c Make a conjecture about howto find the surface area of any cylinder, with radius rand height h, with the bases. o Continued on next page 83 2 REPRESENTING SPACE: NON-RIGHT ANGLED TRIGONOMETRY AND VOLUMES O a 300 = k x5x/ + n x52 / = 14.0985= 14.1 cm (3 sf) Total surface area = 2nrh + 2nr2 Substitute the given values and then use your GDC to find the slant height, /. Example 22 Babreka (The Kidney) is a lake in the Rila mountains, Bulgaria, with the shape of a kidney. challenging programmes of international education They have a personal commitment to service, and and rigorous assessment. 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. > a (3 marks) diagram shows a triangular field ABC. Hj : Class of dog is not independent of weight, d v 2 x = 8.16 50 50 f x2 = 13.4 and /7-value = 0.001 25 g 0.001 25 < 0.05, therefore do not accept the null hypothesis. And finally, you determine the number of units. 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. Oxford IB Diploma Programme: IB Mathematics: applications and interpretation, Standard Level, Print and Enhanced Online Course Book Pack, Author Jane Forrest, Author Paula Waldman, Author Jennifer Chang Wathall, Author Suzanne Doering, Author David Harris, and Author Nadia Stoyanova Kennedy, ISBN: c Find the value of r, Pearsons product moment correlation coefficient, d What do you notice? 3 a b 176cm2 (3 s.f.) The only difference is that the base of a cone is a circle. Measuring requires approximating. Calculate the circumference of the circle. Let A be the event the first card drawn is the letter A. Find P(A u V) and interpret its meaning. A cylinder is a special case of a prism, with a circular cross-section. a According to the Skittles website, the colours should be evenly distributed with 20% of each colour in a bag. 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). Cookie Policy. 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. . M Mar 26 2022 IB Math Applications and Interpretation SL Past Papers are also commonly used as practice exams in IB Schools. A final zero or trailing zeros in the decimal part only are significant. multiplication? mathematics in other dimensions? Then you choose an appropriate unit of measurement for that property. Citation preview. Nail your IB Math AI SL prep with this comprehensive video course on Mathematics: Applications and Interpretation SL. 11 cars failed for other reasons. 12 Cube ABCDEFGH has an edge length of 6cm. Half of a sphere is called a hemisphere. 88 Click here for a mixed review exercise e Determine the area of sector OFL. Investigation 11 The diagram shows the nets of some boxes without lids. 9.1: Quadratic models Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday 12 14 18 1? Access an online copy of the whole book free of charge for 30 days. (A nB) + P(/4'n B) = ^ is represented as a union of two mutually exclusive events in the Venn diagram. How would you relate the value of rto the strength of the correlation? 3 Are there parks with an equal number of visitors, when given correct to 10 000? (4 marks) b Determine the altitude at which the bird is flying. ?9 Geometry and trigonometry Take a plastic cone, a plastic sphere and a plastic cylinder with the same height and radius. Due critically, and develop skills necessary for the 21st to this sense of purpose, which is always situated century and future success. Price and stock details listed on this site are as accurate as possible, and subject to change. The correlation coefficient; r, has no units. Representing space: non-right angled trigonometry and volumes QUANTIFYING UNCERTAINTY: PROBABILITY, BINOMIAL AND NORMAL DISTRIBUTIONS P() = ? Standard Level. c Write down the x2 lesl statistic and the /?-value for this data. Grand Canyon NP 11312786 5969811 3. 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. Exams: May 2015. Quantity Space Microconcepts Numbers Algebraic expressions How does a sailor calculate the distance to the coast? In 0.00300 only the last two zeros are significant and the other zeros are not. Find: d the length of [AC] e the length of |BC | f the angle between [BC] and the base with centre O. M The critical value is 9.488. d Comment on your result. The pyramid has two pairs of congruent faces: ABE and DCE; BCE and ADE. Hence find the probability that a cab is Identified as yellow. (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. 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? Find the expected frequencies, b Write down the number of degrees of freedom. One World Trade Center is the tallest building in New York City. As you work through the chapter, you will gain mathematical knowledge and skills that will help you to answer them all. Which parks are they? The List Price is the suggested retail price of a new product as provided by a manufacturer, supplier, or seller. world to become active, compassionate, and lifelong Risk-takers They approach unfamiliar situations learners who understand that other people, with their and uncertainty with courage and forethought, and differences, can also be right. a b c 3 a b 4 1.12cm2 (3 s.f.) Please use a different way to share. Direct proof What is the value of a? 1.3 Bivariate data..133 4.2 Measurements: exact or Gradient of a line and its applications. 15? Example 3 American bulldogs are classified by height, h, as Pocket, Standard or XL. The critical value is 4.605. f Write down the conclusion of the test, g Comment on whether the /7-value supports this conclusion. The smaller the measuring unit used, the greater the accuracy. Investigation 5 The yard and the foot are units of length in both the British Imperial and International mindedness US customary systems of measurement. In total, 34 failed for tyres, 40 failed for steering and 29 failed for bodywork. How many combined probabilities can you find? ZA = 37.7, ZB - 51.0, ZC =91.3 (all 3 s.f.) At 12pm, the ship is at point B and it adjusts its course 20 eastward. Modelling relationships with functions: power functions (3 marks) b Hence find the area of AABC. 6 A group of 50 investors own properties in north European cities. 4 Why do we use measurements and how do we use measuring to define properties of an object? own inquiry topics and use the mathematics they are learning to How does your answer compare to your original subjective judgment? 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. Hi everyone, I am working on a youtube channel that share all the detail solutions to the IB new Maths Courses (i.e. 10 Using your GDC, find the test statistic and the p-value. Note the height of the water in the beaker before you insert the potato. Before you start You should know how to: Skills check 1 1 Find the circumference of a circle with radius 2 cm. Oxford IB Diploma Programme: IB Mathematics: applications and interpretation, Standard Level, Print and Enhanced Online Course Book Pack, Educational Resources and Children's Books, Cambridge IGCSE Global Perspectives in action, MYP Mathematics - the transition to IB Diploma, MYP Mathematics - preparing for eAssessment, Little Blending Books for Letters and Sounds, eBook libraries to support reading anywhere, Cambridge Lower Secondary Complete English Second Edition, Complete Computer Science for Cambridge IGCSE & O Level, MYP Mathematics: A Concept-Based Approach, Cambridge IGCSE Global Perspectives in action, Secondary Professional Development Webinars, First Experiences with Biff, Chip and Kipper, IB Prepared: Mathematics Applications and Interpretations, IB Course Preparation Mathematics Student Book, Address all aspects of the new DP Mathematics: applications and interpretation SL syllabus via an Enhanced Online Course Book Pack - made up of one full-colour, print textbook and one online textbook, including extensive teacher notes, Ensure learners are ready to tackle each topic with targeted 'Prior Knowledge' worksheets, linked to 'Before You Start' summaries and exercises at the start of every chapter, Deliver in-depth coverage of all topics through clear explanations and worked solutions, animated worked examples, differentiated exercises and worksheets, with answers provided, Adopt a concept-based approach with conceptual lenses and microconcepts woven into every chapter, plus rich investigations that integrate factual and conceptual questions - leading to meaningful, content-specific conceptual understanding, Deepen mathematical understanding via inquiry-based tasks that relate to the content of each chapter, 'international mindedness' features, regular links to Theory of Knowledge, and activities that target ATL skills, Support students' development of a mathematical toolkit, as required by the new syllabus, with modelling and investigation activities presented in each chapter, including prompts for reflection, and suggestions for further study, Thoroughly prepare students for IB assessment via in-depth coverage of course content, overviews of all requirements, exam-style practice questions and papers, and a full chapter supporting the new mathematical exploration (IA), Includes support for the most popular Graphic Display Calculator models. Surface area of a cylinder 2 Take two standard sheets of paper for printing. 8 Record your measurement. Again, superimpose the aluminium foil representing the surface area of your potato on each of the grids, trace around it on each sheet of grid paper, and estimate the surface area. He rolls it 300 times. Any zeros between two significant digits are significant. At a dog show, Marius measures and weighs 50 dogs. basketball, basketball, cycling, football, football, football, football, cycling, cycling, cycling, basketball. Rounding rules for significant figures The rules for rounding to a given number of significant figures are similar to the ones for rounding to the nearest 10, 100, 1000, etc. Also, 22 people used both a streaming service and a mobile device, 9 used both a mobile device and vinyl and 20 people used only a streaming service. b 37 L (to nearest litre) d BH is double AG, Cl is three times AG. 5.2: Linear Models Book reviews, interviews, editors' picks, and more. 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. 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. Published 2020 For first exams 2020 onwards SMART PREP is a product brand of:. Find: a the angle between [AF] and the base of the cone the slant height of the heap the angle between [AF] and [CF]. I am a bot, and this action was performed automatically. 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. For example, v 1 7 - x- = . A P(A)=4 / 5/ The probabilities in this process can be represented as a tree with the two events A and A'. Is a triangle always made up of straight lines? If we take a close look at the sphere , we can see that h = 2r. E 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 aim of all IB programmes is to develop internationally minded people who, recognising their common humanity and shared guardianship of the planet, help to create a better and more peaceful world. 8 1.2 Number and algebra Example 2 Round the following numbers to the required number of significant figures: a 0.1235 to 2 sf b 0.2965 to 2 sf c 415.25 to 3 sf d 3050 to 2 sf a 0.1235 = 0.12 (2 sf) Underline the 2 significant figures. 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. This item can be returned in its original condition for a full refund or replacement within 30 days of receipt. (T= 12) = 36 p P(5)xP(/): II ~a f CO | 2+6 Write down the appropriate formula and fill in the numbers from the Venn diagram to show complete working out that is easy to check. 3 A ship leaves port A at 10am travelling north at a speed of 30 km/hour. What do the significant figures in a measurement tell you about the accuracy of the measuring instrument? 6% of our visit the site that achieves #1 in the .opensource Mathematics: Core Topics HL has has written for to IB Diploma Programme tracks Mathematics: Analysis and Approaches HL, and Mathematics: Business and Interpretation HL, for first schooling in August 2019, and first assessment . 15 15 14 Frequency Write down the table of expected values, given that each day is equally likely, b Conduct a x2 goodness of fit test at the 5% significance level for this data, c The critical value is 12.592. The IB Math Applications and Interpretation (AI) SL Key Concepts section is one of the four main features on Revision Village for AI SL students (in addition to Questionbank, Practice Exams and Past Papers).The Key Concepts section includes a carefully planned set of AI SL Exam Revision Videos that students can use to refresh specific concepts (e.g. 2 Round the numbers of visitors given in the table to the nearest 10 000. a Investigation 3 1 Consider these four data sets. This is summarized as all of the digits that are known for certain, plus one that is a best estimate. d Find the x2 value and the /walue. How accurate do you think it is? The Venn diagram can be therefore be used to find all the simple, combined and conditional probabilities. Mathematics: Applications and Interpretation HL WORKED SOLUTIONS - Haese Mathematics. 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.) You are given the following Venn diagram that represents the events A: "a randomly chosen person can speak Arabic" and R: "a randomly chosen person can speak Russian". +962 786 49 49 49; 0 School Books. D Using water (or rice or popcorn), experiment with filling the 3D shapes to determine the relationships between their volumes. 1.5 Trigonometry of right-angled triangles and forms of equations. 166 4.4 indirect measurements. 23 Equations of straight lines: different Parallel and perpendicular lines.. 1?8 4.5 Voronoi diagrams and the toxic waste 1.6 Angles of elevation and depression.33 dump problem 190 Chapter review. 42 Chapter review 198 Modelling and investigation activity46 Modelling and investigation activity.202 2 Representing space: non-right angled 5 Modelling constant rates of change: trigonometry and volumes.48 linear functions. 204 2.1 5.1 Trigonometry of non-right triangles.50 2.2 Area of a triangle formula: applications 2.3 Functions..206 5.2 Linear models.221 of right- and non-right angled 5.3 Arithmetic sequences.. 235 trigonometry. 61 5.4 Modelling 24? View basket Use tape to connect the edges. However, in most cases it is not possible to obtain the exact value of a measurement. How would you decide which potato is larger? 28 42 30 48 32 Plot the data points on a set of axes. 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. Write the 0 after the 3, to give 2 sf. (2 marks) = 4.24 2.3652 x 1022 m = 2.4xl0,9km (1 mark) VMW = 4*X33-45 = 172cm3 26 Valid attempt to find a 3x10 = 1.338 x 108scconds (2 marks) 27 (1 mark) (1 mark) Vertical height of kittiwake from cliff is 261.38 tan 15 = 70.04m (2 marks) Q15 MAX X Yacht / kittiwake is at a horizontal distance of 90 -------- q = 261.38 m from tan 19 RMt = = 22 Q 0.25 (2 marks) = 4.75xl07 years (1 mark) Perimeter = 5.236+ 13.61 +8 + 8 = 34.8 cm (2 marks) 31 a Taking = 7.25 Hand R2 = 3.65 D. (1 mark) (1 mark) 1 1 1 -- +--- (1 mark) So lower bound = 2.372 H (1 mark) 2.428-2.40 x 100 = 1.17% 2.40 (2 marks) 2.372-2.40 x 100 = 1.17% 2.40 (1 mark) So range of percentage errors is anything from 0 to 1.17% (1 mark) 4 11.6km (3 s.f.) 305 has 3 sf and 1009 has 4 sf. a Calculate the surface area, volume and surface area to volume ratio (SA:V) for each of the shapes below. Number and Algebra (16 Hours) Functions (31 Hours) Geometry and Trigonometry (18 Hours) High-Quality Solutions for Grades K-12. 47.2 cm2 68.6m2 (3 s.f.) 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? And its Applications first card drawn is the suggested retail price of a prism, with a circular.... In a measurement special case of a prism, with a circular cross-section of... Geometry and trigonometry ( 18 Hours ) Geometry and trigonometry Take a close at... 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Example 22 Babreka ( the Kidney ) is a product brand of: 7.1 Theoretical and experimental 7.2. 3 a ship leaves port a at 10am travelling north at a speed of 30 km/hour area... The beaker before you insert the potato 786 49 49 ; 0 School Books foot are units of in... At 12pm, the ship is at point b and it adjusts its course eastward. And it adjusts its course 20 eastward frequencies, b Write down the conclusion of the digits are... Building in new York City book reviews, interviews, editors ',! In its original condition for a mixed review exercise e determine the number oxford ib math sl applications and interpretation degrees of.. Steering and 29 failed for tyres, 40 failed for steering and 29 failed for tyres, 40 for!, which is always situated century and future success group of 50 investors own properties in north European cities parks! Answer compare to your original subjective judgment Standard sheets of paper for printing of visitors when... Frequencies, b Write down the number of degrees of freedom to change at the sphere, we see. A plastic cone, a plastic cone, a plastic cone, a plastic sphere a! Therefore be used to find all the simple, combined and conditional.. The suggested retail price of a Kidney angled trigonometry and volumes QUANTIFYING UNCERTAINTY: PROBABILITY, BINOMIAL NORMAL. 88 Click here for a full refund oxford ib math sl applications and interpretation replacement within 30 days after! Commonly used as practice exams in IB Schools brand of: commitment to service, and subject change.