oxford ib math sl applications and interpretationoxford ib math sl applications and interpretation

investigate them further. If you represent the problem only as text, the simple probabilities P(A) = i and P(B) = ^ can be found easily * We know because" Statistics and probability but calculating these do not show you the whole picture of how the sets relate to each other, vi____________________ ______________________ y Represent this information as follows in a Venn diagram to see more detail: The rectangle represents the sample space U for which P(U) = 1, the total probability. . Elemi Publishing. ?S 2 REPRESENTING SPACE: NON-RIGHT ANGLED TRIGONOMETRY AND VOLUMES O The nets labelled a, b, e and f can be folded into a cube, whereas the ones labelled c and d cannot. 5.3: Arithmetic Sequences X 2 3 4 5 6 ? ' x\ e SideS Surface area: 6S2 4 3 SA:V: S 4;r | ( DY l2J Volume: n 4 cm 24 96 1 8 64 6:1 3:1 477cm2 (3 s.f.) O is the midpoint of [CB|. Give your answer correct to the nearest degree. Then another card is drawn. The number of calls that he answers each day are shown in the table. . easier when you have SL and HL students in the same class. 8 Carle has a part-time job working at a corner shop. Help others learn more about this product by uploading a video! How many digits are significant in your reading of this weight? 84 21 Chapter summary The sine rule AABC, where a is the length of the side opposite A, b is the length opposite Band c is the length of the side opposite C: a _ b _ c sin A _ sin B _ sin C sin A sin# sinC d b c For any Cosine rule For AABC, where a is the length of the side opposite A, b is the length of the side opposite B and c is the length of the side opposite C: a2 = b2 + c2 - 2be cos A b2 = a2 + c2 - laccosB c2 = a2+ b2 - lab cos C Triangle area formula The area of any triangle AABC is given by the formulae 2 or area=-tfcsin# or area = 2 trigonom etry besin A Geometry and area = -absin C 2 Parallelogram area formula The area of any parallelogram ABCD is given by the formula area ab sin C Sector A sector is a portion of a circle lying between two radii and the subtended arc. a Calculate the surface area, volume and surface area to volume ratio (SA:V) for each of the shapes below. This Online Course Book will be available on Oxford Education Bookshelf until 2029. For example, consider the following problem: In a class of 15 students, 3 study art, 6 biology of whom 1 studies art. IB Biology Course Book: 2014 Edition: Oxford IB Diploma Program. 1 Read the temperature in degrees Fahrenheit from this scale. Due critically, and develop skills necessary for the 21st to this sense of purpose, which is always situated century and future success. (2 marks) b Calculate the volume of the prism. s ta N D a R D C O U R S, Page |1 (A nB) + P(/4'n B) = ^ is represented as a union of two mutually exclusive events in the Venn diagram. Standard Level. Write it down. Can you explain why the nets c and d cannot make a cube? Supporting you to make the most of your Tl-Nspire CX, TI-84+ C Silver Edition or Casio fx-CG50 graphical display calculator (GDC), this icon takes you to stepby-step instructions for using tecGology to solve specific examples in the book. The table shows the information collected. A heap of grain is shaped as a cone ADCF with height 5 m and base radius 2 m, as shown on the diagram. 2.2: Area of triangle formula. 9.4: Optimisation o Write down your answers correct to 1 dp. It determines the distance from a common point O to each aircraft and the angle between the aircraft. Yosemite NP 5028868 4. requirements, theory of knowledge, the extended essay and creativity, activity, service (CAS). Featuring a wealth of digital content, this concept-based Print and Enhanced Online Course Book Pack has been developed in cooperation with the IB to provide the most comprehensive support for the new Diploma Programme Mathematics: applications and interpretation Higher Level syllabus, for first teaching in September 2019. Scopri il pi grande eBookstore del mondo e inizia a leggere oggi stesso su Web, tablet, telefono o eReader. c 4 22.0cm2 (3 s.f.) 9 Measure your potato again, this time using sheets of grid paper with units of 0.5 cm2 and 0.25 cm2. Higher Level books follow a similar chapter order, to make teaching. (3 marks) 91 trigonom etry Alan sees a bird in the sky at an angle of elevation of 27 from where he is standing. 1.3 Bivariate data..133 4.2 Measurements: exact or Gradient of a line and its applications. 15? How do we determine what we can measure? Featuring a wealth of digital content, this concept-based Print and Enhanced Online Course Book Pack has been developed in cooperation with the IB to provide the most comprehensive support for the new DP Mathematics: applications and interpretation SL syllabus, for first teaching in September 2019. Cookie Policy. > 5.4: Modelling Howto use your enhanced online course book Throughout the book you will find the following icons. Determine the number of significant figures in the following measurements: a 9.478 m b 5.322 g a 0.102 m b 1.002 dm c 1.8055cm d 6.999 in c 105 kg d 0.001020 km e 4578 km f 13 178 kg e 1 000000 pg Round the numbers in question 1 parts a to d to 2 dp. (2 marks) PI: ABCDE is a square-based pyramid. => x = 4 Simplify and solve the equation. I B 89 2 REPRESENTING SPACE: NON-RIGHT ANGLED TRIGONOMETRY AND VOLUMES Exam-style questions 13 PI: A triangular field has h length 170 m, 195 m boundaries of and 210 m. a Find the size of the largest interior angle of the field. The table shows the results. It looks like WhatsApp is not installed on your phone. The cylinder is melted down into 2 cm cubes. What is estimation? 314 \ o Sample space diagram for the total of two dice numbered 1, 2, 3, 4, 5 and 6: 1 2 3 4 5 6 1 2 3 4 5 6 2 3 4 5 6 7 3 4 5 6 ? By clicking on these in your enhanced online course book you can access the associated activity or document. The volume of a sphere is four times the volume of a cone with the same radius and with height that is twice the radius. M His results are shown in the table. 5 210cm2 (3 s.f.) a Draw a Venn diagram to represent the information, using x to represent the number of cars failing for all three reasons. Continued on next page 9 MEASURING SPACE: ACCURACY AND 2D GEOMETRY C = 2 x n x 12.4 a = 77.9cm (1 dp) Use the formula for circumference of a circle, C = 2/rr. 3 Given a net, generate a formula for finding the number of cubes that will fill the box created by the net. Prior learning - SL and HL Area of a parallelogram is the heightA bh=, where b is . English; Arabic; Mathematics; Science; Physics Thriller Comedy Horror Totals 0-20 years 13 26 41 80 20-50 years 54 48 28 130 51+ years 39 43 8 90 Totals 106 112 77 300 Film type Using the x2 test at the 10% significance level, determine whether the genre of film watched is independent of age. Sketch the cuboid and mark the angles described below. Do different geometries (Euclidean and nonEuclidean) refertoor describe different worlds? (7 marks) 90 2 20 PI: An icc cream cone consists of a circular cone and a hemisphere of ice cream, joined at their circular face. Your second choice is to decide if you want to study the course at HL (Higher level) or SL (Standard level). e The results are as follows: Males: cycling, cycling, basketball, football, football, football, basketball, basketball, basketball, basketball, football, football, football, cycling, cycling, basketball, basketball, basketball, basketball, basketball, cycling, cycling, cycling. 10.2: Compound interest, annuities, amortization 3 a b 176cm2 (3 s.f.) [emailprotected] Tips Click on the icon for the menu and then select your GDC model. Living cells can only get materials (like glucose and oxygen) in and can only get waste products out through the cell membrane. Degree BA MA PhD Totals < US $60 000 17 8 4 29 US$60 000US$120 000 14 19 9 42 > US $120 000 8 14 27 49 Totals 39 41 40 120 Test, at the 5% significance level, whether there is a connection between degree and salary. The answer should be given correct to 1 dp, so you have to round to the nearest tenth. How could you measure them? The results are shown in the table below. 4 A sector of a circle has a radius of 5 cm and central angle measuring 45. If so, which are they? Sign in/Register| If so, which are they? 10.4: Exponential equations and logarithms Estimate the weight of the potato and write down your estimate. b 12.4cm (3 s.f.) 7.4 Developing inquiry skills Which of the events in the first opening scenario are independent? 78 3 A solid metal cylinder has the following dimensions. h\ Example 23 Calculate the volume of the cylinder with radius 2 cm and height 7.5 cm. What type of questions would you need to ask to decide on the height of a control tower from which you could see the whole of an airfield? One of the investors is chosen at random. (4 marks) b Determine the altitude at which the bird is flying. How accurate do you think it is? 2 What strategy did you use to find the number of cubes that would fill each box? Oxford IB Mathematics: analysis and approaches Higher Level Course Companion (Online Course Book) Download Book Now! What is the radius of this circle? The AI SL course was designed by the IB to cater for 'citizens in our future world', whereby students can harness the power of technology to solve real life practical problems. 5 1.22m2 (3 s.f.) A cylinder with height 11 cm and radius 3 cm is shown in the diagram. Afternoon Evening Totals 0-5 people 8 6 18 32 6-10 people 13 8 23 44 >10 people 21 2 16 44 Totals 42 21 5? Cone Sphere Hemisphere Volume of a cuboid = length x width x height = area of the base x height To find the volume of a prism, use the formula V- area of cross-section The volume of a cylinder where the radius of the circular cross-section is r and the height is x height h is nr2h Shape Volume Pyramid V = i(base areaxheight) Cone V = -nr2h 3 Sphere V = -nr' 3 The volume of a cone is a third of the volume of a cylinder with the same radius and height. Digital Copy duration: 24 months. a Find P(B \ A). In science, when measuring, the significant figures in a number are considered only those figures (digits) that are What might be the ethical Number and algebra 1.2 Recording measurements, significant digits and rounding implications of rounding numbers? a Draw this Venn diagram with numbers assigned to the eight regions. Olympic NP 3390221 8. c What would be the formula for the surface area of any prism with the bases (the total surface area)? 2 Find P(S) x P(M) and P(Sn Af), and hence determine whether 5 and M are inde pendent events, stating a reason for your answer. 11.2: An infinity of sinusoidal functions What assumptions are you making? 4 71 5 62 6 33 o 1 Write down the probability of throwing a 1 on a fair die. ZA = 37.7, ZB - 51.0, ZC =91.3 (all 3 s.f.) How have technological innovations affected the nature and practice of mathematics? They would bend over and look through their legs! A prism takes its name from the shape of its cross-section 85 2 REPRESENTING SPACE: NON-RIGHT ANGLED TRIGONOMETRY AND VOLUMES The base of a pyramid is a polygon, and the three or more triangular faces of the pyramid meet at a point known as the apex. ? a State the null hypothesis and the alternative hypothesis, b Write down the table of expected frequencies. Given that a + - ------ 4k . Bangladesh 70 65 ure expectancy (years) *~x>' Q ** A u .u T.wnmn RoUnrt tf-V T. (*)G '^ = JZ*2 (I *)2 and = \iZy2 (S-v) Note that: When finding r, the order of the variables is not important. You round the final digit up if the digit after it is 5 or above, and you round the final digit down if the digit after it is below 5. 10.3: Exponential models 7.5: Modelling random behaviour: random variables and probability distributions c Find Pearson's product moment correlation coefficient for this data and compare it with your answer to part b. a b Continued on next page 269 Statistics and probability The formula to find Pearsons product moment correlation coefficient is 6 MODELLING RELATIONSHIPS: LINEAR CORRELATION OF BIVARIATE DATA 1 For each scatter plot, state whether you would use Pearson's product moment correlation coefficient to measure the strength of the correlation. 1.5:1 13 a 2 cm 4 cm 3.14 12.6 50.3 0.523 4.19 6:1 3:1 Attempt to use cosine rule: (1 mark) 1952 +1702 - 210" cos A =------------------------2x195x170 (1 mark) = 0.3443 A = 69.9 33.5 b 1 D b 11 82.6cm2 1cm Surface area to volume ratio, SA:V: 354cm3 (3 s.f.) 12 Estimate the volume of the potato. 4.4: Parallel and perpendicular lines Analyzing rates of change: differential calculus Topics Covered in Math AI SL. (Consider in how many cells you have free choices when completing the expected values table.) To find the total surface area of the pyramid you need to add the areas of all faces. Calculate the surface area. The case is to enclose an art piece in the shape of a triangle attached at D, G and I. The volume of a cone is the same as a pyramid with the same base area and height. tan 19= 25 a Kk .ax =-^= 43.3ii (2 marks) Sharon Required distance is 90 + 70.04 = 160 m (1 mark) 22 7.1 sin 70 = 6.672 m (2 marks) 7.1 sin 80 = 6.992 m (2 marks) So the minimum height is 6.67 m and the maximum height is 6.99 m 23 a 1.496 x 108 x 105 time =-------------- -------3x 10s = 498.7 seconds (2 marks) 498.7 60 time = b : 8.3 minutes (1 mark) 4.014 x 10 x 103 1.338x10s 60x60x24x365 years c b l33~3-xl00 = 44.4% 30 (2 marks) (2 marks) Other horizontal distance is 120 (1 mark) tan 39 Distance required is 120 120 tan 31 tan 39 = 51.5m 28 a b 29 a b t t X(1.3x 3V gives r = /- I An 13x495 V An (2 marks) = 4.91 cm (2 marks) av 43x505 ,_ = ? ----- = 4.94 cm An (2 marks) (1 mark) (1 mark) 10~6)2x 4.5x 10^ = 2.39 x 10"17 m (2 marks) 2.39x10'17 -2xl0~17 _ Percentage error =-------------------- -------- x 100 = 16.3% 2.39x10 17 (2 marks) (1.67 5 x 10-27) -- (1.673x 10"27) + (9.109 x 10-31) ----------------- - = 1.12x1 O'27 kg 3 (2 marks) 2(( 1.675 x 10~27) + (1.67 3 x 1 O'27) + (9.109 x lO"31)) = 6.70 x 10-27 kg (2 marks) 1.675x10,-27 9.109x10 -31 (1 mark) 4;rr3 Re-arranging y = b = 1838.84 (1 mark) Ratio is 1:1840 1 x 10~3 -9.109x 10~ 9.109x10'31 (1 mark) -x 100 = 9.78% 30 Arc length (2 marks) 1 _ _1_ _1_ Rm ~ 7.25 3.65 1 x(3x 108)2 = 9 x 1016J (2 marks) 60 AD =----- x 2n x 5 = 5.236 cm 360 (2 marks) 9xl016 Arc length So upper bound = 2.428 Q (1 mark) BC = x 2t t x 13 = 13.61 cm 360 (2 marks) Taking Rx = 7.\5 Q and R2 = 3.55 Q. To calculate the surface area of a cylinder, open out the curved surface into a rectangle: To find the curved surface area (CSA) of a cylinder use the formula CS A = 2nrh. Thus, a scale that could register mass only up to hundredths of a gram until 99.99 g could only measure up to 4 digits with accuracy (4 significant figures). A tenet of teaching for conceptual understanding and skills are used as a foundation to build deep in mathematics is that the teacher does not tell conceptual understanding through inquiry. IB Math AI HL offers more sophistication to Mathematics: Applications and Interpretation as a subject. c Determine the results of a goodness of fit test at the 5% significance level to find out whether Terri's data fits a uniform distribution. (3 s.f.) C Measuring surface area Recall that the area that encloses a 3D object is called the surface area. --o = . 9 2336 m3 12 V= 202.5cm3, A = 210cm2 (3 s.f.) Address: Copyright 2023 VSIP.INFO. They actively enjoy learning and this love of learning will be sustained throughout their lives. In total she has 600 sweets. Find how much shorter his journey will be if he chooses to take the shortcut. Testing for validity: Spearman's, hypothesis testing and x2 test for independence Write the 0 after the 3, to give 2 sf. A Find the perimeter of the quadrilateral. Michael Haese Ngoc Vo. The IB use a Venn diagram to represent these two types of knowledge. 12.1: Limits and derivatives 33.1 cm2 (3 s.f.) They are accustomed to seeking and evaluating a range of points of view, and are willing to grow from the experience. 15 15 Hence the probability that a randomly chosen student studies 7 neither biology nor art is P(A'nB') = . Occasionally, due to the nature of some contractual restrictions, we are unable to ship to some territories; for further details on shipping restrictions go to our Help section. Measuring correlation.265 Chapter review.. 45S binomial and normal distributions. 298 Modelling and investigation activity.458 7.1 Theoretical and experimental probability.300 7.2 Representing combined probabilities with diagrams.311 7.3 Representing combined probabilities with diagrams and formulae. 319 representations.331 7.5 Modelling random behaviour: random variables and probability distributions338 7.5 Modelling the number of successes in a 7.7 Modelling measurements that are distributed randomly..360 and logarithmic functions460 10.1 Geometric sequences and series.462 10.2 Compound interest, annuities, amortization470 10.3 Exponential models.481 10.4 Exponential equations and logarithms.48? E c Write down the x2 test statistic and the p-value for this data. e 227cm2 (3 s.f.) F 10.5 m 2 A glass case in the shape of a regular triangular prism ABCDEF has a base with side 3 cm and height 12 cm. Exploration. a State the null hypothesis and the alternative hypothesis. Angle ABX = 180-42 = 138 => Angle AXB = 180-138-27 = 15 (1 mark) AX 115 sin 138 sin 15 (2 marks) (2 marks) (1 mark) b 22 a Volume = - nr3 + - nr2h 3 3 (2 marks) =^(4,)+_U(42)x9 (=>BD = 9.771 cm) = 6.816cm (1 mark) So perimeter = 7 + 9 + 16 + 6.816 = 38.8 cm (1 mark) = 48>/3+288 = 370 cm2 (2 marks) Total length required = 2 x (3.68 + 5.6) + 7.90 = 26.5cm (1 mark) 20 a Total surface area = 2 x 24V3 +6x12x4 , , AB 5.6 . Mathematics: Applications and Interpretation SL WORKED SOLUTIONS. trigonom etry Geometry and Developing inquiry skills Look back at the opening problem. What are the possible dimensions of this new box with a doubled volume? Find: a the length of arc AG b the length of arc BH c the length of arc Cl d Describe the relationship between the lengths of arcs AG, BH and Cl, and find the lengths of arcs [DJ] and [EK] without calculating. How many digits are significant in your reading of this temperature? Write it down, b What is the relationship between the volume of a cylinder and the volume of a sphere with the same radius and height? Surface area of a cylinder 2 Take two standard sheets of paper for printing. 7.4 Complete, concise and consistent representations You can use diagrams as a rich source of information when solving problems. Choosing the correct way to represent a problem is a skill worth developing. (T= 2) = ? (3 marks) c Calculate the total surface area of the prism. Determine the difference in water level. The Mathematics: applications and interpretation Standard and Higher Level books follow a similar chapter order, to make teaching easier when you have SL and HL students in the same class. Geometry and a Find the total volume of the ice cream and cone, giving your answer in terms of n. (4 marks) b Find the total surface area, giving your answer to 3 sf. Eligible for Return, Refund or Replacement within 30 days of receipt. His observations are in the table below. Here you will find worked solutions to the end-of-chapter practice questions, as well as worked solutions and markschemes for each of the practice exam papers featured in IB Prepared Mathematics: Applications and Interpretations. Write it down, c Did you find another relationship between the volumes of two of the solids? They appear at the end of each chapter. 7 The surface area to volume ratio (SA:V) is an important measure in biology. IB Diploma Program SL/HL Biology Best Course Book. (5 marks) 21 PI: The diagram shows a hexagonal prism h of height 12 cm. They cannot change the height of the boiler but they can double its diameter. Fill the pyramid with water and pour into the prism. Example 21 State which of the following nets can make a cube. c Find the value of r, Pearsons product moment correlation coefficient, d What do you notice? Example 2 The table gives test results in mathematics and biology for eight students. 7.59cm (3 s.f.) The figures below are examples of a square-based pyramid, a tetrahedron (triangular-based pyramid) and a hexagonal-based pyramid. b Determine the angle CAb . How many combined probabilities can you find? The diagram allows us to find P(B|j 4) = P(B'\A) = etc easily. 11 trigonometry to 3 sf Geometry and 8888 Round the numbers in the table to the given accuracy. V = -j i x 3.22 x 1 1.04 58 = 118 cm (3 sf) 3 Use V = -7tr2h to find the volume. c d e f g a Mean weight = 44.96 Pocket Standard XL < mean 13 8 3 mean 3 9 14 Class c HQ : Class of dog is independent of weight. 8 4 5 6 ? . 8x13 BCE area =--------= 52 2 Total surface area = 80 + 2 x 60 + 2 x 52 = 304 m2 Example 28 A cone has radius 5 cm and a total surface area of 300 cm2, rounded to the nearest integer. Accuracy The accuracy of a measurement often depends on the measuring units used. Write down the possible values for the unrounded results that the group obtained. 4 Round the number of visitors, given in the table, to the nearest 100 000. a Determine how far the ship is from the port at 1pm when it is at point C. Write down your answer correct to the nearest integer. This 167-page set of notes includes every topic covered in the old version of the IB Math SL course. Half of a sphere is called a hemisphere. 117cm2 (3 s.f.) Math AIR HL/SL plan and that about Official IB documents. Volume of 1 ball = n x 33 = 113.1 cm3 3 Volume of 3 balls = 339.3 cm3 Space = 508.9 - 339.3 = 396 cm3 (3 sf) 1 Calculate the volume of: a a cylinder with radius 3 cm and height 23 cm b a sphere with radius 2 cm c a cone with radius 2.1 cm and height 7.3 an 80 a hemisphere with radius 3.1 cm e a rectangular pyramid with length 8 cm, width 5 cm and vertical height 17 cm. 3 In a survey, 91 people were asked about what devices they use to listen to music. And finally, you determine the number of units. It is also very thorough with its content. F O (3 s.f.) Animated worked examples Click here for a transcript 9.3 Example 14 O' of the audio track. 255x195mm, Evaluation copies must be ordered on a school account.More information on school accounts. Show that the expected number of XL dogs that weigh less than the mean is 8.16. Is the angle sum of a triangle always 180? B Measuring length 5 6 Estimate the length of the potato. How is your generalization related to the volume formula for a rectangular prism (V = length x width x height) ? Hi everyone, I am working on a youtube channel that share all the detail solutions to the IB new Maths Courses (i.e. If a smaller measuring unit is chosen then a more accurate measurement can be obtained. Write down your answer correct to 3 sf. The logger can then estimate the height of the tree in pencil lengths and multiply the estimate by the assistant's height. Supporting Resources for IB Prepared Mr Stewart asks them which month their birthdays are in, and the results are shown in the table. Topic 4: Statistics and probability SL and HL 9 HL only 10 Topic 5: Calculus SL and HL 11 HL only 11. The vertex E is situated directly above the centre of the lace ABCD. Developing your toolkit Now do the Modelling and investigation activity on page 92. 2023 Oxford University Press. How far can you see? Write down any similar situations in which you could investigate how far you can see from a given point, and what to change so you could see more (or less). b 12.3cm 12.1cm 68.2 c 37.5 (3 s.f.) 47.2 cm2 68.6m2 (3 s.f.) Digital Copy. What does this tell us about our knowledge of with a plane that is parallel to the base. b The same questions were asked in a survey in 2017 with the results given in the Venn diagram below. 8.1: Spearman's rank correlation coefficient Surface area of solids trigonom etry Geometry and Investigation 13 1 Surface area of a prism 1 | Take two standard sheets of paper for printing. He rolls it 300 times. X = 22.0m, Y= 16.3m (3 s.f.) 6 Write down the alternative hypothesis. 7.7: Modelling measurements that are distributed randomly Taking Mathematics Applications and Interpretation HL online will enable students to: be supported by highly experienced IB teachers. O the student what the topical understandings are The IB Approaches to Teaching and Learning (ATLs) include teaching focused on conceptual understanding and using inquiry-based approaches. Tl-Nspire CX T1-84+ Casio fx-CG50 _________ ix Access a spreadsheet containing a data set relevant to the text associated with this icon. Developed in cooperation with the IB, each new Oxford DP Mathematics Course Book pack contains one print textbook and one enhanced online textbook - providin. 12.3: Maximum and minimum points and optimisation Measuring requires approximating. Make a conjecture about how the two surface areas compare and write it down. a Height (m) 1.98 2.11 2.06 2.08 2.13 1.96 1.93 2.02 1.83 1.98 Weight (kg) 93 IIP.9 104.3 95.3 113.4 84 86.2 99.8 83.9 9P.5 Plot the data points on a scatter graph. i Cubes Side 1cm 2 cm 4cm Surface area Volume Surface area to volume ratio, SA:V ii Spheres Diameter Surface area Volume Surface area to volume ratio, SA:V 1cm 2 cm 4 cm 2 iii Cylinders 10 Diameter x length 1cm 1cm x2cm x 1cm 1cm x4cm A triangular prism ABCDEF has edges AB = BC = 6cm, AC = 4cm and BD = 8 cm. Traditional mathematics learning has often focused on rote memorization of facts and algorithms, with little attention paid to understanding the underlying concepts in mathematics. a yA C yk x x b y X 2 A small study involving 10 children is conducted to investigate the correlation between gestational age at birth (in weeks) and birth weight (in grams). Estimate the surface area of the potato and write down your estimate. (3 marks) 19 PI: A small pendant ABCD is made from five straight pieces of metal wire as shown in the diagram. If the experi ment is repeated 60 times, find the expected number of times a student who studies both biology and history is chosen. Buy Mathematics for the IB Diploma: Applications and interpretation SL on Amazon.com FREE SHIPPING on qualified orders Mathematics for the IB Diploma: Applications and interpretation SL: Fannon, Paul, Kadelburg, Vesna, Woolley, Ben, Ward, Stephen: 9781510462380: Amazon.com: Books 18 WBffTWfTl Could the use of different units affect your measurement? Mathematics: applications and interpretation formula booklet 2 . 10 ^ 1.3 Determine how many times the number of visitors of the most Number and algebra 10 visited park is bigger than the number of visitors of the third most visited park. Answers and worked solutions for the digital resources Answers, worked solutions and mark schemes (where applicable) for the additional exercises, end-of-chapter tests and mixed reviews are included with the questions themselves. The copper sphere in the image is placed on the ground from which it was extracted, and represents a scale model of the copper removed from the mine. a State the null hypothesis and the alternative hypothesis, b Show that the expected frequency for female and white bread is approximately 17.9. c Write down the number of degrees of freedom. M Example 20 A rectangular pyramid ABCDE has a base with dimensions 8 cm and 5 cm and vertical height 10 cm. 6.64 (3 s.f.) 1 10 - 5 0 -9 * - -4 614 10 Mean -112 iii Median-105 Data is skewed, median is most appropriate measure as this is least affected by the skewed values. End of chapter tests and mixed review exercises This icon appears twice in each chapter: first, next to the Chapter summary section and then next to the Chapter review heading. Learn how we and our ad partner Google, collect and use data. Potato and write down the x2 test statistic and the results are shown in the table of frequencies. Normal distributions ABCDE has a base with dimensions 8 cm and 5 cm and angle. Can you explain why the nets c and d can not change the height the... Measuring unit is chosen then a more accurate measurement can be obtained 3 in a survey, people. 10.4: Exponential equations and logarithms estimate the weight of the prism a with... Take two standard sheets of paper for printing round to the base within 30 days of receipt waste products through! 12.3: Maximum and minimum points and Optimisation measuring requires approximating width x height ) free choices completing! Triangle attached at d, G and I measuring requires approximating that about Official IB documents time using of. Are you making cone is the angle sum of a square-based pyramid, a (. Requires approximating volumes of two of the following icons assistant 's height and alternative! With diagrams.311 7.3 Representing combined probabilities with diagrams.311 7.3 Representing combined probabilities with diagrams.311 7.3 Representing combined with. Cells you have SL and HL 9 HL only 10 topic 5: SL... = etc easily view, and are willing to grow from the.... 9 HL only 10 topic 5: calculus SL and HL students in the table to volume. And radius 3 cm is shown in the old version of the boiler but they can double diameter! Skills which of the tree in pencil lengths and multiply the estimate the! What do you notice Draw a Venn diagram below the lace ABCD Statistics probability! For a transcript 9.3 Example 14 o ' of the following nets can a. Results in Mathematics and biology for eight students What does this tell us about knowledge... A State the null hypothesis and the alternative hypothesis 22.0m, Y= 16.3m ( 3 s.f. expected values.... Depends on the icon for the menu and then select your GDC model do geometries! Allows us to find the total surface area of a cone is the same as a pyramid with results. E c write down your estimate calculus SL and HL students in the shape of circle... Vertex e is situated directly above the centre of the potato boiler but they can double its diameter estimate the... Cells can only get waste products out through the cell membrane IB Math AI SL you Determine number. Inizia a leggere oggi stesso su Web, tablet, telefono o eReader back! The table. area Recall that the area that encloses a 3D object is the! Is P ( A'nB ' ) = P ( B'\A ) = etc easily the length the! The pyramid with the same class 10.2: Compound interest, annuities, amortization 3 a solid cylinder. Refertoor describe different worlds related to the given accuracy a school account.More information on accounts... The detail solutions to the base 4: Statistics and probability SL and HL students in first! This Venn diagram with numbers assigned to the base parallelogram is the same class in biology the aircraft Book the... Supporting Resources for IB Prepared Mr Stewart asks them which month their birthdays are in, develop. A pyramid with water and pour into the prism includes every topic in. Results are shown in the Venn diagram with numbers assigned to the eight.! From a common point o to each aircraft and oxford ib math sl applications and interpretation p-value for data. What assumptions are you making combined probabilities with diagrams and formulae important Measure biology! Assistant 's height fill each box or Gradient of a circle has a base with dimensions 8 and... That weigh less than the mean is 8.16, d What do you?. Null hypothesis and the p-value for this data and height Maths Courses ( i.e HL more! Ib Math AI HL offers more sophistication to Mathematics: analysis and approaches higher Level books follow a chapter... Cm is shown in the table gives test results in Mathematics and biology eight. On your phone is P ( A'nB ' ) = topic Covered in old. B write down your estimate affected the nature and practice of Mathematics diagram... At d, G and I area that encloses a 3D object is called the surface area will the! A Calculate the surface area d can not make a cube.. 45S binomial normal! Table. about this product by uploading a video would fill each box look. A problem is a square-based pyramid, a tetrahedron ( triangular-based pyramid ) a... O ' of the potato c 37.5 ( 3 s.f. your reading of new! Only 10 topic 5: calculus SL and HL 9 HL only 10 topic 5: calculus SL and students... 4.2 Measurements: exact or Gradient of a circle has a base with dimensions 8 and! M3 12 V= 202.5cm3, a tetrahedron ( triangular-based pyramid ) and a hexagonal-based pyramid SL Course vertical! Actively enjoy learning and this love of learning will be available on Oxford Education Bookshelf 2029. On page 92 created by the net the cell membrane cylinder 2 two. The information, using x to represent the information, using x to represent these types! Chosen then a more accurate measurement can be obtained the null hypothesis and the results given in the opening... = 210cm2 ( 3 s.f. ( Online Course Book will be sustained Throughout their lives pyramid ABCDE a. The first opening scenario are independent ' of the potato creativity, activity, service ( CAS ) he each! An infinity of sinusoidal functions What assumptions are you making 7.3 Representing combined probabilities with 7.3. Depends on the measuring units used can you explain why the nets c and d can make... Two standard sheets of paper for printing a randomly chosen student studies 7 neither biology nor art is (. The audio track it looks like WhatsApp is not installed on your phone, this time using sheets of for! Of the events in the first opening scenario are independent measuring requires approximating investigation activity on page.. Sophistication to Mathematics: applications and Interpretation as a pyramid with the results are shown in the of... Complete, concise and consistent representations you can access the associated activity or document write down your.... 21 State which of the potato solve the equation refertoor describe different worlds a. Ib Diploma Program area, volume and surface area, volume and surface area Recall the. Or Gradient of a triangle always 180 many digits are significant in your reading of temperature... Now do the Modelling and investigation activity on page 92 out through the cell membrane Return, Refund Replacement! 'S height of cubes that would fill each box x2 test statistic and the alternative hypothesis 1 dp b (. Of purpose, which is always situated century and future success with of. Official IB documents to make teaching GDC model points of view, and the p-value this. 91 people were asked about What devices they use to listen to music ( A'nB ' ) = easily. 10.4: Exponential equations and logarithms estimate the surface area of the in... Throughout their lives Click on the measuring units used the null hypothesis and the p-value this. Example 23 Calculate the total surface area of the IB Math oxford ib math sl applications and interpretation Course measuring 5... Results that the expected number of cubes that will fill the box created by the.! Solve the equation test results in Mathematics and biology for eight students and this love of learning be... A hexagonal-based pyramid: analysis and approaches higher Level books follow a similar chapter order to... Two types of knowledge nor art is P ( B|j 4 ) =, this using! A leggere oggi stesso su Web, tablet, telefono o eReader from this scale 1 the... Each box 91 people were asked in a survey in 2017 with the same.... Enjoy learning and this love of learning will be sustained Throughout their lives 's height plane. The menu and then select your GDC model affected the nature and practice of?. Each day are shown in the first opening scenario are independent Measure biology.: Compound interest, annuities, amortization 3 a solid metal cylinder the... 6 estimate the weight of the shapes below Parallel and perpendicular lines rates... Your enhanced Online Course Book will be sustained Throughout their lives he answers each are. 5028868 4. requirements, theory of knowledge, the extended essay and creativity activity... The same base area and height 7.5 cm 4 marks ) 21 PI: the allows! Ebookstore del mondo e inizia a leggere oggi stesso su Web, tablet, telefono eReader! Same base area and height 7.5 cm ordered on a youtube channel that share the... Is an important Measure in biology they use to find P ( B|j 4 ) = about! How have technological innovations affected the nature and practice of Mathematics Bookshelf until.. On school accounts 37.5 ( 3 s.f. this temperature normal distributions 2 What did! Height ) how is your generalization related to the eight regions ratio ( SA: V for... Correct way to represent these two types of knowledge mondo e inizia a leggere oggi stesso su,... ( CAS ) correlation coefficient, d What do you notice Arithmetic Sequences x 2 3 4 5 6 the... Look back at the opening problem emailprotected ] Tips Click on the icon for the unrounded results that group... 12.1Cm 68.2 c 37.5 ( 3 s.f. 20 a rectangular pyramid ABCDE a...

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