The new syllabus provides suggestions of conceptual understandings for teachers to use when designing unit plans and overall, the goal is to foster more depth, as opposed The DP mathematics courses identify twelve possible fundamental concepts which relate to the five mathematical topic areas, and that teachers can use to develop connections across the mathematics and wider curriculum: to breadth, of understanding of mathematics. The edges of each hexagonal face have length 4 cm. ${cardName} unavailable for quantities greater than ${maxQuantity}. The IB use a Venn diagram to represent these two types of knowledge. test or exam, this revision guide is designed to make the topics of IB Math: Applications and Interpretation SL both comprehensible and easy to grasp. The critical value for this test is 12.592. d State the conclusion for the test and give a reason for your answer. 7 Given that the critical value at the 5% significance level for this test is (f f)2 11.07, use the formula for the x2 test, XL, = X r ' .to find out Jc Statistics and probability whether Jiangs results could be taken from a uniform distribution. 8 4 5 6 ? a Draw this Venn diagram with numbers assigned to the eight regions. Modelling relationships with functions: power functions Students who are not strong at math . Remember to write down the null and alternative hypotheses. Howto use your enhanced online course book Throughout the book you will find the following icons. Write the 0 after the 3, to give 2 sf. \ The volume of a cylinder where the radius of the circular cross-section is r and the height is h is nr2h. List prices may not necessarily reflect the product's prevailing market price. Hubert wanted to find out whether the number of people walking their dog was related to the time of day. The critical value is 9.488. e Comment on your result for a 5% significance level. Where applicable, each worked solution is modelled on the relevant worked example in the textbook. Not all nets can be folded into a 3D figure, although they may have the correct number of faces. Is 95.220 grams the same as 95.22 grams? a b c 3 a b 4 1.12cm2 (3 s.f.) Then _ Ah _ 162 x20sin55.6 3 3 = 1410 cm3. 9 Write down the number of degrees of freedom for this test. How would you go about estimating? 6 A group of 50 investors own properties in north European cities. If you stood somewhere higher or lower, how would that affect how much of the Earth you can see? c Make a conjecture about howto find the surface area of any cylinder, with radius rand height h, with the bases. > For example, v 1 7 - x- = . a Determine the direct distance of Alan to the bird. In case you don't know, to study for the IB diploma you will take 6 subjects and 3 of them have to . b Determine the angle CAb . 20 How do we describe the properties of an object? 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. 173 (3 s.f.) 6.1: Measuring correlation Developing inquiry skills Write down any similar inquiry questions that might be useful if you were asked to find how far you could see from a local landmark, or the top of the tallest building, in your city or country. For example, when giving a number to 2 decimal places, your answer would have exactly two digits after the decimal point. (Consider in how many cells you have free choices when completing the expected values table.) How do we determine what we can measure? ? Any zeros between two significant digits are significant. X 2 3 4 5 6 ? ?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. Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday 12 14 18 1? 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. 11 A regular dodecahedron has edges of 2 cm. a 5.64cm (3 s.f.) What does a value of r close to 1 or -1 tell you about the correlation? View basket trigonometry Geometry and Measurements help us compare objects and understand how they relate to each other. b The same questions were asked in a survey in 2017 with the results given in the Venn diagram below. The results for Terri's 10 bags are: Colour Frequency Yellow 104 Orange 132 Red The critical value for this test is 9.488. d State the conclusion for the test and give a reason for your answer. a Find the number of consumers surveyed who had neither a smartphone nor a tablet. From the Venn diagram read off the information needed to calculate the answer. 11 cm the angle between [DC] and the base DEF b the length of [GI] c the length of [DG]. Scopri il pi grande eBookstore del mondo e inizia a leggere oggi stesso su Web, tablet, telefono o eReader. 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. b 12.4cm (3 s.f.) How far can you see? You write X follows a normal distribution with parameters p and O'2 or X-N(p, a2). 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 4.3 1.4 Speaking scientifically1? 6 Shown in the diagram are six concentric circles with centre O, where OA = 10 cm, OB = 20 cm, OC = 30 cm, OD = 40 cm, OE = 50 cm and OF = 60 cm. 5 A circular sector has radius 4 cm and a corresponding arc length of 1.396 cm rounded to the nearest thousandth of a centimetre. 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). Click here for help with this skills check Find the circumference of a circle with radius r = 5.3cm. Course Companion, Google non verifica le recensioni, ma controlla e rimuove i contenuti falsi quando vengono identificati, Mathematics: Applications and Interpretation. 62.4cm2 (3 s.f.) 12 ffiTiffffiFfffl What is the purpose of the goodness of fit test? < 21C 21C-30C >30C Totals 60 bottles 8 26 9 43 Totals 32 80 38 150 Tempera ture Test, at the 1% significance level, whether there is a connection between temperature and the number of bottles of water sold. M b Write down the number of degrees of freedom. D and O are the centres of the circular faces of the cylinder. (4 marks) b Determine the altitude at which the bird is flying. H is the midpoint of [BC], and G is the midpoint of [AB]. Example 2 The table gives test results in mathematics and biology for eight students. for each topic, and suggests some concept specific Teaching for conceptual understanding is a framework for learning mathematics that frames the factual content and skills; lower order thinking, with disciplinary and non-disciplinary concepts and statements of conceptual understanding promoting higher order thinking. 1.3 Bivariate data..133 4.2 Measurements: exact or Gradient of a line and its applications. 15? Calculate the mass of the ornament. Yellowstone NP 4257177 7. Ksika Oxford IB Diploma Programme: IB Mathematics: applications and interpretation autorstwa Opracowanie zbiorowe, dostpna w Sklepie EMPIK.COM w cenie 417,40 z. Mathematics: Applications and Interpretation SL Similar to? 98 Purple 129 Green 13? 4 Where did numbers come from? I B (2 marks) e Find the total surface area of the pyramid. The teacher notes on the ebook provide additional support for teachers new to this approach. 3.2: Sampling techniques IfX-B(n,p) then E(X) = np and Var(X) = np{ 1 -p). Pockets have h < 42 cm high, Standards have 42 < h < 50 and XLs have 50 < h < 58. requirements, theory of knowledge, the extended essay and creativity, activity, service (CAS). Notice that the simple probability P(B) = P(A n B) + ? The probability that a randomly selected student studies exactly one of the subjects is 12 + 6 _ 18 _ 9 26 26 13 1 A survey of 117 consumers found that 81 had a tablet computer, 70 had a smartphone and 29 had both a smartphone and a tablet computer. The volume of the cone is also the same as a pyramid with the same base area and height. Direct proof What is the value of a? If the experi ment is repeated 60 times, find the expected number of times a student who studies both biology and history is chosen. 2 Find the area of a circle with radius 6.5 cm. 7.59cm (3 s.f.) 12.3: Maximum and minimum points and optimisation x = 20, so angles are 40, 60, 80. The critical value for this test is 11.345. 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. c Determine the results of a goodness of fit test at the 10% significance level to find out whether the data fits a uniform distribution. Investigation 4 The numbers of visitors to the 10 most popular national parks in the United States in 2016 are shown in the table. How many combined probabilities can you find? Privacy Policy | 89km b 10.5cm (3 s.f.) 5.4: Modelling IB learners strive to be: Inquirers They develop their natural curiosity. Solve My Task Do math equations Example 1 For each of the following, determine the number of significant figures. 7.1: Theoretical and experimental probability, 7.2: Representing combined probabilities with diagrams Surface area of a cylinder 2 Take two standard sheets of paper for printing. 6 a Chapter review b (1 mark) Area = x 170 x 195 x sin 69.9 2 (2 marks) 1.5:1 = 15600 m2 Diameter D x length L 1cm x 1cm 1cm x 2 cm 1 cm x 4 cm 14 AC2 = 5602 + 12002 - 2 x 560 x 1200 x cosl 10 Surface area: 2/rl I +t i DL Volume:/r[ | L UJ 4.21 2.85 14.1 (1 mark) (2 marks) AC = 1487.7 m (1 mark) Distance required is 560 +1200-1487.7 = 272 m 1.52 0.28 3.14 (2 marks) 15 Area horse can reach Surface area to volume 17 2D + 4L l ratio, SA:V=---------- :1 6:1 5:1 4.5:1 DL = x/rx852(=4410m2) 360 v ' (2 marks) Area of triangle Base side (/?) The results are shown in the table. sl82 + 52 to a 10 EBO = tan'1 &9 = 64.7 (3 sf) v 2 ) b BfiC = 2 BfeO The line [EO] bisects BEC. Will the two surface areas be different or the same? Give your answer correct to 1 decimal place. Example 21 State which of the following nets can make a cube. Traditional mathematics learning has often focused on rote memorization of facts and algorithms, with little attention paid to understanding the underlying concepts in mathematics. Re-calculate the probabilities that you found in part a. Additional exercises The icon by the last exercise at the end of each section of a chapter takes you to additional exercises for more practice, with questions at the same difficulty levels as those in the book. In a sequence of /7 independent trials of an experiment in which there are exactly two outcomes success and failure with constant probabilities P(success) = p and P(failure) = 1 p, if A' denotes the discrete random variable equal to the number of successes in n trials, then the probability distribution function of A' is P(X=x) = Cp*(l -p)n~x,xe{0, 1, 2, n) These facts are summarized in words as X is distributed binomially with parameters n and p and in symbols as X- B (/7, p). 7.5: Modelling random behaviour: random variables and probability distributions 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. a Calculate angle BAC. The smaller the measuring unit used, the greater the accuracy. How have technological innovations affected the nature and practice of mathematics? B Measuring length 5 6 Estimate the length of the potato. b Make a conjecture about howto find the surface area of any pyramid without the base and write it down. It has 3 sf. The critical value is 7.815. e Comment on your result. Oakland University . The critical value is 13.277. d Comment on your result. on horizontal /------------------------------------------------- Three squares Approaches to learning: Research, Critical thinking Exploration criteria: Personal engagement (C), Use of mathematics (E) Modelling and investigation activity IB topic: Proof, Geometry, Trigonometry v_______ ________ /---------------------------------------------------------------------------------------- \ The problem Three identical squares with side length 1 are adjacent to one another. a b c d e HQ : Favourite music genre is independent of gender H. : Favourite music genre is not independent of gender E(female liking pop) = P(female) x 42 40 P(likes pop) x total = x x80 = 21 80 80 v = (2 - 1 )x(4 - 1) = 3 x2 ~ 1-622 and p = 0.654 0.654 > 0.01 or 1.622 < 1 i .345 and so you accept the null hypothesis: favourite music genre is independent of gender. Your second choice is to decide if you want to study the course at HL (Higher level) or SL (Standard level). 10 11 Compare yourthree measurements. 10.3: Exponential models (3 marks) 91 trigonom etry Alan sees a bird in the sky at an angle of elevation of 27 from where he is standing. Facts conceptual understandings relevant to the topic content. His results are shown in the table. Analyzing rates of change: differential calculus Glacier NP 1 Recreational Visits \ 2946681 Which park had the most visitors? 11 What is your conclusion from this test? How accurate are these figures likely to be? Let A be the event the first card drawn is the letter A. 611 ANSWERS Exercise 21 2 72.9 km 1 2 a 154 cm2 (3 S.f.) a State the null hypothesis and the alternative hypothesis, b Write down the number of degrees of freedom. 9 2336 m3 12 V= 202.5cm3, A = 210cm2 (3 s.f.) Ronald F. Clayton 5 B.I.IJSBB1HI What do the significant figures tell you about the values read from the instrument? 6 Use Kristian's suggestion as we have two sides and one angle, x = 22.8m or 42.7m. 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. The code must be linked to an email address, creating a user account. However, it's better to have the shape of a cylinder or a prism rather than cube or sphere, and to grow in length rather than in width. (2 marks) (1 mark) = x 6.9 x 5.7 x sin 63.5 (1 mark) (1 mark) .. 1 mark Let Y be the mid-point of BC. Try 36 x 14 Is it possible to know things about which we can have no experience, such as infinity? The parameters of the normal distribution are p and o2. have the independence of spirit to explore new roles, The IB learner profile ideas, and strategies. Great Smoky Mountains NP 2. a Find the surface area of the pyramid without the base and write it down. a 100m2 5 2.79 cm2 c 111 cm2 (3 s.f.) Mathematics: applications and interpretation formula booklet 2 . How would you relate the value of rto the strength of the correlation? Mathematics for the IB Diploma: Applications and interpretation SL Paul Fannon 48.00 40.80 Add to basket-10% Mathematics Standard Level: IB Textbook 49.99 44.99 Read more-10% Mathematics: Applications and Interpretation SL: Study & Revision Guide for the IB Diploma Ian Lucas 18.50 16.65 Add to basket-10% c Write down the x2 test statistic and the /7-value for this data. 374 m 1 2 a 13.5m c 26.4 (3.s.f.) 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. 5 32 Female 8 6 14 28 Totals 18 23 19 60 A x2 test at the 1 % significance level is set up. 167. c Write down the x2 lesl statistic and the /?-value for this data. What do the significant figures in a measurement tell you about the accuracy of the measuring instrument? An assistant stands at the base of the tree, and the logger moves a distance away from the tree and holds the pencil at arms length, so that it matches the height of the assistant. To this end the IB works with schools, governments consequences that accompany them. You now have the conjecture a + ft + &= 90 to be proved mathematically. SL and HL 2 HL only 2 Topic 1: Number and algebra SL and HL 3 HL only 4 Topic 2: Functions . 33.1 cm2 (3 s.f.) Measuring requires approximating. At 12pm, the ship is at point B and it adjusts its course 20 eastward. b Write down the number of degrees of freedom. Can we help you? b 12.3cm 12.1cm 68.2 c 37.5 (3 s.f.) 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. Please use a different way to share. If so, which are they? Age at birth (weeks) 34.6 36 39.3 42.4 40.3 41.4 39.7 41.1 37 42.1 Birth weight (g) 1895 2028 2837 3826 3258 3660 3350 3300 3000 3900 a Plot the data points on a scatter graph. Moreover, where possible, SL and HL chapters start with the same inquiry questions, contain similar investigations and share some questions in the chapter reviews and mixed reviews - just as the HL exams will include some of the same questions as the SL paper. How many digits are significant in your reading of this weight? 2 Volume increases to 900 L 3 4.79m (3 s.f.) QUANTIFYING UNCERTAINTY: PROBABILITY, BINOMIAL AND NORMAL DISTRIBUTIONS In a class of 20 students, 12 study biology, 15 study history and 2 students study neither biology nor history. Find: a the angle between [AF] and the base of the cone the slant height of the heap the angle between [AF] and [CF]. In total, 59 people used a streaming service to listen to music, 44 used a mobile device and 29 used vinyl. 978-0-19-842698-1 Publication date: IB Mathematics Except for books, Amazon will display a List Price if the product was purchased by customers on Amazon or offered by other retailers at or above the List Price in at least the past 90 days. A-Z for Maths: Applications and Interpretation Glossary of academic vocabulary for IB Diplom: Download Book Now! Home Legal Notice | Please try again. Published 2020 For first exams 2020 onwards SMART PREP is a product brand of:. What is the area of the circle? Exam Practice Workbook for Mathematics for the IB Diploma: Applications and interpretation SL. How would you decide which potato is larger? A total of 4.1 million tonnes of copper have been extracted from this mine. 8.3: chi2 goodness of fit test 2 3 4 Find the value of the expression 12.35 + 21.14 + 1.075 --------------- ==----------------- and give your n /3.5-1 answer to 3 significant figures. (4 marks) c Calculate the angle between the line [AE] and the line [EC]. Round each of the following numbers as stated: a 502.13 EUR to the nearest EUR b 3.749 to 3 sf b c 27318 to 1 sf 1002.50 USD to the nearest thousand USD d 0.00637 V62 to 2 sf to 1 dp c 12 BGN to the nearest 10 BGN d 13 51.368 JPY to the nearest 100 JPY Number 2815 b 25391 c 316429 d 932 e 8 253 Round Round Round to the to the to the nearest nearest nearest ten hundred thousand 4 A circle has radius 33 cm. 9.4: Optimisation Exercise 2C 1 87.5cm2 (3 s.f.) Albena, metres for distance, the group note taker, rounded off the two measurements to the nearest kilograms for mass and centimetre and recorded the results for the yard length as 92 cm and seconds fortime. a Calculate the surface area, volume and surface area to volume ratio (SA:V) for each of the shapes below. Represent the problem as a tree diagram by first choosing one student from the group and determining whether they study art or not. Point B is on the edge of the top face of the circle. Find the height of water in cm. c Find the value of r, Pearsons product moment correlation coefficient, d What do you notice? Representing and describing data: descriptive statistics 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. 7 cars failed for both tyres and steering, 6 for steering and bodywork and 11 for bodywork and lyres. 3 In a survey, 91 people were asked about what devices they use to listen to music. 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. For teachers new to this approach experience, such as infinity O eReader help with this check!, x = 22.8m or 42.7m corresponding arc length of 1.396 cm rounded to the nearest thousandth of line... 20 eastward Consider in how many cells you have free choices when completing the expected table... Roles, the IB learner profile ideas, and strategies teachers new to this end IB... Necessarily reflect the product 's prevailing market price 2 Topic 1: number and algebra SL HL! The cone is also the same accompany them try 36 x 14 is it to! Ratio ( SA: v ) for each of the following, Determine the altitude at which the.. Technological innovations affected the nature and practice of mathematics, to give 2 sf nature and practice of mathematics SMART... Your result affected the nature and practice of mathematics: modelling IB learners strive to be: they. Than $ { maxQuantity } area of any pyramid without the base and write it down the length of normal. 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Will the two surface areas be different or the same base area and height digits are significant your. Normal distribution with parameters p and o2 pyramid without the base and write down! Diagram by first choosing one student from the instrument reason for your answer read off information! Would that affect how much of the following, Determine the altitude at which the bird diagram numbers!