LINES

Horizontal Line

The equation of a horizontal line is y = a (where a is a real number) or Ay + B = C (where A,B, C are real numbers. Examples: 1) y = 3 is the equation of a horizontal line. 2) 2y + 1 = 5 is the equation of a horizontal line. Solve for y and the result is y = 2.

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To Graph the equation of a horizontal line.

• Solve for y when possible; let y = a • Choose any 3 values for x; the y coordinate will be the same value (the real number, a) • Plot the ordered pairs and draw the horizontal line through the points.

Example 1: Graph the linear equation: y = –3

Solution: If the equation is of the form y = a (a is a real number), the graph of the line will be a horizontal line.

step 1) 3 values for x were chosen; let x = -1, 0, 3 step 2) The y value paired with each x coordinate is -3 . The ordered pair (x, y) was formed.

x (chosen)

y = –3 y Ordered pair

– 1 –3 A (-1, –3) 0 –3 B (0, –3) 3 –3 C (3, –3)


A B C

Example 2: Graph the linear equation: 5y – 10 = 10

Solution: If the equation is of the form y = a (a is a real number), the graph of the line will be a horizontal line. step 1) solve for y: 5y = 20 y = 4 step 2) 3 values for x were chosen; let x = -2, 0, 6 step 3) The y value paired with each x coordinate is 6 . The ordered pair (x, y) was formed.

x (chosen)

y = –3 y Ordered pair

– 2 4 A (-2, 4) 0 4 B (0, 4) 6 4 C (6, 4)

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Example 2: (con’d) Graph the linear equation: 5y – 10 = 10

A B C

Vertical Line

The equation of a vertical line is x = a (where a is a real number) or Ax + B = C (where A,B, C are real numbers.

Examples: 1) x = 3 is the equation of a vertical line. 2) 2x + 1 = 5 is the equation of a vertical line. Solve for x and the result is x = 2.

To graph the equation of a vertical line.

• Solve for x when possible; let x = a • Choose any 3 values for y; the x coordinate will be the same value (the real number, a) • Plot the ordered pairs and draw the vertical line through the points.

Example 1: Graph the linear equation: x = 5

Solution: If the equation is of the form x = a (a is a real number), the graph of the line will be a vertical line.

step 1) 3 values for y were chosen; let y = -1, 0, 3 step 2) The x value paired with each y coordinate is 5. The ordered pair (x, y) was formed.

x (chosen) x = 5 y Ordered pair 5 – 1 A (5, –1) 5 0 B (5, 0) 5 3 C (5, 3)


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Example 1: (con’d) Graph the linear equation: x = 5

A

B

C

Example 2: Graph the linear equation: 4 – 2x = 10

Solution: step 1) Solve for x: 4 – 2x = 10 – 2x = 6 x = – 3 step 2) 3 values for y were chosen; let y = -1, 0, 3 step 3) The x value paired with each y coordinate is – 3. The ordered pair (x, y) was formed.

x (chosen)

x = 5 y Ordered pair

– 3 – 1 A (– 3, –1) – 3 0 B (– 3, 0) – 3 3 C (– 3, 3)


C

B

A

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CARTESIAN COORDINATE SYSTEM CLASSWORK PROBLEMS Plot each ordered pair. 1) A (0, 5) 2) B (4, 8) 3) C (7, – 3) 4) D (8, 0) 5) E (– 6, – 2) 6) F (– 3, 1) 7) G (5 ½ , – 9) 8) H (–6.4, 0)

Determine in which Quadrant or on which axis the ordered pair lies. 9) (7, 14) 10) (– 3, – 3) 11) (0, – 8) 12) (6 ½ , – 5) 13) (2.5, 1.3) 14) (– 10 ¼ , – 2.3) 15) (12, 0) 16) (– ¾ , 2) Determine if each ordered pair is a solution to the equation, 3x – 2y = 6.

17) (0, – 3) 18) (2, 0) 19) 20) (4, 2)

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Graph each linear equation. Clearly label at least 3 points. 21) x + y = 2 22) x – y = 5

23) 2x + y = 3 24) 3x – y = 1

25) x + 2y = – 1 26)

28

27)

28) 4x + 2y = 8

29) 3x – 2y = 6 30) y = 2x – 1

31) y = – x + 4 32)

29

33) y = 2x 34)

35)

36) x = 5

37) y = – 6 38) 3y + 5 = 2

30

39) 7 – x = 11 40) y = – x

41) x + y = – 4 42) 2(x – 4) + y = 2x

43) x + 3(4 + 2y) = y – 5( – 2 – y) 44)

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CARTESIAN COORDINATE SYSTEM HOMEWORK EXERCISES Determine the coordinates of each ordered pair. 1) A 2) B 3) C 4) D 5) E 6) F 7) G 8) H

G H C

A B

F

E

D

Determine in which Quadrant or on which axis the ordered pair lies. 9) (– 5, 10) 10) (2, – 3) 11) (– 8, 0) 12) (– 5, – 1 ¾ ) 13) (0, 2.5) 14) (15, 15) Determine if each ordered pair is a solution to the equation, 5x + 3y = 9.

15) (0, – 3) 16)

17)

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Graph each linear equation. Clearly label at least 3 points. 18) x + y = – 3 19) x – 2y = 6

20) 3x + y = 2 21)

22) 2x – 3 = – 1 23) y = x + 5

33

24)

25) 7y + 20 = 6

26) y = – 3x 27) x + y = 2

28) y = 8x + 3 – 4(2 + 2x) 29)

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Make copies of this page if you would like more graph paper to use for notes.

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ACF 92 WORKBOOK ANSWERS (Send an e-mail to [email protected] if you find an incorrect answer.) Answers to Simplify Expressions with Integers 1) -2x 8) 82a + 35 15) 4x 22) 103a + 72 2) -16y 9) 12y 16) -34y 23) 18y 3) -a + 19b 10) 30x + 30y 17) 37b 24) 49x + 8y 4) 20m – 13n – 6 11) -9a + 66 18) 10m – 10n – 4 25) 68 – 4a 5) 27x2 – 5y2 + 21xy 12) -10b + 64 19) 11x2 – 10y2 + 6xy 26) -20b + 42 6) 19x2 – 10y2 – 9xy 13) 10a – 50b 20) 27x2 – 5y2 + 21xy 27) 50a – 130b 7) 44m + 9 14) 13x – 33y 21) 42m + 24 28) 12x – 33y Answers to Simplify Expressions with Fractions

1) 6) 17y – 4 11) 16) -4x + 33y – 6

2) 7) x + 6 12) 17) 2x +

3) 8) 5a – 13b + 2c 13) 18) a – 5b + 7c

4) 9) x – 20y + 24 14) 19) -x – 53y + 47

5) 8x – 1 10) -2x – 11y + 12z 15) 14x – 5 20) -4x – 12y + 13z Answers to Simplify Expressions with Decimals 1) -0.2x 8) 15m – 15n – 72 15) -5x – 3y + 17

2) -1.7a – 3.9b 9) 16) 1.225a – 1.456b +

0.955c

3) -25.35x + 6.56y – 22.7 10) 17)

4) 0.001m – 0.02n – 0.002 11) -0.1y 18) 11m – n – 9

5) 2x – 4y + 7 12) 11.4x – 22.3y 19)

6) 0.37a + 0.2b – 0.35c 13) -30.95x + 7.76y – 15.3 20)

7) 14) 0.004m – 0.08n – 0.008

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Answers to Laws of Exponents Classwork Problems

1) 1013 2) 422 3) 916 4) (-5)13 5) (-21)39 6) 7) 8) (xy)19 9) (4abc)35 10) (x + y)8 11) (2a – 3b)9 12) (m – 2n)14 13) x16 14) 8x14 15) x7y16

16) 6x3y6z5 17) -10x10y22 18) 15a12b9c9 19) -54m11n18 20) 21) -x19y21 22) 58 23) 210 24) (-3)15 25) 92 = 81 26) 104 = 10000 27) (- 4)6 28) x5 29) y3 30) xy

31) a8 32) 2x2 33) 34) x6y4 35) a18b22 36) -2x6y6z6 37)

38) 39) 40) a15b21 41) x63y70z77 42) 8x12 43) 81x20y12z4

44) 216a27b63c12 45) 25x16y14 46) – a110b132c154 47) -243x10y25 48) 16m44n84p12 49)

50) 51) 52) 53) 54) 55) 56) 57)

58) 59) 1 60) 1 61) 62) 63) 64)

65) 2 66) 67) – 4 68) 69) 70) 71) 72)

73) 74) 75) 76) 77) simplified already 78) 79) 2x5

80) -3x10 81) x3y9 82) 83) 84) 85) 86) 87)

88) 89) 90) 91) x12y17 92) -6x15y17 93) 24x11y8 94) -21a16b9c12 95) 125x9 96) – 40x17y7 97) x31 98) 216x57 99) x54y57 100) -16x10y16

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101) -675x58y61z45 102) 103) 104) 105) 21x6 106) 60a6b4

107) – 1 108) 109) 110) -27x18y21 111) 112) 16a24b12c20

113) 114) 115) 116) 117) 118)

119) 120) 121) 122) 123) 124) 125)

126) 127) 128) 129) 130) x36y8 131) 132)

133) 134) 135) 136) 137) 138) 139) x35

140) x44 141) 142) 143) 144) 145) Answers to Laws of Exponents Homework Exercises

1) 313 2) 623 3) (-8)15 4) 5) (2x + y)10 6) x21 7) 30x9y16 8) -9m9n10p14

9) 10) 103 = 1000 11) (-2)6 = 64 12) 1210 13) x6 14) -6x5 15)

16) 17) x6y10z12 18) 1024x30y35z40 19) 26x16y14 20) – x15y30z45 21)

22) 23) 24) 25) 1 26) 27) 28) 3 29)

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30) – 5 31) 32) 33) 34) 35) 36)

37) 3x10y5 38) 39) 40) 41) -8x12y12 42) -120x9 43) 256x32

44) x54y57 45) 25x34y34z36 46) 47) -15x4y7 48) 49) x2y4 50) – 4

51) 52) 53) 54) 55) 56) Answers to Cartesian Coordinate System Classwork Problems # 1 – 8) see graph below. B

A

F H D E

C

G

9) I 10) III 11) on y-axis 12) IV 13) I 14) III 15) on x-axis 16) II 17) yes 18) yes 19) no 20) no

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Answers to Cartesian Coordinate System Classwork Problems (con’d) 21) 22)

23) 24)

25) 26)

40


29) 30)

31) 32)

41


35) 36)

37) 38)

42


41) 42) 8

43) 44)

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Answers to Cartesian Coordinate System Homework Exercises 1) A (2, 1) 2) B (3, 0) 3) C (– 5, 5) 4) D (1 ½ , – 8) 5) E ( 1, – 7) 6) F (– 3, – 4) 7) G (0, 6) 8) H (8.5, 5.5) 9) II 10) IV 11) on x-axis 12) III 13) on y-axis 14) I 15) no 16) yes 17) no 18) 19)

20) 21)

44

Answers to Cartesian Coordinate System Homework Exercises (con’d) 22) 23)

24) 25)

26) 27)

45

Answers to Cartesian Coordinate System Homework Exercises (con’d) 28) 29)

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