MATH HISTORY ACTIVITY

Transcription

1 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 Laws of Exponents Homework Exercises.. p Cartesian Coordinate System Notes... p Cartesian Coordinate System Classwork Problems... p Cartesian Coordinate System Homework Exercises.. p Blank Graph Paper. P. 34 Answers.. p MATH HISTORY ACTIVITY 1

2 CONTACT INFORMATION: NAME: phone number: 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. 2

3 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 ) for notes & examples 3

4 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) 5x 2 4y xy y 2 8xy + 22x 2 6) 7x 2 7y xy 3y 2 19xy + 12x 2 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) x 2 9y xy y 2 7xy + 10x 2 20) 8x 2 4y xy 2y 2 41xy + 12x 2 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 ) for notes & examples 4

5 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 ) for notes & examples 5

6 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) x + 3.5y 11.1x y 1 4) 0.01m 0.02n m m 5) 0.5(12x 6y + 4) 0.25(16x + 4y 20) 6) 0.1(2.5a + 3.5b 4.5c) (12a 15b + 10c) 7) 8) 0.9(20m 10n 90) 0.03(100m + 200n 300) 9) 10) 5x y 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) x + 2.7y 20.2x y 1 14) 0.04m 0.08n m m 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 y 2.6z + LAWS OF EXPONENTS NOTES 6

7 The following laws of exponents are for multiplying and dividing monomials. PRODUCT RULE: a m a n = a m+n (when multiplying like bases, add the powers) Examples: 1) x 4 x 5 = x 4+5 = x 9 2) = = ) a 7 a a 12 = a = a 20 4) (3x 6 )(2x 4 ) = (3 2)x 6+4 = 6x 10 5) (4m 8 n 2 )(-2mn 4 )(5m 4 n 3 ) = (4-2 5)(m )(n ) = -40m 13 n 9 POWER RULE: (a m b m ) n = a mn b mn (when taking a monomial to a power, multiply the powers including the coefficient s) Examples: 1) (a 4 b 3 ) 2 = a 4 2 b 3 2 = a 8 b 6 2) (3m 2 n 5 ) 4 = m 2 4 n 5 4 = 3 4 m 8 n 20 = 81 m 8 n 20 3) (-2xy 7 z 2 ) 5 = (-2) 5 x 5 y 35 z 10 = -32x 5 y 35 z 10 4) (6a 9 b 6 ) 2 = 6 2 a 18 b 12 = 36a 18 b 12 (-c 4 d 2 ) 5 (-1) 5 c 20 d 10 -c 20 d 10 QUOTIENT RULE: a m = a m - n (when dividing with like bases, subtract the powers) a n (Note: it is always the numerator's power minus the denominator's power) Examples: 1) x 6 = x 6 4 = x 2 2) m 5 n 7 = m 5-4 n 7-10 = mn -3 x 4 m 4 n 10 3) 8a 3 b 7 = 8 a 3 - (-5) b 7-9 = 2 a 8 n -2 4a -5 b 9 4 ZERO POWER RULE: 7

8 a 0 = 1 (any term to the zero power is one) Examples: 1) (m 5 n 7 ) 0 = 1 2) (4m 8 n 2 )(-2mn4) 0 = (4m 8 n 2 )(1) = 4m 8 n 2 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 = a n (take the reciprocal of only the variable that is to the negative power) a n a -n Examples: 1) 3x -4 = 3 1 = 3 2) -5m -8 n 2 = -5y 5 n 2 x 4 x 4 x 10 y -5 m 8 x 10 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 (12 8 ) = =12 4 (product rule) or = (negative power rule) 12 4 = = 12 4 (quotient rule) 2) (5a 4 b 6 )(12abc) 0 (-2a 2 bc 5 ) = (5a 4 b 6 ) (1) (-2a 2 bc 5 ) (zero power rule) -10a 6 b 7 c 5 (product rule) 3) -42m 6 n -3 p 5 = -7m 6-11 n -3-(-5) p 5-5 (quotient rule) 6m 11 n -5 p 5 = -7m -5 n 2 p 0 = -7n 2 (negative power and zero power rule) m 5 4) (-3ab 6 ) 5 = (-3) 5 a 5 b 30 (power rule) (-a 5 b 2 ) 7 (-1) 7 a 35 b 14 8

9 = -243a 5 b 30-1a 35 b 14 = 243a 5-35 b (quotient rule) = 243a -30 b 16 = 243b 16 (negative power rule) a 30 5) 2m 7 n 3 (3mp 8 ) 3 = 2m 7 n 3 27m 3 p 24 (power rule) (3n 5 p -3 ) 2 2mn 6 9n 5 p -6 2mn 6 = 54m 10 n 3 p 24 (product rule in numerator & denominator) 18mn 11 p -6 = 3 m 10-1 n 3-11 p 24 - (-6) (quotient rule) = 3m 9 n -8 p 30 = 3m 9 p 30 (negative power rule) n 8 6) (7xy)(-x 4 y 3 ) 5 (2x 5 y 6 ) -2 = (7xy)(-1 5 x 20 y 15 )(2-2 x -10 y -12 ) (power rule) = (7xy)(-x 20 y 15 )(x -10 y -12 ) (negative power rule) 2 2 = -7 x y (product rule) 4 = -7 x 11 y 4 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 9

10 Simplify. Use the Product Rule. 1) ) ) ) (-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) x 3 x 5 x 8 14) 2x 9 2x 4 2x 15) (x 4 y 7 ) (x 3 y 9 ) 16) (3xy 5 z) (2x 2 yz 4 ) 17) (-5x 3 y 12 ) (2x 7 y 10 ) 18) (3a 5 b)(-5a 6 b 7 c 8 )(-abc) 19) (9m 3 n 2 )(-2m 5 n 7 )(3m 3 n 9 ) 20) 21) Simplify. Use the Quotient Rule. 22) ) ) (-3) 25 (-3) 10 25) 26) 27) 28) x 15 x 10 29) y 7 y 4 30) (xy) 18 (xy) 17 31) 32) 33) 34) 35) 36) 37) 38) 39) Simplify. Use the Power Rule. 10

11 40) (a 5 b 7 ) 3 41) (x 9 y 10 z 11 ) 7 42) (2x 4 ) 3 43) (3x 5 y 3 z) 4 44) (6a 9 b 21 c 4 ) 3 45) (-5x 8 y 7 ) 2 46) (-a 10 b 12 c 14 ) 11 47) (-3x 2 y 5 ) 5 48) (-2m 11 n 21 p 3 ) 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) ) ) (-5) -2 64) (-2) -5 65) 66) 67) 68) 69) 70) x -5 71) x -3 y -2 72) x -10 y 6 73) 2x -9 74) -3x -8 75) 4x -11 y ) -5x -3 y -5 77) -7x 8 y 2 78) -10x -9 y 4 z -1 79) 80) 81) 11

12 82) 83) 84) 85) 86) 87) 88) 89) 90) Simplify. Write final answers with positive powers. 91) (x 3 y 7 )(x 9 y 10 ) 92) (2x 11 y 12 )(-3x 4 y 5 ) 93) (4x 8 y)(3xy)(2x 2 y 6 ) 94) (-7a 10 b 3 )(-a 4 b 2 c 5 )(-3a 2 b 4 c 7 ) 95) (5x 3 )(5x 3 )(5x 3 ) 96) 5(4x 5 y 7 )(-2x 12 y 0 ) 97) (x 8 ) 2 (x 3 ) 5 98) (2x 7 ) 3 (3x 12 ) 3 99) (x 7 y 5 ) 6 (x 4 y 9 ) 3 100) (-2xy) 4 (-9xy) 0 (-x 2 y 4 ) 3 101) (5x 5 y 3 z 2 ) 2 (-3x 8 y 9 z 3 ) 3 (x 6 y 7 z 8 ) 4 102) 103) 104) 105) 106) 107) 108) 109) 110) 111) 112) 113) Simplify. Write final answers with positive powers. 12

13 114) 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) Simplify. Use the Product Rule. LAWS OF EXPONENTS HOMEWORK EXERCISES 13

14 1) ) ) (-8) 3 (-8) 5 (-8) 7 4) 5) (2x + y) 7 (2x + y) 3 6) x 5 x 7 x 9 7) (2x 4 y 9 )(5x 3 y 2 )(3x 2 y 5 ) 8) (-3m 3 n 2 p 4 )(-m 5 n 7 p 9 )(-3mnp) 9) Simplify. Use the Quotient Rule. 10) ) (-2) 8 (-2) 2 12) 13) x 7 x 14) 15) 16) Simplify. Use the Power Rule. 17) (x 3 y 5 z 6 ) 2 18) (4x 6 y 7 z 8 ) 5 19) (-5x 8 y 7 ) 2 20) (-xy 2 z 3 ) 15 21) 22) 23) 24) 25) Simplify. Use the Negative Power Rule. Final answers must have positive powers only. 26) ) (-2) -5 28) 29) 30) 31) 32) Simplify. Use the Negative Power Rule. Final answers must have positive powers only. 14

15 33) a -3 b -2 34) a -7 b 9 35) 3x -5 y -2 36) -8a -4 b 4 c -1 37) 38) 39) 40) Simplify. Write final answers with positive powers. 41) (4x 9 y 5 )(-xy)(2x 2 y 6 ) 42) -2(3x 3 )(4x 3 )(5x 3 ) 43) (4x 8 ) 2 (2x 4 ) 4 44) (x 7 y 5 ) 6 (x 4 y 9 ) 3 45) (5x 5 y 3 z 2 ) 2 (-3x 8 y 9 z 3 ) 0 (x 6 y 7 z 8 ) 4 46) 47) 48) 49) 50) 51) 52) 53) 54) 55) 56) CARTESIAN COORDINATE SYSTEM NOTES 15

16 René Descartes, ( ), 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 16

17 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 E D 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. 17

18 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 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 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) = 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. 18

19 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) x + y = 1 y Ordered pair 2(-3) + y = y = 1 y = 7 2(0) + y = y = 1 y = 1 2(2) + y = y = 1 y = -3 7 A (-3, 7) 1 B (0, 1) -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. 19

20 Example 2: Graph the linear equation: y = 3x + 4 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 = -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 y = 3( 1) + 4 y = y = 8 y = 3(0) + 4 y = y = 4 y = 3(3) + 4 y = y = 5 8 A (-1, 8) 4 B (0, 4) -5 C (3, 5) 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 20

21 Example 3: Graph the linear equation: ½ x 2y = 5 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 = -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 ½ ( 2) 2y = 5 1 2y = 5 2y = 6 ½ (0) 2y = 5 0 2y = 5 2y = 5 y = -5/2 ½ (6) 2y = 5 3 2y = 5 2y = 2 y = -1-3 A (-2, -3) B (0, -2 ½ ) -1 C (6, 1) 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. Note: It is possible for coordinates to be fractions or decimals. B C A 21

22 Example 4: Graph the linear equation: y = x 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, 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 y = 3 y = -3-3 A (-3, -3) y = 0 y = 0 0 B (0, 0) 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. 22

23 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 y = 3 y Ordered pair (chosen) 1 3 A (-1, 3) 0 3 B (0, 3) 3 3 C (3, 3) step 3) Plot each point and draw a line through the points. Include the arrows. 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 y = 3 y Ordered pair (chosen) 2 4 A (-2, 4) 0 4 B (0, 4) 6 4 C (6, 4) 23

24 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) step 3) Plot each point and draw a line through the points. Include the arrows. 24

25 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 x = 5 y Ordered pair (chosen) 3 1 A ( 3, 1) 3 0 B ( 3, 0) 3 3 C ( 3, 3) step 4) Plot each point and draw a line through the points. Include the arrows. C B A 25

26 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) 26

27 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) 27

28 27) 28) 4x + 2y = 8 29) 3x 2y = 6 30) y = 2x 1 31) y = x ) 28

29 33) y = 2x 34) 35) 36) x = 5 37) y = 6 38) 3y + 5 = 2 29

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) 30

31 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 C G H 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) 31

32 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

33 24) 25) 7y + 20 = 6 26) y = 3x 27) x + y = 2 28) y = 8x + 3 4(2 + 2x) 29) 33

34 Make copies of this page if you would like more graph paper to use for notes. 34

35 ACF 92 WORKBOOK ANSWERS (Send an to if you find an incorrect answer.) Answers to Simplify Expressions with Integers 1) -2x 8) 82a ) 4x 22) 103a ) -16y 9) 12y 16) -34y 23) 18y 3) -a + 19b 10) 30x + 30y 17) 37b 24) 49x + 8y 4) 20m 13n 6 11) -9a ) 10m 10n 4 25) 68 4a 5) 27x 2 5y xy 12) -10b ) 11x 2 10y 2 + 6xy 26) -20b ) 19x 2 10y 2 9xy 13) 10a 50b 20) 27x 2 5y xy 27) 50a 130b 7) 44m ) 13x 33y 21) 42m ) 12x 33y Answers to Simplify Expressions with Fractions 1) 6) 17y 4 11) 16) -4x + 33y 6 2) 7) x ) 17) 2x + 3) 8) 5a 13b + 2c 13) 18) a 5b + 7c 4) 9) x 20y ) 19) -x 53y ) 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 ) -1.7a 3.9b 9) 16) 1.225a 1.456b c 3) x y ) 17) 4) 0.001m 0.02n ) -0.1y 18) 11m n 9 5) 2x 4y ) 11.4x 22.3y 19) 6) 0.37a + 0.2b 0.35c 13) x y ) 7) 14) 0.004m 0.08n

36 Answers to Laws of Exponents Classwork Problems 1) ) ) ) (-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) x 16 14) 8x 14 15) x 7 y 16 16) 6x 3 y 6 z 5 17) -10x 10 y 22 18) 15a 12 b 9 c 9 19) -54m 11 n 18 20) 21) -x 19 y 21 22) ) ) (-3) 15 25) 9 2 = 81 26) 10 4 = ) (- 4) 6 28) x 5 29) y 3 30) xy 31) a 8 32) 2x 2 33) 34) x 6 y 4 35) a 18 b 22 36) -2x 6 y 6 z 6 37) 38) 39) 40) a 15 b 21 41) x 63 y 70 z 77 42) 8x 12 43) 81x 20 y 12 z 4 44) 216a 27 b 63 c 12 45) 25x 16 y 14 46) a 110 b 132 c ) -243x 10 y 25 48) 16m 44 n 84 p 12 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) 2x 5 80) -3x 10 81) x 3 y 9 82) 83) 84) 85) 86) 87) 88) 89) 90) 91) x 12 y 17 92) -6x 15 y 17 93) 24x 11 y 8 94) -21a 16 b 9 c 12 95) 125x 9 96) 40x 17 y 7 97) x 31 98) 216x 57 99) x 54 y ) -16x 10 y 16 36

37 101) -675x 58 y 61 z ) 103) 104) 105) 21x 6 106) 60a 6 b 4 107) 1 108) 109) 110) -27x 18 y ) 112) 16a 24 b 12 c ) 114) 115) 116) 117) 118) 119) 120) 121) 122) 123) 124) 125) 126) 127) 128) 129) 130) x 36 y 8 131) 132) 133) 134) 135) 136) 137) 138) 139) x ) x ) 142) 143) 144) 145) Answers to Laws of Exponents Homework Exercises 1) ) ) (-8) 15 4) 5) (2x + y) 10 6) x 21 7) 30x 9 y 16 8) -9m 9 n 10 p 14 9) 10) 10 3 = ) (-2) 6 = 64 12) ) x 6 14) -6x 5 15) 16) 17) x 6 y 10 z 12 18) 1024x 30 y 35 z 40 19) 26x 16 y 14 20) x 15 y 30 z 45 21) 22) 23) 24) 25) 1 26) 27) 28) 3 29) 37

38 30) 5 31) 32) 33) 34) 35) 36) 37) 3x 10 y 5 38) 39) 40) 41) -8x 12 y 12 42) -120x 9 43) 256x 32 44) x 54 y 57 45) 25x 34 y 34 z 36 46) 47) -15x 4 y 7 48) 49) x 2 y 4 50) 4 51) 52) 53) 54) 55) 56) Answers to Cartesian Coordinate System Classwork Problems # 1 8) see graph below. B A H F 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 38

39 Answers to Cartesian Coordinate System Classwork Problems (con d) 21) 22) 23) 24) 25) 26) 39

40 Answers to Cartesian Coordinate System Classwork Problems (con d) 27) 28) 29) 30) 31) 32) 40

41 Answers to Cartesian Coordinate System Classwork Problems (con d) 33) 34) 35) 36) 37) 38) 41

42 Answers to Cartesian Coordinate System Classwork Problems (con d) 39) 40) 41) 42) 8 43) 44) 42

43 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) 43

44 Answers to Cartesian Coordinate System Homework Exercises (con d) 22) 23) 24) 25) 26) 27) 44

45 Answers to Cartesian Coordinate System Homework Exercises (con d) 28) 29) 45