But how do we go about measuring the space around us? 3.1: Collecting and organising univariate data 10 x 12 ABE area =--------- = 60 2 trigonom etry Base area = 10 x 8 = 80 Geometry and Find the total surface area of a rectangular-based pyramid whose base has dimensions 10 m and 8 m, and where the slant heights for the faces ABE and BCE are 12 m and 13 m, respectively. As you work through the chapter, you will gain mathematical knowledge and skills that will help you to answer them all. 67.0cm2 (3 s.f.) Some of the early methods of measurement are still in use today, and they require very little equipment! 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. 1.1: Measurements and estimates Remember to write down the null and alternative hypotheses. 5.3: Arithmetic Sequences To add the following enhancements to your purchase, choose a different seller. Example 2 Eighty people were asked for their favourite genre of music: pop, classical, folk or jazz. The critical value is 7.815. e Comment on your result. 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. English; Arabic; Mathematics; Science; Physics Notice that the simple probability P(B) = P(A n B) + ? 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. 21.35, 1.25, 305, 1009, 0.00300, 0.002 21.35 has 4 sf and 1.25 has 3 sf. IB Mathematics Applications and Interpretation (AI) Standard Level (SL) is one of the four math courses introduced in the current IB Mathematics curriculum (2021-2027). a Calculate the surface area, volume and surface area to volume ratio (SA:V) for each of the shapes below. Using water (or rice or popcorn), experiment with filling the 3D shapes to determine the relationships between their volumes. 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. The answer should be given correct to 1 dp, so you have to round to the nearest tenth. 305 has 3 sf and 1009 has 4 sf. rvalue Correlation 0 < |r| < 0.25 Very weak 0.25 26 x = 22 Since 4 study neither history nor geography the sum of these three regions must be 22. V= (7- 1) = 6 Using GDC, x2 = 1.60 and /rvalue = 0.953. c 0.95 > 0.05 or 1.60 < 12.592, so you can accept the null hypothesis: the data does satisfy a uniform distribution. For example, v 1 7 - x- = . b 12.4cm (3 s.f.) 88 Click here for a mixed review exercise e Determine the area of sector OFL. 7.5: Modelling random behaviour: random variables and probability distributions I am a bot, and this action was performed automatically. If not, how are the two measurements different? (2 marks) d Find the volume of the pyramid. 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: analysis and approaches SL syllabus, for first teaching in September 2019. Complete IB Math Topics Overview: Standard Level. b A = n( 12.4)1 23456789 Use the formula for area of a circle, A = nr2. What is the area of the circle? a State the null hypothesis and the alternative hypothesis, b Write down the number of degrees of freedom. The results are shown in the table below. Modelling periodic phenomena: trigonometric functions 5.1: Functions Half of a sphere is called a hemisphere. 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? The critical value is 13.277. d Comment on your result. For these pairs of events, state whether they are mutually exclusive, independent or neither. 7.1: Theoretical and experimental probability, 7.2: Representing combined probabilities with diagrams Normally you would solve this using your GDC, which may ask you to enter the degrees of freedom. Is the angle sum of a triangle always 180? IB Mathematics Analysis and Approaches SL Study Guide.pdf. Howto use your enhanced online course book Throughout the book you will find the following icons. Example 24 Find the volume of the triangular prism whose base is an isosceles triangle where the equal sides are 12 cm and the angle between them is 130. c 4 22.0cm2 (3 s.f.) trigonometry Geometry and Measurements help us compare objects and understand how they relate to each other. A cylinder with height 11 cm and radius 3 cm is shown in the diagram. You may want to cut out the nets and fold them into boxes. Slowly and carefully place the potato in the water, and again note the height of the water. Below you will find all the revision materials you need to excel in your examinations. What measures can you use to decide? What does this tell us about our knowledge of with a plane that is parallel to the base. To find the total surface area of a cylinder, find the curved surface area and add on the areas of the two circular ends: Total surface area = 2nrh + 2nr2 The formula for the surface area of a sphere is S A = 4nr2 The curved surface area of a cone uses the length of the slanted height /: CSA = nrl To find the total surface area of the cone, add the area of the circular base: SA = 7tr/+ nr2 To find the total surface area of a pyramid, add together the areas of all the faces. Statistics and probability a Plot the data points on a scatter graph, b Comment on the correlation. a Draw this Venn diagram with numbers assigned to the eight regions. The Native American method Native Americans had a very unusual way of estimating the height of a tree. c a b h2 = P-r2 h = 414.09 8 52 52 = 13.2 cm (3 sf) v y b V. ..V-l. 0 f=5cm y Now that you know the radius and the slant height you can find the cone height, h, from the triangle OBC by using the Pythagorean theorem. They are brave and articulate in defending their beliefs. Point B is on the edge of the top face of the circle. Find how much paint is needed if 1 L of paint covers 8.5 m2 of surface. Here's a complete set of IB Math notes you can use in your review. a Set up a contingency table to display the results. mathematics in other dimensions? How many digits are significant in your reading of this weight? Modelling rates of change: exponential and logarithmic functions a Draw a Venn diagram to represent the information, using x to represent the number of cars failing for all three reasons. The critical value for this test is 17.275. d State the conclusion for the test and give a reason for your answer. A total of 4.1 million tonnes of copper have been extracted from this mine. The smaller the measuring unit used, the greater the accuracy. 255x195mm, Evaluation copies must be ordered on a school account.More information on school accounts. The earliest references to trigonometry are in Indian mathematics. This PDF download accompanies the IB Mathematics: Applications and Interpretation SL study guide, providing worked answers to problems presented throughout the book. They would bend over and look through their legs! 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. Factual How accurate are your measurements? All IB Diploma students have to follow a maths course at either standard or higher level. 10 11 Compare yourthree measurements. The potato is to be submerged in water and you will measure the distance the water level is raised. M To find the total surface area of a cylinder, find the curved surface area and add on the areas of the two bases: 82 2.3 b 1 Total surface area = 2nrh + 2/rr2 The formula for the surface area (SA) of a sphere is S A = 4nr2 The curved surface area of a cone uses the length of the slanted height /: CSA = nrl To find the total surface area of the cone, add the area of the circular base: SA = nrl+ nr2 To find the total surface area of a pyramid, add together the areas of all the faces. Prior learning Clicking on the icon next to the Before you start section in each chapter takes you to one or more worksheets containing short explanations, examples and practice exercises on topics that you should know before starting, or links to other chapters in the book to revise the prior learning you need. 10.2: Compound interest, annuities, amortization IB DIPLOMA PROGRAMME Raw 7% ^ ' x\, \ JjS Jennifer Cr Suzanne D 4Li /jl Jane Forre David Harri Nadia Stoy Paula Wald OXFORD Course Companion definition The IB Diploma Programme Course Companions are designed to support students throughout their two-doing, they acquire in-depth knowledge and develop understanding across a broad and balanced range of disciplines. The Guide aims to help the IB student by both revising the theory and going through some well-chosen examples of the new IB Mathematics: Applications and Interpretation SL curriculum. 4.5: Voronoi diagrams and toxic waste problem Quantifying uncertainty: probability, binomial and normal distributions 374 m 1 2 a 13.5m c 26.4 (3.s.f.) Privacy Policy | Topic 4: Statistics and probability SL and HL 9 HL only 10 Topic 5: Calculus SL and HL 11 HL only 11. Significant figures Measuring instruments have limitations. To this end the IB works with schools, governments consequences that accompany them. 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. Mathematics: Applications and Interpretation SL WORKED SOLUTIONS. 11 A regular dodecahedron has edges of 2 cm. 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. View basket 3.4: Bivariate data 7 The surface area to volume ratio (SA:V) is an important measure in biology. This book gives you fully worked solutions for every question in Exercises, Review Sets, Activities, and Investigations (which do not involve student experimentation) in each chapter of our textbook Mathematics: Applications and Interpretation SL. Modelling random behaviour: random variables and probability a Plot the data points on a scatter graph, Comment! Independent or neither should be given correct to 1 dp, so you have to a! And again note the height of the early methods of measurement are still in today... Water ( or rice or popcorn ), experiment with filling the 3D shapes to determine the between. And carefully place the potato in the water level is raised with the... 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