Dividing in Scientific Notation Name (page 778)

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1 LESSON 111 Dividing in Scientific Notation Name (page 778) To divide powers of 10, subtract the exponents = = 10 3 To divide numbers in scientific notation: 1. Divide the decimal or whole numbers to find the decimal or whole number part of the quotient. 2. Divide the powers of 10 to find the power-of-10 part of the quotient. 3. Write the expression in the proper form of scientific notation. Example: Divide Divide whole (or decimal) numbers: 3 6 = 0.5 Practice Set (page 780) Write each quotient in scientific notation. 2. Divide powers of 10: = = The quotient is Teacher Note: Review Scientific Notation for Numbers Powers of 10 on page 21 in the Student Reference Guide. 3. Rewrite the expression in the proper form of scientific notation. 3. ( ) 10 3 = = = c = d = e = f = g = h = i. When d numbers in scientific notation, s the exponents of the powers of t. Saxon Math Course 2 L Adaptations Lesson 111

2 Written Practice (page 780) 1. Include all years y = 600 y = % Natural History + 100% Planetarium + 100% Total y + 15 = 4. A(0, 3), B(0, 0), C(4, 0) Translate 1 unit left and 1 unit down. 5. Use exponents. ) 1024 ) 1024 ) 1024 ) 1024 ) 1024 ) 1024 ) 1024 ) 1024 ) 1024 ) = A ( 1, 2), B (, ), C (, ) 6. See the Student Reference Guide. c. See page Multiply the probabilities. + 3 red + 4 white + 5 bluee + 5 total c. 9. 2x = x = Saxon Math Course 2 L Adaptations Lesson 111

3 Written Practice (continued) (page 781) Solve for c 2 : c 2 b 2 = a 2 The sum of the measures of a t is. c 2 = 12. h = 105 c. d. 13. Find F to the nearest degree when C is 17. F = 1.8C x y Use work are 15. Upward slope (positive) or downward slope (negative)? Find points on the line. Draw legs of right triangle. Write the ratio rise run. 16. Round to the nearest square inch. (, ) 360 area = 17. First convert to feet. Use 3.14 for π. 18. Capacity means volume. First convert to feet. Use 3.14 for π. Saxon Math Course 2 L Adaptations Lesson 111

4 Written Practice (continued) (page 782) 19. 2x = 19 2x 2 1 = 19 x =, 20. ( 1, 2), ( 1, 1) (3, 1) perimeter x =, 21. $5000 principal 5% interest 5 years Use a calculator. Enter 1 plus percent of interest. Enter M. Enter amount of principal. Enter x, MR, and = for the number of years = = x + 3x = x x = x = x = 27. ( 1) 6 + ( 1) 5 = ( 10) 6 ( 10) 5 = 28. Cancel matching factors. (4a 2 b)(9ab 2 c) = 6abc x(x c) + c 2 x 2 = 29. ( 3) + (+2)( 4) ( 6)( 2) ( 8) = _ = 0.03 Saxon Math Course 2 L Adaptations Lesson 111

5 LESSON Name 112 Applications of the Pythagorean Theorem (page 784) Any triangle with sides in the ratio of 3 to 4 to 5 is a right triangle = 5 2 The numbers 3, 4, and 5 satisfy the Pythagorean Theorem. They are sometimes called a Pythagorean triplet. Multiples of are also Pythagorean triplets Example: The numbers 5, 12, and 13 are a Pythagorean triplet = 13 2 What are the next three multiples of this Pythagorean triplet? To find the next three multiples of , multiply each number by 2, by 3, and by The Pythagorean Theorem has many uses in everyday life. One application of the Pythagorean Theorem is to calculate measures like how high a kite is flying. Example: Serena went to a level field to fly a kite. She let out all 200 ft of string and tied it to a stake. Then she walked out on the field until she was directly under the kite, 150 feet from the stake. About how high was the kite? a 2 + b 2 = c 2 a 2 = c 2 b 2 a 2 = (200 ft) 2 (150 ft) 2 a 2 = 40,000 ft 2 22,500 ft 2 Pythagorean Theorem rearranged substituted simplified a 2 = 17,500 ft 2 subtracted a = 17,500 ft square root a 132 ft Use a calculator to find that the height of the kite was about 132 ft. Teacher Notes: Review Pythagorean Theorem on page 29 in the Student Reference Guide. The activity in the Student Edition is optional. solved Practice Set (page 787) A 12-foot ladder was leaning against a building. The base of the ladder was 5 feet from the building. How high up the side of the building did the ladder reach? Write the answer in feet and inches rounded to the nearest inch. a 2 + b 2 = c 2 Saxon Math Course 2 L Adaptations Lesson 112

6 Practice Set (continued) (page 787) Figure ABCD illustrates a rectangular field 400 feet long and 300 feet wide. The path from A to C is how much shorter than the path from A to B to C? a 2 + b 2 = c 2 c. A contractor checks the forms for a concrete sla He marks the forms at 8 ft and at 6 ft. Then he measures between the marks and finds that the distance is 10 feet 2 inches. Is the corner a right angle? How do you know? A Pythagorean triplet is If the corner is a right angle, the distance would be exactly ft. The distance is ft in., so the corner a right angle. Written Practice (page 788) 1. $3000 principal Use a calculator. 8% interest Enter 1 plus percent of interest. 3 years Enter M = Enter amount of principal. Enter x, MR, and = for the number of years. 3. Score Class Quiz Scores Number of Students 4. km hr? Find the profit. Saxon Math Course 2 L Adaptations Lesson 112

7 Written Practice (continued) (page 788) 8. 50% of 50% of $ $1 9. multiple choice + short answer m total m 10. (3, 11), ( 2, 1),( 2, 11) 11. km hr 0.6 mi 1 km = 12. is of =? The percent should be l than 100% but more than %. 13. Multiply the probabilities. favorable to unfavorable to mo = yr $4000 $ = = 17. Pythagorean triplets Use work are Saxon Math Course 2 L Adaptations Lesson 112

8 Written Practice (continued) (page 789) 18. Solve for t: d = rt 19. y = x 20. Use 3.14 for π. t = Use work are = = = Find the pattern. x = 8f = Take half of the exponent of each prime factor. 23. surface area = 48 f x 3 = 21 f = x = [10 10( )] = ( ) = = ( 3)( 2)( 1) + ( 5)(4)( 3)(2) 1 = 30. surface area = 4πr 2 Use 22 for π. 7 Saxon Math Course 2 L Adaptations Lesson 112

9 LESSON Name 113 Volume of Pyramids, Cones, and Spheres (page 791) Volume of a prism = area of base height A pyramid is a geometric solid that has three or more faces that are triangles and a base that is a polygon. Teacher Notes: Introduce Hint #60, Comparing Volumes. Review Geometric Solids on page 30 in the Student Reference Guide. Volume of a pyramid = 1_ area of base height 3 Volume of a cylinder = 1_ area of base height 3 The volumes of cones and spheres are related to the volume of a cylinder. A cone is 1_ the volume of a cylinder. 3 A sphere is 2_ the volume of a cylinder. 3 Volume of a cone = 1_ area of base height 3 Volume of a sphere = 2_ 3 Practice Set (page 795) volume of a cylinder with the same diameter and height = 4_ 3 πr3 Pictured are two identical cylinders whose heights are equal to their diameters. In one cylinder is the largest cone it can contain. In the other cylinder is the largest sphere it can contain. Packing material is used to fill all the voids in the cylinders not occupied by the cone or sphere. Use this information to answer questions a e. What fraction of the cylinder is occupied by the cone? What fraction of the cylinder containing the cone is occupied by the packing material? c. What fraction of the cylinder is occupied by the sphere? d. What fraction of the cylinder containing the sphere is occupied by the packing material? e. If the cone and sphere were removed from their cylinders and all the packing material from both cylinders was put into one cylinder, what portion of the cylinder would be filled with packing material? A of the cylinder would be f. ( = ) f. A pyramid with a height of 12 inches and a base 12 inches square is packed in the smallest cubical box that can contain it. What is the volume of the box? What is the volume of the pyramid? Saxon Math Course 2 L Adaptations Lesson 113

10 Practice Set (continued) (page 795) Find the volume of each figure below. Leave π as π. g. h. Written Practice (page 796) ,000,000,000 10,000,000,000 S C mean median 4. Nelda hr $ Christy hr $?? per per c. more per of yards 8 7. Multiply the probabilities. 8. is of =? Saxon Math Course 2 L Adaptations Lesson 113

11 Written Practice (continued) (page 796) 9. 50% = is of? 10. $5000 principal 4% interest 3 years Use a calculator. Enter 1 plus percent of interest. Enter M. Enter amount of principal. Enter x, MR, and = for the number of years ft = in. 13. (0, 4), ( 3, 2), (3, 2) 14. Draw an altitude to form 2 right triangles in # V = 2 3 πr3 Round to the nearest 10 cm Use 3 for π. 16. ( )( ) = 17. (AC) 2 + (BC) 2 = (Shortcut) 2 Saxon Math Course 2 L Adaptations Lesson 113

12 Written Practice (continued) (page 797) 18. Solve for h: A = 1 2 bh Use the formula A = 1 2 bh to find h when A = 16 and b = 8. h = 19. Upward slope (positive) or downward slope (negative)? Find points on the line. y x Draw legs of right triangle. Write the ratio rise run. slope: 20. V = 1 (area of base)(height) 3 h = Use work are 21. V = 1 (area of base)(height) The triangles are similar d = c. d = Saxon Math Course 2 L Adaptations Lesson 113

13 Written Practice (continued) (page 798) w + 17 = {4 2 [3 2 ( )]} = w = = = = = ( ) ( ) = 29. ( 7) + 3 (2)( 3) + ( 4) ( 3)( 2)( 1) = 30. V = 1 (area of base)(height) 3 Saxon Math Course 2 L Adaptations Lesson 113

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15 LESSON Name 114 Volume, Capacity, and Mass in the Metric System (page 799) Metric units of volume, capacity, and mass are related. One cubic centimeter can contain 1 milliliter of water, which has a mass of 1 gram. Teacher Note: Review Equivalence Table for Units on page 1 in the Student Reference Guide. Water 1 cm 3 1 ml 1 g Volume Capacity Mass One thousand cubic centimeters can contain 1 liter of water, which has a mass of 1 kilogram. Water 1000 cm 3 1 L 1 kg Volume Capacity Mass A container with a volume of 1000 cm 3 has a capacity to hold 1 L of water. Practice Set (page 801) What is the mass of 2 liters of water? What is the volume of 3 liters of water? c. When the bottle was filled with water, the mass increased by 1 kilogram. How many milliliters of water were added? d. A tank that is 25 cm long, 10 cm wide, and 8 cm deep can hold how many liters of water? Written Practice (page 801) Saxon Math Course 2 L Adaptations Lesson 114

16 Written Practice (continued) (page 801) 3. 6 red 9 green + 12 blue 27 total doz = pencils $? c. to 5. 6 mo = yr Label graph. is of 1 4 music 1 3 talking? read? V = 2 3 πr3 Use 3 for π % = 11. (3, 2), (6, 2), ( 2, 2), ( 2, 2) 10. is of is of? =? Saxon Math Course 2 L Adaptations Lesson 114

17 Written Practice (continued) (page 802) 12. least to greatest 6, 6 2, 6, ,,,,, Use work are = 15. ( )( ) = = km 2 km km km km = 17. Solve for d: C = πd Use the formula C = πd to find d when C is (Use 3.14 for π.) d = d = 18. See the Student Reference Guide = Use 3.14 for π. 20. surface area volume of pyramid = 1 (volume of cube) 3 Saxon Math Course 2 L Adaptations Lesson 114

18 Written Practice (continued) (page 803) Use 3.14 for π. c m 1.2 = 6 m = 25. 3(x 4) < x = x < kg = g 28. (1.2) ( ) = = 30. ( 3)( 2) (2)( 3) ( 8) + ( 2)( 3) + 5 = Saxon Math Course 2 L Adaptations Lesson 114

19 LESSON Name 115 Factoring Algebraic Expressions (page 804) To factor a monomial: 1. Write the number as prime factors. 2. Write the letter(s) as a product of factors. 3. List all factors. Example: Factor 6x 2 y 3 6 = 2 3 x 2 y 3 = xxyyy To factor some polynomials: 6x 2 y 3 = (2)(3)xxyyy 1. Factor each term and find the GCF of the terms. 2. Divide each term by the GCF to find the remaining polynomial. 3. Write the factored form, which is the GCF times the remaining polynomial. Example: Factor 3x 2 y + 6xy 2 Practice Set (page 806) Factor each algebraic expression. 1. Find the GCF. 3 x x y and 2 3 x y y 3xy 2. Divide each term by the GCF. 3x 2 y 3xy + 6xy2 3xy = 3 x x y 3 x y x y y 3 x y 3. Rewrite the expression in factored form. 3x 2 y + 6xy 2 = 3xy(x + 2y) Monomials: one term 6x 2 y 3 8m 2 n 12mn 2 Algebraic Expressions Binomials: two terms 3x 2 + 6y 2 = x + 2y ( )( )( ) ( )( )( ) Polynomials: two or more terms Trinomials: three terms x 2 + 2x + 4 c. 18x 3 y 2 ( )( )( ) d. 8m 2 n + 12mn 2 e. 8xy 2 4xy f. 6a 2 b 3 + 9a 3 b 2 + 3a 2 b 2 g. The type of polynomial in f is a t. Saxon Math Course 2 L Adaptations Lesson 115

20 Written Practice (page 806) 1. 9 months = year $7000 $7000 M $7000 by 4% to find the 2. Multiply the probabilities. c. to interest in one year. 9 months is one year, so multiply the interest by. of qt = 32 oz oz $ oz $?? Does the bottle or container cost more per ounce? 5. per is of is of 3? 5? S C Saxon Math Course 2 L Adaptations Lesson 115

21 Written Practice (continued) (page 807) 10. ( 3, 4), (5, 2), ( 3, 2) 11. full mass of water half mass of water mass of empty aquarium kg kg kg 12. Use work are min = seconds 14. ( )( ) = beats seconds 17 15? = ft = in. 1 in. = 2.54 cm in. cm? 16. Solve for b: A = 1 2 bh Use the formula A = 1 bh to find b when 2 A is 24 and h is 6. c. Solve for h: A = 1 2 bh b = b = 17. Upward slope (positive) or downward slope (negative)? Find points on the line. y = 2x Draw legs of right triangle. Write the ratio rise run. c. h = slope: Use work are Saxon Math Course 2 L Adaptations Lesson 115

22 Written Practice (continued) (page 808) 18. area 19. surface area volume c. 100 cm = m c. 20. volume of cylinder 21. volume of sphere = 2 (volume of cylinder) 3 c volume of pyramid = 1 (volume of cube) 3 = WV n = y = = n = y = yd 2 ft 1 in. 3 yd 2 ft 1 in = ( ) = (3)( 2)(4) ( 6)(2) + ( 8) + ( 4)(+5) (2)( 3) = Saxon Math Course 2 L Adaptations Lesson 115

23 LESSON Name 116 Slope-Intercept Form of Linear Equations (page 809) The slope-intercept form of an equation is a special form that shows the slope ( rise run ) of a line on a graph and the point where the line crosses the y-axis. Slope-Intercept Form y = mx + b When an equation is written in slope-intercept form: The number in the m position is the slope. The number in b position is the y-intercept. The y-intercept is the point where the line intersects the y-axis. Example: Transform this equation so that it is in slope-intercept form. 3x + y = 6 3x + y 3x = 6 3x y = 6 3x y = 3x + 6 equation subtracted 3x from both sides simplified Commutative Property Example: Graph y = 3x + 6 using slope and y-intercept. The slope is ( 3) or ( 3 +1 ). The y-intercept is Mark a point at the y-intercept. (0, 6) 2. From that point, move right 1 unit and down 3 units and mark another point. (1, 3) 3. Draw a line connecting the two points. Practice Set (page 813) Write each equation below in slope-intercept form. y = mx + b 2x + y = 3 y = y 3 = x y = c. 2x + y 3 = 0 y = d. x + y = 4 x y = Using only slope and y-intercept, graph each of these equations on the coordinate plane. The line on the plane is e. e. y = x 3 f. y = 2x + 6 g. y = 1 x 2 2 h. y = x + 3 i. I found the y-intercept:. I know the slope is, so I drew another point unit right and 1 unit. Then I drew the line. Saxon Math Course 2 L Adaptations Lesson 116

24 Written Practice (page 813) 1. See the Student Reference Guide = 1 kilobyte 2 10 = c. to bytes 3. The better sale seems to be the 40% 4. sale which is % off the r price instead of % off the r price. Use work are Use work are 5. A(0, 3), B(0, 0), C(4, 0) Rotate 180 about the origin. 6. The number of triangles in a polygon is 2 less than the angles. See the Student Reference Guide. 7. exterior interior 8. A (, ), B (, ), C (, ) kg 2.2 lb 1 kg = Saxon Math Course 2 L Adaptations Lesson 116

25 Written Practice (continued) (page 814) 10. 2x = = 180 x = 12. Solve for C: 13. perimeter F = 1.8C + 32 C = Use 3.14 for π. 14. surface area 15. volume 16. A = 1 (a + b)h y y 18. 3x 2 5 = yx = x = yx ; ( 0, ) ; ( 0, ) x x =, Saxon Math Course 2 L Adaptations Lesson 116

26 Written Practice (continued) (page 815) 20. The p is because the numbers are r and the product of reciprocals is. 21. Factor. 9x 2 y 10a 2 b + 15a 2 b abc Use work are 22. volume = 2 3 πr3 Round to the nearest in m BCD = m BAC = c. m ACD = d. The three t are s. Use 3.14 for π. Use work are 24. BD BC =? CA 25. x 15 = x + 2x (m 5) = 0.96 x = m = 27. a(b c) + b(c a) = 28. Cancel matching factors first. (8x 2 y)(12x 3 y 2 ) = (4xy)(6y 2 ) 29. ( 3) 2 + ( 2)( 3) ( 2) 3 = = 30. Saxon Math Course 2 L Adaptations Lesson 116

27 LESSON 117 Copying Geometric Figures Name (page 817) To copy a segment: 1. Draw a point that will be the endpoint of the copied segment. 2. Place the pivot point of the compass on one end of the original segment. 3. Open the compass until the pencil point is on the other end of the original segment. 4. Without changing the compass, draw an arc from the point. 5. Draw a segment from the point to anywhere on the arc. Teacher Notes: Students will require a protractor and a compass to complete this lesson. The activity in the Student Edition is optional. Original Segment Copy Copy To draw parallel lines that are the same distance apart as two other parallel lines: 1. Set the compass to the distance between the original parallel lines. 2. Draw a line. 3. Without changing the compass, draw arcs from two points on the line. 4. Draw a second line that just touches the two arcs. To copy an angle: Original Lines Copy Copy 1. Begin by drawing a ray to form one side of the angle. 2. Set a compass with the pivot point on the vertex of the original angle, and draw an arc across both rays. 3. Draw an arc of the same size from the endpoint of the ray. 4. Reset the compass to equal the distance between intersection points A and B on the original angle. On intersection point A of the copied angle draw an arc that intersects the first arc. 5. Draw the second ray of the copied angle through the point where the arcs intersect (point B ). To copy a triangle, copy the bottom segment and then mark the lengths of the other two sides. Saxon Math Course 2 L Adaptations Lesson 117

28 Practice Set (page 820) Use a protractor to draw an 80 angle. Then use a compass and straightedge to copy the angle. With a protractor draw a triangle with angles of 30, 60, and 90. Then use a compass and straightedge to copy the triangle. c. To copy a pair of parallel lines, I would set the compass to the d between the parallel lines. Then I would draw a l and swing two arcs using the c. Finally I d draw a s line that just touches the two a. Written Practice (page 821) 1. $10,000 principal 7% interest 4 years Use a calculator. Enter 1 plus percent of interest. Enter M. Enter the amount of principal. Enter x, MR, and = for the number of years. Subtract the principal to show the interest. 2. hits at-bats = to Saxon Math Course 2 L Adaptations Lesson 117

29 Written Practice (continued) (page 821) A( 1, 3), B( 3, 0), C(0, 2) Reflect across the y-axis. 6. Use work are c. diagonals A ( 1, 3 ), B (, ), C (, ) See Lesson ft 2 = 10. 3x 2 = x + 12 < Solve for c 2 : c 2 a 2 = b 2 x =, x < c 2 = Saxon Math Course 2 L Adaptations Lesson 117

30 Written Practice (continued) (page 823) volume of cylinder volume of cone = 1 (volume of cylinder) 3 c. to 14. (0, 4), (3, 0), ( 1, 3), ( 4, 1) c. 17. y 16. V = lwh x h = h = (, ) c. y = 18. y + 5 = x 2x + y = Factor: 24xy 2 3x 2 + 6xy 9x mm y = y = Saxon Math Course 2 L Adaptations Lesson 117

31 Written Practice (continued) (page 823) 21. mm 2 = 22. side side = 5 3 = w 3w + 18 = 9(w 4) 26. 3x(x 2y) + 2xy(x + 3) = w = ( 1) 3 = 28. ( 3) + ( 2)[( 3)( 2) (+4)] ( 3)( 4) = = a 2 b 3 c 12ab 2 c = Saxon Math Course 2 L Adaptations Lesson 117

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33 LESSON 118 Division by Zero (page 825) Name It is not possible to divide by zero. When choosing values for x in division problems, the divisor cannot be zero. Example: In the following equation, what number may not be used in place of x? 12 y = 3 + x The divisor, 3 + x, cannot be zero. To find what number may not be used for x: 1. Set the divisor equal to zero. (3 + x = 0) 2. Solve for x. Practice Set (page 828) 3 + x = x 3 = 0 3 x = 3 When x = 3, the divisor is zero. So, 3 may not be used in place of x. 3. Write the answer in proper form. x 3 (This means x does not equal 3. ) Use a calculator to divide several different numbers of your choosing by zero. Remember to clear the calculator before entering a new problem. What answers are displayed? The error message is. The numbers in the multiplication fact 7 8 = 56 can be arranged to form two division facts. If we attempt to form two division facts for the multiplication fact 7 0 = 0, one of the arrangements is not a fact. Which arrangement is not a fact and why? is not a fact because division by z is not possible. For the following expressions, find the number or numbers that may not be used in place of the variable. c. 6 w f. y + 3 y 3 w d. y g. i. Explain your answer to g. 3 x 1 8 x 2 4 x e. 4 2w x, h. 3ab c w c Squaring both 2 and 2 results in and 4 4 = 0. So x 2 or because the denominator of a fraction cannot be. Saxon Math Course 2 L Adaptations Lesson 118

34 Written Practice (page 828) cm = m 3. Armando can select a P t like to verify when he has formed a r angle. For example, he can measure and mark from a corner meters along one line and meters along a proposed p line. Then he can check if it is meters between marks. Use work are 4. Round to the nearest foot. 5. width on drawing in. m ft ? length on drawing in. Each inch is 10 feet. Find the are 6. See the Student Reference Guide. 7. (4, 6), ( 1, 6) Draw legs of right triangle. Use the Pythagorean Theorem. 8. See Lesson 114. c. to Saxon Math Course 2 L Adaptations Lesson 118

35 Written Practice (continued) (page 829) 9. 1 x = 10. m a + m e = x = 11. 3x + y = I wrote the equation x y = = 180, solved for x, and found the x x 13. volume of cube = measure of each a. volume of pyramid = x + y = surface area of sphere = 4πr = y = x Use 3 for π. AD = x = y = 17. y 2x + 5 = y = c. y = Saxon Math Course 2 L Adaptations Lesson 118

36 Written Practice (continued) (page 831) perimeter estimate copy Use 22 for π. 7 Use work are = 22. Factor: x 2 + x 12m 2 n mn 2 24m 2 n w = x2 + 1 = ( ) 2 2 = w = x =, % of 5 of [ 3 + ( 4)( 5)] [ 4 ( 5)( 2)] = Cancel matching factors. (5x 2 yz)(6xy 2 z) 10xyz = 29. x(x + 2) + 2(x + 2) = 30. a 2 + b 2 = c 2 and Saxon Math Course 2 L Adaptations Lesson 118

37 LESSON 119 Graphing Area and Volume Name Formulas (page 832) We have graphed straight lines. Now we cover graphs that are curves. We can graph the relationship between the side of the square and its area: A area in units 2 s side length of square The graph of the function rapidly becomes steeper as the side of the square becomes longer. For some equations the graph is so steep that the vertical and horizontal scales must be different. Practice Set (page 833) Half of the area of a square is shaded. As the square becomes larger, the area of the shaded region becomes greater, as indicated by the function table in which A represents the area of half of a square and s represents the length of a side of the square. Complete the table. Then graph the function. A s Graph the function V = e 3 using the function table. V represents the volume of a cube and e represents the edge length of a cube. V e c. Doubling s length of a square quadruples the a. Saxon Math Course 2 L Adaptations Lesson 119

38 Written Practice (page 834) 1. green left marbles left Convert to percent greater than or equal to 3 less than 2 4. See the Student Reference Guide. Use work are Use another sheet of paper, and attach it to this lesson worksheet. Use work are c. 7. (6 105 ) ( ) = 8. Factor: ( ) 2x 2 + x 3a 2 b 12a 2 + 9ab 2 9. Each cube is 1 cm surface area Saxon Math Course 2 L Adaptations Lesson 119

39 Written Practice (continued) (page 835) 11. Solve for h: A = 1 2 bh Find h when A is 1.44 m 2 and b is 1.6 m. h = = 100 h = 13. a 2 + b 2 = c y m l x y = y = 15. The product of the slopes is. The slopes are negative r. 16. $8000 principal 6% interest 4 years Use a calculator. 17. Round up to the next square yard ft 2 = Use work are w m w m Saxon Math Course 2 L Adaptations Lesson 119

40 Written Practice (continued) (page 836) 19. x c B D A 20. x z y = y = z DA = 21. V = 2 3 πr3 22. Use work are m = (3 x) = x + x + 12 = 5x m = x = x = x 2 = ,000 = 28. x(x + 5) 2(x + 5) = 29. x =, (12xy 2 z)(9x 2 y 2 z) = xyz 2 3 % of 0.12 of Saxon Math Course 2 L Adaptations Lesson 119

41 LESSON 120 Graphing Nonlinear Name Equations (page 837) Equations whose graphs are lines are called linear equations. Equations whose graphs are curves are called nonlinear equations. To graph nonlinear equations: 1. Make a table of ordered pairs (including negative values). 2. Graph the points on a coordinate plane. 3. Draw a smooth curve (or curves) through the points. Practice Set (page 840) Complete each table and graph the curve. Graph: y = 12 x Graph: y = x 2 2 Compare your graph to the graph in Example 1. c. Graph: y = 10 Compare your graph to x the graph in Example 2. d. Graph: y = 2x 2 Compare your graph to the graph in Example 1. Saxon Math Course 2 L Adaptations Lesson 120

42 Written Practice (page 841) 1. See the Student Reference Guide. 2. to million 280 million = 4. Change to a percent ( )( ) = Use work are 7. Factor. 3y 2 y 6w 2 + 9wx 12w 8. volume of cone = 1 (volume of cylinder) 3 volume of cone volume of cylinder = Use 3.14 for π. Saxon Math Course 2 L Adaptations Lesson 120

43 Written Practice (continued) (page 842) 11. Solve for m: E = mc boys girls m = 13. line m: y = y 14. The p of the line n: y = m n s is. The slopes are n x r. Use work are Use work are 15. $1000 principal 20% interest Use a calculator. 16. Round to the nearest inch ft 21 ft 1 2 ft = 18. cu ft = m y 5 y + 5 m c x z y a c a = a? Use work are b y Saxon Math Course 2 L Adaptations Lesson 120

44 Written Practice (continued) (page 843) 21. surface area = 4πr L cm 3? Write answer as a decimal x = 3x x 16 = 74 3 x = x = 25. m 2 4 = m = m =, m = 27. x(x 5) 2(x 5) = 28. (3xy)(4x 2 y)(5x 2 y 2 ) 10x 3 y 3 = ( 7) [( 4)( 5) 3( 2)] = _ (0.9) 0.03 = Saxon Math Course 2 L Adaptations Lesson 120

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