What is the radius of this circle? 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. Note the height of the water in the beaker before you insert the potato. What would happen if the diameter of the tank is tripled? Please use a different way to share. 3 Are there parks with an equal number of visitors, when given correct to 10 000? Fold each sheet to make two open-ended prisms and use tape to connect the edges. One week he answers 840 calls. O is the centre of the base and is directly below the apex E. trigonom etry Geometry and Find the size of the angle between the edge |BE| and the base ABDC of the pyramid b between the edges [EB] and [EC] c EMO, where M is the midpoint of [AC]. a State the null hypothesis and the alternative hypothesis, b Write down the number of degrees of freedom. You write X follows a normal distribution with parameters p and O'2 or X-N(p, a2). This is summarized as all of the digits that are known for certain, plus one that is a best estimate. How can you calculate the distance travelled by a satellite in orbit? M Calculate the mass of the ornament. 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. 8 9 y 12 10 10.5 9 9.3 9 8.2 ? 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. Estimate the surface area of the potato and write down your estimate. 6 Estimate the volume of a cube with side 4.82 cm. Representing and describing data: descriptive statistics The lines |AB] and |OD) are parallel. New topics are italicized. Calculate the surface area. Modelling constant rates of change: linear functions 2 Consider another four data sets. eg 2n(2) = 12.6cm (12.5663) 2 Find the area of a circle with radius 2 cm. Statistics and probability a Plot the data points on a scatter graph, b Comment on the correlation. For example, when measuring your weight, you can get a more accurate measurement if you use a balance scale that measures to a greater number of decimal places. At a dog show, Marius measures and weighs 50 dogs. Make a conjecture about how to find the surface area of any cylinder, with radius r and height h, without the bases. Legal Notice | 5 The letters of the word MATHEMATICS are written on 11 separate cards as shown below: a M A T H E A T 1 C S M A card is drawn at random then replaced. He decides to see whether there is a connection between the temperature and the number of bottles of water sold. year Diploma . 8.3: chi2 goodness of fit test The cost to fill the pool is $0.15 per cubic metre of water. 2 Estimate the number of pages of code for the Apollo mission. The List Price is the suggested retail price of a new product as provided by a manufacturer, supplier, or seller. OA = AB = 8 cm and AOD = 0. \ A value is accurate if it is close to the exact value of the quantity being meas ured. a Find P(B \ A). Citation preview. IB Prepared Mathematics: Applications and Interpretations. Rocky Mountain NP 4517585 5. 978-0-19-842698-1 Publication date: Write it down, c Did you find another relationship between the volumes of two of the solids? definitely known, plus one estimated figure (digit). c Find the value of r, Pearsons product moment correlation coefficient, d What do you notice? Written with your needs in mind, our study guides offer comprehensive coverage of the syllabus along with ample opportunities to practice technique and . H 9 Buildings A and B are rectangular prisms with height 8 m, as shown in the diagram. How many cubes can be made? Find the area of the sector and the length of the arc. c Find the value of r, Pearsons product moment correlation coefficient, d What do you notice? a V = i(4 x 3.5 x 7.4) = 34.5 cm (3 sf) Use V = i(base area x height) b height = U.52-3.22 = 1 1.0458 cm* Use the Pythagorean theorem to find the vertical height of the cone. Rounding rule for n significant figures trigonometry Geometry and If the (n + 1 )th figure is less than 5, keep the mh figure as it is and remove all figures following it. Modal class: 50 < s < 55 Mean * 54 Median * 52.5 Data set is well centred with all three measures agreeing well, so mean is best measure of the central tendency as this minimises the error for the guess of the next value. 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. The edges of each hexagonal face have length 4 cm. 3 Three hundred people of different ages were interviewed and asked which genre of film they mostly watched (thriller, comedy or horror). -o = .n'o sin 115 sin 40 (1 mark) =^AB = 3.68 cm (1 mark) b BD2 = 92 + 162 - 2 x 9 x 16 x cos33 (2 marks) =>AX = 297.312 (lmark) b 27 In (1 mark) 3 Surface area hemisphere = 2nr2 = 2n x 42 = 32/r Surface area cone AD = \j9.77l2 -l1 = nrl = n x 4 x \/92 +42 = 4ny/97 23 a b sin A =--------sin 67 -----5.7 6.9 =>A = 49.50 (1 mark) (1 mark) If X is the foot of the vertical line from E, then letting AX = x, by Pythagoras it follows that x2 + x2 = 162. F Compare results 19 Compare your potato measurements with the measurements of another group. Notice that the simple probability P(B) = P(A n B) + ? (2 marks) Exercise 3A 1 A = 4| -Ul6xx/202-82 | +162 (2 marks) = 843 cm2 (1 mark) Chapter 3 Skills check 1 Discrete Continuous c Discrete Discrete e Discrete g Continuous i Continuous g Continuous 1 2 3 4 Continuous f Frequency 21 4 22 6 23 24 5 5 4 Height, in Frequency Age of children 1 3 Major gridlines correspond to 1 cm y 49. 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. e 227cm2 (3 s.f.) Cinzia gives an Frequency Score, x IQ test to all 200 IB Diploma Programme students in the 5 xAY = 7.810 cm (1 mark) tan XAY = - (1 mark) 7.810 XAY = 37.5 1 6.96 m 1.711 km and y = 1.436 km Exam-style questions b 5.36m b 0.511 a* = 14 81.1 cm (3 s.f.) IB Prepared Mathematics: Applications and Interpretations, Educational Resources and Children's Books, Little Blending Books for Letters and Sounds, eBook libraries to support reading anywhere, Cambridge Lower Secondary Complete English Second Edition, MYP Mathematics: A Concept-Based Approach, Secondary Professional Development Webinars, First Experiences with Biff, Chip and Kipper, Free dictionary worksheets and activities, IB Prepared English A: Language and Literature, IB Prepared Environmental Systems and Societies, IB Prepared Mathematics: Analysis and Approaches, Worked solutions for end of chapter questions, Worked solutions and markschemes for practice exam papers. What do you think the answer may be? A P(A)=4 / 5/ The probabilities in this process can be represented as a tree with the two events A and A'. a Set up a contingency table to display the results. Not all nets can be folded into a 3D figure, although they may have the correct number of faces. 394 Height Weight Height Weight Height Weight 36 30 42 38 50 39 37 37 33 42 39 51 41 36 43 36 51 42 38 31 43 44 52 45 38 38 44 42 52 45 39 32 44 48 52 51 39 39 45 46 53 53 39 42 46 49 54 55 40 41 46 38 54 48 40 43 46 42 54 56 40 38 46 55 58 41 38 50 55 51 41 44 47 47 47 52 56 54 41 46 48 49 56 53 41 45 48 48 56 55 41 47 48 42 58 49 53 57 57 59 Find the mean weight of the 50 dogs, Complete the following contingency table: a b Class Standard Pocket XL < mean > mean Write down the null and alternative hypotheses, Write down the number of degrees of freedom. Living cells can only get materials (like glucose and oxygen) in and can only get waste products out through the cell membrane. 3 Given a net, generate a formula for finding the number of cubes that will fill the box created by the net. How accurate do you think it is? Find how much shorter his journey will be if he chooses to take the shortcut. We dont share your credit card details with third-party sellers, and we dont sell your information to others. In total, 34 failed for tyres, 40 failed for steering and 29 failed for bodywork. trigonom etry Geometry and Developing inquiry skills Look back at the opening problem. (2 marks) a Calculate the angle between the line [AE] and the plane face ABCD. 0.002 has only 1 sf, and all zeros to the left of 2 are not sf. I posted my Math HL IA to Turnitin and got a 1 percent similarity score. QUANTIFYING UNCERTAINTY: PROBABILITY, BINOMIAL AND NORMAL DISTRIBUTIONS P() = ? MATH 101. Dimensions: 10.2: Compound interest, annuities, amortization ${cardName} not available for the seller you chose. Write down your answer correct to 1 decimal place. b A = n( 12.4)1 23456789 Use the formula for area of a circle, A = nr2. (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. 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. ISBN: 978-1-925489-84-2. (1 mark) 60 = 1.5x10 seconds (2 marks) 1.5x10' 60x60x24x365 610 VMAV = 4;rX3'33 =187.4 cm3 120 120 eg tan 31 =----- => x =--------- 5x tan 31 (1 mark) 3 x 108 x (2.5 x 106 x 365 X 24 x 60 x 60) = 2.3652 x 1022m (2 marks) 24 a (2 marks) horizontal distance. The number of calls that he answers each day are shown in the table. Students who are not strong at math . Price on Amazon: USD29.10 (Paperback) Publisher: Oxford. 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. 5 210cm2 (3 s.f.) 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. The critical value is 9.210. d Comment on your result. Example 3 A circle has radius 12.4cm. For this series of books, we have identified important topical understandings that link to these and underpin the syllabus, and created investigations that enable students to develop this understanding. Syllabus coverage This book covers all the content of the Mathematics: applications and interpretation SL course. (3 marks) 19 PI: A small pendant ABCD is made from five straight pieces of metal wire as shown in the diagram. Approximating irregular spaces: integration E 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. Modelling relationships with functions: power functions QUANTIFYING UNCERTAINTY: PROBABILITY, BINOMIAL AND NORMAL DISTRIBUTIONS In a survey carried out in an airport, it is found that the events A: "a randomly chosen person has an Australian passport" and V: "a randomly chosen person has three vowels in their first name" are independent. 22 PI: Alan and Belinda stand h ground, 115m apart. Enter each total in the table as shown. 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. Mathematics (x) Biology (y) 20 24 25 20 28 22 30 21 32 25 3? a (3 marks) diagram shows a triangular field ABC. a Investigation 3 1 Consider these four data sets. 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. IfX-B(n,p) then E(X) = np and Var(X) = np{ 1 -p). Sign in/Register| 10.4: Exponential equations and logarithms The figures below are examples of a square-based pyramid, a tetrahedron (triangular-based pyramid) and a hexagonal-based pyramid. Teacher notes This icon appears at the beginning of each chapter and opens a set of comprehensive teaching notes for the investigations, reflection questions, TOK items, and the modelling and investigation activities in the chapter. Example 7 It is claimed that when this pair of Sicherman dice is thrown, and the two numbers obtained added together, the probability of each total is just the same as if the two dice were numbered with 1, 2, 3, 4, 5 and 6. Label the axes, b Find Pearson's product moment correlation coefficient, r. c Comment on the correlation. ${cardName} unavailable for quantities greater than ${maxQuantity}. 3.4: Bivariate data 39B preferring horror films between the ages of 20 to 50 years is 33.4. c Write down the number of degrees of freedom. 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. Are there different possible strategies to find this number? In either case, all figures after the /7th one should be removed if they are to the right of the decimal point and replaced by zeros if they are to the left of the decimal point. How far can you see? CO | II p(s|/) = 4 oo b P(5): f P(5)xP(/). Find the cost of filling the pool. 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. Then another card is drawn. Try 36 x 14 Is it possible to know things about which we can have no experience, such as infinity? PM\- / 5/ P(B'\A) = - s' 0 P(^nB,) = P(WM)=- P(0'|A) = -| 5 P(BU') = 1 12PM1 n 0) = PM')P(BM') = v \ 3 p(g. | > S' P(A' r\ B') = P(/T)P(B' 1 A') = ^ Then apply the multiplication law of probability to find the probability represented at the end of each "branch" of the tree. 1 Round the following measurements to 3 significant figures. Howto use your enhanced online course book Throughout the book you will find the following icons. Digital Copy. a b Find the surface areas of the cylinders without the areas of the bases. 5 The volume of a regular hexagonal prism is 2800 cm3. 12 ffiTiffffiFfffl What is the purpose of the goodness of fit test? Use a piece of aluminium foil to wrap the potato and keep any overlapped areas to a minimum. have the independence of spirit to explore new roles, The IB learner profile ideas, and strategies. Caring They show empathy, compassion, and and international organisations to develop respect towards the needs and feelings of others. Can you explain why the nets c and d cannot make a cube? X = 22.0m, Y= 16.3m (3 s.f.) a Determine the direct distance of Alan to the bird. Math AIR HL/SL plan and that about Official IB documents. b 37 L (to nearest litre) d BH is double AG, Cl is three times AG. In case you don't know, to study for the IB diploma you will take 6 subjects and 3 of them have to . d Write down the x2 test statistic and the /rvalue for this data. (2 marks) b Calculate the volume of the prism. 98 Purple 129 Green 13? The logger can then estimate the height of the tree in pencil lengths and multiply the estimate by the assistant's height. Chapter review..492 Modelling and investigation activity 496 11 Modelling periodic phenomena: trigonometric functions. 498 11.1 An introduction to periodic functions 500 Chapter review.. 373 11.2 An infinity of sinusoidal functions..505 Modelling and investigation activity376 11.3 A world of sinusoidal models. 511 8 Testing for validity: Spearmans, test for Chapter review51? 4 Imagine another box that holds twice as many cubes as Box A. 7.7: Modelling measurements that are distributed randomly Remember to use the unrounded value for / when you calculate the value of h. 1 Find the surface area of each of the following solids: a a cylinder with radius 2.5 cm and height 7.3 cm b a cone with radius 3.5 cm and height 12 cm. 6 Use Kristian's suggestion as we have two sides and one angle, x = 22.8m or 42.7m. Alan and Belinda are standing on the same side of the bird, and they both lie in the same vertical plane as the bird. 10 Most Visited National Parks (2016) Park 1. If I measured the weight of my earrings three times, the electronic scale might produce three different results: 11.23 g, 11.30 g and 11.28 g. Usually, the average of the available measures is considered to be the best measurement, but it is certainly not exact. If I use a balance scale that measures only to the nearest gram to weigh my silver earrings, I will get 11 g. But if I use an electronic scale that measures to the nearest hundredth of a gram, then I get 11.23 g. TOK To what extent do instinct and reason create knowledge? Shape Volume Pyramid V = -(base area x h) Prism Cone base area x h V= nr2h 3 Cylinder Sphere 7tr2xh V = -7rr3 3 The volume of a pyramid is a third of the volume of a prism with the same base and height. The hemisphere has radius 4 cm and the cone's perpendicular height is 9 cm. This method is based on a simple reason: for a fit adult, the angle that is formed as they look through their legs is approximately 45 degrees. The critical value is 7.815. e Comment on your result. Fold along the dotted lines and use tape to connect the edges. . Modelling relationships: linear correlation of bivariate data If you stand on the Observatory floor, 382 m above the ground, how far can you see? If the angle between the two aircraft is 52 and the distances from point O to the two aircraft are 58 km and 75 km, find the distance between the two aircraft. They work effectively and willingly curriculum in terms of a whole-course approach and Principled They act with integrity and honesty, with a include support for international mindedness, the IB strong sense of fairness, justice, and respect for the learner profile and the IB Diploma Programme core dignity of the individual, groups, and communities. Mathematics Sl Applications And Interpretation Oxford 2019 Pdf Pdf Significant Figures Rounding (3 s.f.) PI: The diagram shows a quadrilateral L ABCD. Where applicable, each worked solution is modelled on the relevant worked example in the textbook. h\ Example 23 Calculate the volume of the cylinder with radius 2 cm and height 7.5 cm. Measure the length of the potato. EXAM HINT In exams, give your answers as exact or accurate to 3 sf, unless otherwise specified in the problem. , our study guides offer comprehensive coverage of the cylinder with radius r and 7.5... And normal DISTRIBUTIONS p ( b ) + accurate to 3 significant figures prism 2800... The angle between the line [ AE ] oxford ib math sl applications and interpretation |OD ) are parallel moment correlation coefficient, r. Comment! The solids the prism the Apollo mission, d What do you notice relationship between volumes! Make two open-ended prisms and use tape to connect the edges, our study guides offer comprehensive coverage the. Book Throughout the book you will find the following measurements to 3 significant figures Rounding ( marks! 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