We can use our knowledge of the function to choose more appropriate settings. (a) vote is evenly split A 02395 A 03790 (b) B 04971 6. . 11. Hence, the edges in the Voronoi diagram are parallel which implies there are no vertices. (o) \__/ . To pay off the loan, Phil makes annual deposits of $P at the end of every year in a savings account, paying an annual interest rate of 2%. Express each number in scientific notation. The diameter of the wheel is 8 m. The centre of the wheel, 4, is 2m above the water level. (e) The actual orbital period of Ceres is 4.60 Earth years. 10 14 W L =31 W . There is a rare genetic disease among the population. The constant, ;is called the common ratio of the sequence, and r = forall integers n > 1. For example, the display for the model in Example 9.5 shows how this default view can be very misleading. To the nearest metre, how much closer to the tree is the second view point compared to the initial one? So it is far more. 3579 o3y 3 V3 I ] K V9 16.1 20. Graph: ! (a) (5 1i)and (4 + 3i) (b) (4 + 2i)and (=2 + 1) () (V5 3i)and (2/5 + i) . Z~5.15 + 0.355]Q) 13i (@ {m. () () 23928 (b) 3x% " = 6x> 3x2e = +2) (i) 0.0022 ( () 00249 (i) 2.3681 0.0002; error is divided approx. (b) Find (i) h(29) (i) h(53) (c) State the range of h. 3. Chapter 14 Practice questions Exercise 14.3 6. (a) A(1,3,5),M(2,1,3) (b) E(3,1,2), R(3,2,4) () F(7,1,3V6), 5(4,3,6) Solution @ (2 3-3 -1+22+4 ( GO + o~ o (LALE B ) (20 :(0)%,3) (324 Using similar triangles, we can determine the coordinates of any portion of an entire length if the measurements along the three axes are known. If =2 < C < 2, then whether 2 sinx + Cis positive will depend on the value of x. Ebook. The first type of soil is made of clay and the cost of building the pipeline through this type of soil is $7 million per kilometre. This is shown in the diagram along with a possible route APB. ) Before doing that, however, we give a qualitative analysis of the differential equation. This is an interpretation of the central limit theorem. (a) the largest empty circle (LEC) must be centred on a (b) All vertices in the diagram are adjacent to cell K and 4@ 2+i vertex (15, 8) is the vertex farthest from site K, therefore it must be the centre of the largest empty circle. Particularly interesting for us here is how a different view of mathematics can bring about changes in teaching and learning. complex variables used in el Resistance (R) is a measure used in direct current (DC) circuits. A large lizard known as a Gila Monster is about 16 cm long at birth. Our programmes empower school-aged students to take ownership of their own learning and help them develop future-ready skills to make a difference and thrive in a world that changes fast. Use the information given in Example 5.2 to answer these questions. Does this experiment agree with that theoretical value? (b) Determine if 1 is a term in this sequence. The volume of liquid, vecm in a conical flask is a function of the height, hem of the liquid, given by = 371(107 (10 h)? The higher level courses each have 3 papers and the standard level courses each have 2 papers. 37 21.175 22 -7 5 93 2% 24, 3.2 6 25. This is a position taken by surprisingly many mathematicians. Christine invests in a retirement plan in which equal payments of $1200 are L . To the right ofa decimal point, all leading zeros are not significant, whereas all zeros 0.0043 has 2 s.f, while 0.0043000 has 5 s.f. Using scientific notation this would be written as 1.496 X 10km. + b2 will probably be useful. There are, to add to the puzzle, none that have cycles of 12, 14, 15, 16 or 18 years. Unstable. Then the trigonometric functions can be defined as sing=y cosf=x %, tnf=2 x#0 Now we consider angles in other quadrants, like the other three angles that are 45 from an axis: 135, 225, and 315. Relative to the base, how high is the hill? Our experience with the central limit theorem would suggest that repeated sampling or larger sample sizes should help. 'The initial gift is the present value of the income stream of 20000 per year. (i) Point on function is (4, f(4), fi4) = % +@)-6 i G5 (i) local minimum isatx :% 14. The equation by running regression is (a) A cubic model seems to fit best with 2 = 99.3%. (a) 4i Exercise 6.4 - 9. During that time, we have received many useful comments from both teachers and students. ATalk with Reuben Hersh, Wed, Oct 24, 2018, Used with permission of Edge Foundation Inc. Simple interest is interest calculated only on the initial investment. A circular irrigation system consists of a 400-metre pipe that is rotated around a central pivot point. It is interesting to speculate on how consequences in the classroom flow from a humanist view of mathematics. (a) log;243 (b) log,33 (c) log, 16 (d) log,3V3 (e) 1081(*16) (f) log,2v2 (g) log50 + log20 (h) log4000 log4 (i) mMHve Ine? In this world, mathematicians can explore the patterns they encounter. Thus although not essential it is recommended that you read and study the chapters in numerical order. T o Rl (a) Write down the amount of electrical charge in the battery at t = 0 (b) The line L is the horizontal asymptote to the graph. Each waveform: * is periodic, repeating after a cycle is completed, over a span of n degrees or radians. e e I Solution (a) To determine if a piecewise linear model is appropriate, examine the data using a scatter diagram. (a) x = 100, ; (Lunsumem) _ f 100 (360 0.03x2 60)dx = 2000 0 surplus) ~ :f surplus) ~ Jo 10 (60 0.006x)dx = 4000 (b) x =119.48 ( onsumm)o :f 11948 (300e 99 90.83)dx surplus| ~ Jy . There are also numerous worked examples throughout the book, showing you how to apply the concepts and skills you are studying. 0.2 189 (b) Calculate the value of Pearsons r and interpret it in context. This is a point where the proof arrives at the required result at the end of the chain of reasoning. Consider a taxi company that has the following structure for charging customers. Version 1.1. 8. The most practical circle to use is the circle with a radius of one unit, as shown in Figure 5.12. Conveniently, each real number gets mapped to a point on the unit with an arc length equal to the number. In contrast to the science of the day, the mathematical truths of Pythagoras are just as true today as they were then - indeed his famous theorem is still taught today as can be seen in this book. 770 Since Table 18.8 lists only the observed values, we need to calculate the expected values if the preferences expressed by the two separate groups were the same as the preferences expressed by the groups as a whole. It is a thought-provoking chapter that will stimulate you to think more deeply and critically about the nature of knowledge in mathematics and the relationship between mathematics and other areas of knowledge. A 30 m cable connects the top of an 18 m totem pole to a point on the ground. 19. @) 55 y 3 . Therefore, use the built-in function on the GDC to obtain the graph in the diagram. WebOxford IB Diploma Programme: Oxford IB Diploma Programme: IB Mathematics: applications and interpretation Higher Level Enhanced Online Course Book. The average cost, Alx) = @ 1 A company produces fans with a maximum capacity of 500 units per day. () ? 10. 1.46% Exercise 3.4 1. At the level of significance of& = 0.05, test the statistic given by the app. (b) 8memhr! Mathematics Applications and Interpretation for the IB Diploma Higher Level provides comprehensive coverage of the new c. 3,370 448 152MB. (a) ) + 1L,xeR 4 x+9 130 8x 18 1728 10( | 5 (@ Doy =_ =57+ () y=x Ao (b) 20 ( -1 (b (b) =2 y intercept (3,0 Exercise 2.5 C] 1. For example, finding the 100th term in the sequences in Example 3.8 would be laborious, using the recursive formula. In n the the rigright-angledgled triangle triangle ABD, h 5 sinA==csinA=h & This formula uses two sidesand the included angle, and is thus known by the acronym SAS, & a 5 Figure 4.8 The area of triangle ABC So, if Area = %bh = Area = %b(c sin A) Example 4.10 Find the area of ALMN, given that M = 60, LM = 4 cm, and MN = 10cm L MN ._______________________________________________________________________|] Solution In this instance, | = 10 cm, n = 4 cm, and the included angle, M = 60 Area:%l(nsi.nM) :%- 10-4-5in60 = 20>3 = 103 cm? dx ] Solution (a) Letu = 6x + 11 then calculate du: u=06x+11=du=6dx Since du contains the factor 6, the integral is still not in the proper form Jftu) du. Math is a process of finding solutions to problems. 7 1 dy = f3x2dx:>f(;+ 4y)dy: f3x2dx ln|y| T2y =ik The solution is exact, but implicit, as it cannot be written in an explicit form y = fix). This would mean 20 marked items out of 40. Calculus. One applies the rules (these are rules of algebra typically) to a line in the proof to get the next line. In a series AC circuit there is a resistor of R = 12 ), a reactance across an inductor of X; = 3 Q and a reactance across a capacitor of X; = 8 Q. Wells) value, = A1) = [ o 1000 0d =500(1 e"!) Schools must be authorized to teach our IB programmes. (c) Use your least-squares regression model to predict the marathon time for a runner with a 5 km time of 20 minutes. 829 Bivariate analysis (d) The air temperature in a cave does not vary and is usually equal to the mean temperature of the region. (a) V2 (e) 13 3. For example, the graph of the function fix) = 2x 1is shown in Figure 2.4. In the section, we will examine cubic models of the form fy=ax*+bx>+cex+d Note that a simple cubic model may have b, , and d, equal to zero. should not use the model to predict the length wide. V.B=0 3, VxE=-98 at 4 vxH=D17 at Figure6 Maxwells equations It is perplexing that the whole crazy complex universe can be described by such simple, elegant, and even beautiful equations. In the end, social facts are produced by language acts performances that change the social world. (a) (ii) v= 100 8, 60ms~! Month Fish January May 850 100 ? You usually invest to make a profit. Also, the principal axis must be halfway between the minimum and maximum values, so it must be at 47 +13 =30cm hence d = 30. It is the problem itself that is the motivation, not possible real-world applications. The same is true of a mathematical proof. You recorded the values of the two standard deviations that your GDC gave to 3 significant figures as s, = 5.31 and 0, = 5.22, but forgot to note the sample size. TheIBdevelops inquiring, knowledgeable and caring young people who help to create a better and more peaceful world througheducationthat builds intercultural understanding and respect. Note that the ratio of consecutive terms equals a fixed constant. Hence the sides of the triangle are %, %, and % We rationalise and simplify to obtain V2 v side lengths of %, %, and 1, as shown in Figure 5.18. (b) Atwhat speed is the bicycle travelling along the ground, in kmh~'? Download Mathematics applications and interpretation IB Past papers 2021 PDF and use it for your revision. (a) $5057.31 e a3 u,= 2(8) (b) 59.2% ) 12 () 178 44. (b) Estimate, to 1 significant figure, the coordinates where the local minimum value of the function occurs. Generally it is also possible to identify this point on a graph. We applied logarithms to both variables to obtain the best linearisation, so it is appropriate to plot that data on a log-log graph (Figure 19.35). Author Suzanne Doering, Author David Harris, Author Panayiotis Economopoulos, Author Tony Halsey, Author Michael Ortman, Author Nuriye Sirinoglu Singh, and Author Peter Gray. (c) Interpret the gradients in your piecewise model. where Pis the power in watts A is the area swept by the turbine blades (swept area), in m? The boundary XY between the two types of soil is a straight line running from east to west and point A lies 70 km directly north of it. First examinations 2021 . (a) 2m 4. Consider the function y = tanx 8 sinx. Determine the equation of the line parallel to y = 7%){ + 4 that passes through the point (6, 1) 7. 17. (f) We use the same logic as in the algebraic approach to conclude that a reasonable domain is 0 < t < 4.51(s) and a reasonable range is 0 < h(t) < 56.2(m) Ly (4.51,0) Figure 9.9 GDC screen for solution to Example 9.4(e) In the next few examples we will look at building a quadratic function. IB Math AA vs AI. (b) Determine the amount of the substance remaining as t becomes very large. The full criteria for passing the IB DP are set out below and students need to be aware that a score of 24 points will not always guarantee a pass. (f) Find and interpret the value of R2 (g) Use your model to predict the blood concentration of this drug 4 hours after it is given. WebNew IBDP Mathematics: applications and interpretation courses- Syllabus Topic 1: Number and algebra SL content Topic : SL 1.1 Operations with numbers in the form a and 3xy are reducible, we can use the method suggested above. Also, some may consider the average to be 2845 12 _ 537 since the 284.5 is the total for 12 months and we average by dividing by 12. For this part, we can see that the lifeguard will swim the hypotenuse of a right-angled triangle, so we can add some more information to our diagram and we can use Pythagoras theorem to model the distance the lifeguard will swim, Ds. Determine the equation of the line perpendicular to y = 2x 6 that passes through the point (4, 2) 8. (a)Fyexaa =1 dy (b) P (c) e7dy = xdx dy=x2xy*+1 (e) (xylnx)y = (y + 1) () o () (1 +tany)y' =x* +1 ) %: (i) ysecOdy = esin0 G) dy i 1427 s % =efl+y?) + 1000(100) = 50 000 euros (d) Clearly, our model doesnt make much sense if the price p is less than zero. Find the value of k. (c) Calculate the time needed for the seat to complete a full rotation, giving your answer correct to one decimal place. After ts, the height of the bucket above the water level is given by h = a sin bt + 2 (a) Find the value of a. (b) Linearise the data using logarithms to find the best-fit model for this data, using v for speed and F for fuel consumption. Predict its flying speed. o 012345678910% Day Figure 9.38 The logistic model found by a GDC for the student example 339 Modelling real-life phenomena To help us determine C and k, it is helpful to realise that the logistic curve has rotational symmetry around a point with y-coordinate equal to y = % (this point is also a point of inflection). - 20dx 16.5 Evaluate (a) fej"dx (b) fsinlxcosxdx ( [2sinGx 5)dx () (@ [Joxds [emtndx Fa)=2 671 Solution (a) Letu = 3x, then du = 3dx tdy petde= Ly f ax dx = 3fe3x( 3dx) = fedu 1 s = 3e3+c du = cosxdx, and hence (b) Let u = sinx = fsmzxcosxdx f 2clu*:; 3+c*sm3x+c (c) Letu =3x 5,thendu= 3dx f25m(3x 5)dx = 2-fsm(3x = *%cosu (e *gcos(Sx = o)k 3 (d) Let u = mx + n, then du = mx fe"*"dxL 5)3dx = 3fsmudu femetnmdy= L m [en du*leu+[ lemx+n+c () F(x) = [x(xdr= [xide=2% Ry =21i+c=2+ Therefore F(x)= % '+ Examples 16.4 and 16.5 make it clear that Table 16.3 is limited in scope, because we cannot use the integrals directly to evaluate composite integrals. Tartaglia did not take Fiors money though; the honour of winning was enough. B @)N Bigenvalues : ; 1,2, eigenvecto rs = Gt Gt Comt 4 200 oI g =T iz *2i. What is the magnitude of the current? Best help when you need extra help on any math equation. Therefore, the watered area = % 7(3)2 = 3.75m~ 11.8 m? (a) Find ABC (b) Find the exact area of the sector BCD. The Platonist might want to try to find them somewhere in nature. A positive angle is produced when a ray ebTRL side is rotated in an anti-clockwise direction, initial side and a negative angle when a ray is rotated in a clockwise direction. An influenza epidemic hits a large city and spreads at the rate of 12e%2 new cases per day, where # is the number of days since the epidemic began. To do this, the boat travels directly out from the shore and measures the depth of the water continuously. (a) -z:%wzw = (=27 9(-22+20=4 (b) f'o0 =3x> 3x> 18x (c) f'(3)=3(3) 3(3)> 18(3) = 0 thereforex = 3isa stationary point. (c) Calculate how long it takes for the temperature of the water to reach 56C. (1.2) or log(~2) have no meaning at all. ( capital . (a) fit) = 60% 56 (b) f(30) ~ 24150 8. 9 Theory of knowledge Ma matics and personal qualities There are undoubtedly special qualities well-suited to doing mathematics. Webyou could enjoy now is Mathematics For The Ib Diploma Analysis And Appro Pdf below. The IV bag initially contains 0.5 litres and the drip rate is set at 2 m/ per minute. 123 A regular pentagon has equal sides of 24 cm. 0.0000 [0.2000 | 0.4360 | 0.7074 | 1.0140 | 1.3561 5 . So, a5 =3 +49 X 5 =248 = S5 = 25(3 + 248) = 6275 metric series A geometric series is the sum of the terms in a geometric sequence. P(Y>40 1) ! Scribd is the world's largest social reading and publishing site. 2 o ) go=b--3 (c)}ZbVb:5 (d) Point of tangency is at g(1) = 3 = (1, 3), gradient is 3 (given), equation of Tisy 3 = 3(x )= y = 3x. (a) Find the amount in his account after 5 years. These modelling assumptions give rise to a pair of coupled differential equations: (1) %:Ax*Bxy @ 22 3 =-O+g+p Dy A modern computer package gives the following evolution of prey and Population size predators over time: prey predator Time () Figure 1 Evolution of prey and predator populations over time 901 Theory of knowledge 59 4 ' || 254 | i: a4 'i ii I ioy L5 b4 v 3 1\4\\ 054 a wa w B w w s stastiiat SsrIRLIANIR: GAxNALE S va CRIRRFLNESNR EXNAETEAA AN SRR A by Eaa CrEtE et }Ci R s sv AR IRF IR sz b ae sl AERF NN Liibidtinii Friesreriay - i R WA CE iR iE W S reAambatecdl e s ,,,,,,,,,,,,, * o < = 0 02 04 06 08 1 12 14 16 18 2 Figure 2 A phase space diagram. 1 () (1,-1,2) 0 I 1 2 o),B: (vl) (a) Det=0 (b) A=5 @-3t1+41 = sera=s(_2)() (a) 0.772,0.129,0.099 (b) 0.756, 0.139,0.106 3 = g h %) =D=pP1ap= 1 0 14. The table shows the extension of the spring (cm) for each mass (g). In this case, we can construct a piecewise linear model by partitioning the data set into two or more subsets. @ 3) 21. The person who had solved the most after 30 days would take all the money. (d) Since the first maximum is reached 5 minutes after the first minimum (when the person board the Riesenrad, we can conclude that one complete rotation takes 10 minutes. These cicadas have a curious life cycle. 28. Some of the data collected is shown in the table. In electrical notation, Z represents impedance, and Z = R + j(X; X,). We see that a person would be at least 100 feet above the ground for 2.31 = t < 7.69 minutes. A sphere is carved out of a cube. SoIIIIInI gra L PPs N . 8. (a) ~384 () u, = 3-2" () 4,g = 2u, andu, =3 o) 935 u, = 10.15 0.1n u, = t,_, 0.1 and u, = 10.05 93 (b) u, =101 n u, = u, , 1and u, = 100 ) u,=972( -y and u, = 972 3) z( 3)3\ ) u, = 2uy yanduy = -2 390625 28 @ Y7689 ) (b) u, = 35(7)o u, :;u" Sl =35 5 . Find the equation of each line. 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