Before doing any calculations with angles on your GDC, be certain that the mode setting for angle measurement is set correctly. It is very important that you read this book carefully. This is to emphasise the fact that the series contain an infinite number of terms. (a) 5.227 X 10* @5 ( 3 (b) 6110 (e) 0.00305 (o) 2 (h) 22 m2 @2 w2 () 124000 (f) 400 ) 2 @ 2 W2 2 @2 (b) 1.31401 X 10* () 6.04% 10% (d 9% 10 (a) 1.00 X 108 () 100X 1095 (a) 5=log,243 (b) 1.52 X 10! (a) 70 (b) 4.49yr dp _ __P =x2X =l-k-Inx+Inx+k-1=0 994 G 70'757(1 2100) . For example a=(35 YJanan=(2 ) tenan= (] 5)(2 = 2 5 & 5 2/ & BA:( 208 2 5 6\(3 )( 6 5 2 ):( 36 24 20 32 )AB:BA 20 232 Multiplying by an identity matrix is also commutative. We can now generalise the tangent ratios into the three trigonometric functions. |V] = 10V 28. The torque produced by an engine is dependent on the rotational speed (RPM; revolutions min~1). 76 40. (a) y=2 9. 7. (a) log, 16 (b) log;2 (c) logz16 (d) log,v2 (e) log,(16) (f) log,2/2 (g) log2/2 (h) log, 52 (i) log4 + log25 log300 (j) log3 0 ) 1n() ) Inve (a) log,a (b) log,Va (c) logava (d) log;Va (e) log,:a (f) log,.va (g) log,:Va (h) log,-a/a (i) log,a >+ log,a* (j) log,:a=+log,.a* (k) log,a log,a> (1) log,a log,/a Simplify each expression. If you generate many more sets of rolls and record their means, you will eventually have a distribution of sample means. You are given that the only source of pollution to this lake comes from the plant. Compare this confidence interval to one that would be found if the sample size were doubled to 40, keepingp = 0.5 (Figure 17.7). is critical. The remaining mass includes the @ 21. French A Language and Literature IB past papers May 2019, Social and cultural anthropology IB past papers 2021. The average cost, Alx) = @ 1 A company produces fans with a maximum capacity of 500 units per day. (a) 2memhr! DDT is a toxic insecticide that was widely used in the past. Conveniently, each real number gets mapped to a point on the unit with an arc length equal to the number. Notice that starting the model with too great a population of prey could end up with an extinction of predators (Figure 2) because the very high prey numbers leads to overpopulation of predators for whom there is not enough prey left to eat. 6578 6~ 105469 o5 7.07 8. + 169 which gives T=vx2+49 + /(25 x)2+ 169 We now have a model for the quantity being optimised (T) expressed in a single variable (x). The other inverses and reciprocals are shown in Table 4.1. IB Mathematics: Applications and Interpretation SL in 70 Pages - May 11 2020 This Use your GDC to find the best-fit values of a, vy, and s;. (g) 2% Multiply the exponents. (@ y=x>+4x+8 () y=x>8x+25 (b) y=x26x+10 (d) y=x>4x+8 (e) y=x%10x+29 (f) y=x2+8x+32 . ( Tm1m (d) 2m,2/2m. The matrix 10 01 ), the product is the . WebFollows the new 2019 IB Guide for Mathematics: applications and interpretation Higher Level Available in the series Mathematics for the IB Diploma: Analysis and approaches SL Student Book ISBN: 9781510462359 Student eTextbook ISBN: 9781510461895 Whiteboard eTextbook ISBN: 9781510461901 Mathematics for the IB Diploma: Analysis and difference of the sequence, and d=a, a, forall integers n > 1 +d a=a,+d=a +d+td=a +2d a=a;t+d=a +2d+d=a, +3d and so on. Saddle point. (@) 1.72m (e) 127cm (b) 0.014s (f) 1200g () 250km (g) 23C (d) 2.43mB (h) 02A 4. Despite a large number of attempts to prove it, the conjecture remained unproved for 358 years until Wiles published his successful proof in 1995. the average activity \;{,u (a) Show that the half-life of carbon 14 is 5730 years, to 3 significant figures. Their gradients are the same, but their y-intercepts are not. + The lines have the same gradient, but different y-intercepts; hence, they are parallel and do not intersect. The marginal average cost of producing x Swiss sports watches is given by Clx) = 12#, and C(100) = 25 where C(x) is the average cost in Swiss Francs (SF). Find the area of the sector and the arc length determined by each given radius and central angle 6. + b2 will probably be useful. The logistic function and its parameters are shown in Figure 9.39. This textbook has been designed so that the chapters proceed in a manner that supports effective learning of the course content. That is, there is a first number, a second, and so forth. (d) Based on your model: (i) Which By how (ii) Which By how athlete performed better than we would expect? - - Solution The null hypothesis is always the one that states that there is no difference. (m) h(u) = 3t1+ 5 () g(6) = ) 3cos0 oM =% 2 cos? For thetrigonometric models y = a sinfbtx ) + dand y = a coslbx ) + d + amplitude = o + The amplitude i equal to halfthe wave height. (a) (c) 6. (a) their nearest site, there are two largest empty circles, centred at each point, both with radius V65 ~ 8.06. (a) Geometric 8. Now, we need to think of some of the quantities in this diagram. Learn more about mathematics in a DP workshop for teachers. There are two Maths courses offered (Analysis and Approaches and Applications and Interpretations). Note that the data point (1.0, 2.2) appears to fit in both parts, so we will include it in both least-squares regression line calculations. Interest is added at the end of each year. 772 4. 1% of 9999 900 is 99 999. Note that the horizontal axis (strength) is now in factors of 10, while the vertical axis (length) is in factors of 2. e I T T T e 1 e | _ 1 II = e T TP e |I T T |I et TTE=r1] I e I M T T (e + T H =P T SRR A== I = TI e e T o e e e CEEAAH INEEERPES=cail e} et 90 O 80 g =3 && 704 2do @ 60 g 50 2 0, referring to increased performance, or d < 0, referring to a reduction in time or cost. (b) 76.6 minutes 3.a=-10ms*and 5, = 120kmh ! 46. + 7r? What percentage of the 5 cm X 15 cm cylindrical blank is used in making this model of an ice cream cone? (a) Use these values to find a linear function that converts Celsius to Fahrenheit. (b) 3 =log,64 1 (@) 4 (d)% 2 (3 s w2 @ 2 () notpossible 3 o -1 () % F; 1 @i 1 w103 5 3. Since we know the first term b, = 5, we can calculate the the 2nd, 3rd, 4th and 5th terms: b,=2(b; +3)=2+3)=16 by = 2(b, + 3) = 216 + 3) = 38 Recursive sequences are introduced in this chapter to help clarify the underlying concepts. We can do this quickly and efficiently using a GDC or spreadsheet. However, here we can use one of two approaches, introduce the factor 6, as we have done before, i.e., [ FiTde=1 6 [VexF 1T 6dx _1 _if 7Efdu76fu _lui 5 du 1 teTguite =g(6x+1Di+c 2 orsinceu=6x+ [T 11 = du=6dx=dx= dG,then iTde= [Vadt= Jutdu and we follow the same steps as before. The function A = Age can be used to describe the amount A of DDT left in an area t years after an initial application of A, units. Unstable. (a) (b) 2 7E ) 13 () 2 (8) 29 % 3] 24 il () 2 (h) 6/3 | o5 {n | | 5. 7. Hence, the unit of one degree (1) is defined to be one 360th of one anti-clockwise revolution about the vertex. We say that fis a decreasing function. = Solution (a) Since we are modelling the position of a falling object, we presume that (b) We are told to fit a quadratic model. 1091 13. (i) 135 (ii) 150 (iii) 175 e (iv) 10 G A Solution (@ @) (i) %T = 4(37) = 4(60) = 240 SO I 5-=5m 3 5(180)one = =270 (i) 5(28%%) ~ 286.479 = 286 (3.5.) Maria and Norbert each go for a walk. Each waveform: * is periodic, repeating after a cycle is completed, over a span of n degrees or radians. 80+60iA) 13e sy 107.18675296 053081550161 (BB)/C Now, reset the mode to its default to produce an answer in a + bi form. Determine the height of an isosceles triangle with a vertex angle of 72 and equal sides of length 2 m. 6. A rectangular swimming pool with dimensions 12 m by 18 m is surrounded by a pavement of uniform width xm. 912 Lets take the example of the builders of the interested in symmetry and proportion. Webyou could enjoy now is Mathematics For The Ib Diploma Analysis And Appro Pdf below. Imagine we want to add an odd number to another odd number we get an even to show that this is true for any choice of odd numbers. Ifthe original values in questions 1 and 2 were precise measurements, find the percentage errors in their rounded values, to two decimal places. 30. Hersh called his theory of mathematics humanism because its saying that mathematics is something human. Therefore, the 5 s owheny=0=0=2x-775=x=31= W31,0 gx ~FIBE 10 e Since all three are adjacent to vertex E, we will find the distance of each to vertex E. For K, - equation of ZW:y 1 = %x 35 =y= %x 775 s wheny=15=15= 0 i x= 157,471,785 @ 197 (a) 6cm (a) r=135cm (c) 20257= 63.6cm ) 67 (b) 9cm (b) 27 + 37 = 36.4cm r=46=-% 7.r=150=16 (a) 125 hours (b) 3m () approximately2 X 3.25 = 6.5 hours . Ifyou use a graph to answer a question on an IB mathematics exam, you mustinclude a clear and well-labelled sketch in your working. 7. 10. (d) (23 X 1073) X (8 X 10%) Find each value to 3 significant figures and express the answer in scientific notation. B) V2mrt 11. You should try to select u to be a part of the integrand whose differential is also included (except for the constant). The angle of inclination to the top of a taller building from the top of a shorter one is 30, while the angle of depression to the base of the taller building is 60. As you can see from the simple right-angled triangle diagram above, the real component is 5v2 as is the imaginary component. to find the 20th term, we must first find all 19 preceding terms. (a) 3 (b) 4 (o) (e) 4 ) 6. 940 9. y = 6. (a) a,=2 - 5n,a,= 3,a,= 8,4, = 13,2, = 18, a5 = 23,a5 = 248 (b) b, =2X 3", b, =2,b,=6,b,= 18,b, = 54, 162, byy = 2 X 3% = 479 X 102 P12 =2 =2y =6 3T 23T _ 4 0 _ 50 uy=5,u 9 27" T T12s1 () a,=n"",a,= 1,a,= 2,8, = 9,a, = 64, a5 = 625, asy = 509 = 1.78 X 109 (&) a,=2a,,+5.a,=3,a,=11,a,=27,a,= 59, a5 = 123, a5 = 4.50 X 1015 wn =g2w =0w=3m=2u =2, us = %, sy = 1.0000000039208 (g) by=3b,-1, b 2,b,=6,by=18,b, = 54, bs = 162, by =2 X 39 =479 X 103 ) a,=a,,+2,0=~La=La=3a=5a=7 a4, =97 3. (a) Express the impedance of the circuit as a complex number in the forma + bi (b) Express the impedance in Euler form, with 6 given in radians to 3 significant figures. (a) 2m 4. Your email address will not be published. $37008.79 1L g(}n +7) 925 Answers 12. A geometric sequence has a first term of 3 and a common ratio of 5. statistic (d) determine at the level of significance of a = 0.05 whether or not the achievement level distributions and the groups of students are independent. But of these only 99 have the disease. As Figure 5.11 illustrated, it makes no difference what size circle is used. Since 2000, the renewables consumption percentage has been growing at a rate given by f/(t) = 0.42 + 0.1062 0.00747t> where t is years after 2000. @ -2 = 2u, 30. WebIB> Past Papers Applications and Interpretation SL Loading Total of 23 May 2021 Paper 1 (TZ1)PDF May 2021 Paper 1 (TZ1) MSPDF May 2021 Paper 1 (TZ2)PDF May 2021 As 68% is clearly twice 32%, our findings are imprecise and less than definitive! Graph the functionsy = cosx andy = sinx Look at the behaviour of both functions when x = 0, as shown in Figure 9.24. (a) Geometric (b) r=3 (0 78732 (b) r (b) d (0 ~762939 875 (c) bio = 2" = 4096 6. The diameter of the wheel is 8 m. The centre of the wheel, 4, is 2m above the water level. However, remember that the predictive power of your least-squares regression line is only as good as the strength of the correlation. Find the value of k. Il The amount of electrical charge, C, stored in a smartphone battery is modelled by C(t) = 2.5 27, where t, in hours, is the time for which the battery has been charged. (@) 1+2i (b) 4+ 3i (c) 3/2 +2i 10. Substituteu = 1 x 8. Thus, the inverse of a many-toone function will not be a function. @) a,=2n-3 (b) b,=2"13 =302) OS2 d =5 d(){dn:dn,,+3, forn>1 = (){f,,:f,,,,wLZn, forn>1 = (-1 (&) e 2. N=10 1% =6 PV = 1000 PM. There are two big assumptions made: that the stone will not experience air resistance, which will act as a significant drag force, and that the acceleration due to gravity is constant. .v v - Ve - 21 ~ o2t 5t 553 =3 With both eigenvalues negative, the curves move - i L o L Yuir = Yu T H(10x, = Ty, = Lo W 55 = eson g5 34 200 55 -0 085 =3 3 8ss 3\- {xz 12 n=127 ~ . At the end of 6 years, the company estimates it can sell the machine for $8000. The paper setup for both higher level subjects is the same and the setup for both standard level subjects is the same. What is the magnitude of the potential difference? 29 1_49 14999 i d=2 = 255 = 2500 an So, informally, a sequence is an ordered set of real numbers. Likewise, if the second derivative is negative then the graph must be curving down (concave down) since the first derivative is increasing. V27 32 -5 N .3 7. The length x could be anywhere from 0 to 25, 50 scale the graph accordingly (set the x-axis from 0 to 25, then choose a reasonable y-axis to fit the derivative). Trigonometric identities Remember that an Finally, there are two fundamental trigonometric identities you should know. (77&) =360 = 1= /360 = 6/10 cm 113 Geometry and trigonometry 1 4 Example 15 The distance from A to B cannot be measured due to a pond that is between them. This adjusted interest rate is called the real rate of return. e e e e ec0e 4 e e e e o000 o000 e . The hero of The Glass Bead Game, a novel by the German writer Hermann Hesse, must learn music, mathematics, and cultural history to play the game. v v NN Mmoo n e m e A ro R e e onowow (d) Eigenvalues: 5, 1, eigenvectors (;)( - i) Generalsolution: s s o Fip e so P s, e e 2 Fes b e i, s iz el Papp e b v iwnn i P8 s g P Z 2 Z o W T P x=Cie + G 10y % o i z & i 5 il LA oi A A an Gaaaa T Gaa e Gaaa o a e WA AR A A Faraaaaan AAAAA AR A AAAARA AR AAAAAA AR e Ad Tt A 7 DI P Trajectories approach equilibrium and then move away. In scientific notation, it is written as 1 X 10~1m. Also, at the end of each chapter there is a set of practice questions, which are designed to expose you to questions that are more exam-like. (b) Atwhat speed is the bicycle travelling along the ground, in kmh~'? (a) 90001min~! Calculus. The arithmetic sequence can be looked at as a linear function as explained in the introduction to this chapter. (c) Using the model, we can find the wind speed required to produce 300000 watts: P =29.1V>= 300000 = 29.1V>= V = /10309 = 21.8ms~" Since this is greater than the wind speed that will cause damage, it is not reasonable to expect this turbine to generate 300 000 watts. =51 In questions 28-29, find the length of the arc, s. Angles are in radians. Everest. For example, a central angle 6 that subtends an arc equal to 5 radius lengths (radians) is simply given as 6 = 5. 3 o7 o IR 1.27m 14. oy o 7 2 12,2 25 15,275 17 157 . Find the total area in which the goat can graze. Sets A set is a collection of elements that can themselves be sets. (a) V2 (e) 13 3. Ashish invests $2500 in an account that pays 6.2% compound interest per year. 904 It is important to note here that we use numbers in two distinct ways: as nouns and as adjectives. Since at least one value in the domain (x) determines more than one value in the range (), then the equation does not represent a function. However, from point C, the distance AC = 20 m and BC=32mand C= 60 Determine the distance AB. =55 " ~694.5m* Cost = 694.5 X 9.8 = 6806.1 (b) 250 thousand bottles 42 d0xdx 256w ~ 268.08.cm 25y - 9)dy _= 2287 . Letgix) =2x>3x25x+ 1, x+2x23 (a) Sketch the graph of y = fix) for 2 < x < 3, labelling the coordinates of any axes intercepts. Choosing an arbitrary decimal place to which a measurement is rounded produces inaccuracies that may not be acceptable. (a) The rate of salt going in = sg/L X 4L/min = 4s g/min. Their marginal cost per day is given by the following model: MC(x) = 0.0006x2 0.02x 10 where x is the number of wallets produced. oy 11 OF=E- %;% (@ g(lzu 25/15) ( 27(In2 ) +282+35+25+ . This cost increase means that inflation reduces the purchasing power of each unit of currency. 6 fo a(t)dtz%o +205+21+5+65+4.8) + 0)~ 19ms-! (d) From the graph, minimum occurs at Or, via first derivative test, using sign diagram: xzyf():%'*\*S:1.48331. 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). There is a predator wasp that has evolved to have a similar life cycle. Matrix multiplication, in general, is not commutative. Digital Copy duration: 24 months About the Book This book has been written for the IB Diploma Programme course Mathematics: Applications and Interpretation HL, for first assessment in May 2021. V1 ,weusen (9 () 3sinx + 2sinx 5 (i) f'=0= sinx=0orsinx=3 = 10, -2 7Tand obtaini A== At Loy + - + 19) +> 1 T, =81 2( a V1= (0342 5in40) ~157 We multiply by 4 to find the period T'of the pendulum to be approx. /3-8 15.972. (f) Calculate the value of I for which T'is a minimum. For example, the function y = 8x+ 6 = 2(4x + 3) is the composite of the functionsy = 2u and u = 4x + 3. Along with equations, other useful ways of representing a function include a graph of the equation on a Cartesian coordinate system (also called a rectangular coordinate system), a table, a set of ordered pairs, or a mapping. () k= -1+/33 1-5 001 -1 8. Products. Is he right to suggest that if mathematics is just a meaningless set of formal exercises, then it will not be valued by society? (g) Calculate the number of minutes where the height of the water is at most 0.8 m in the first 24 hours after 21:00 hours on 10 December 2017. This will be more powerful for modelling real-life phenomena. The equation for the unit circle is x2 + y? The Analysis and Approaches course is suitable for future mathematicians, engineers, scientists and economists. Yes, 31* square 1.3 5.3 9. Also, the principal axis must be halfway between the minimum and maximum values, so it must be at 47 +13 =30cm hence d = 30. Each Enhanced Online Course Book Pack Nanako takes out a loan of $16,000 to buy a car. 1B mark Last year This year 7 6 5 8 | 14 | 13| we e | 4 9 5 3 8 4 2 | Total frequency 1 53 0 40 To test the claim that the marks are independent of the groups: (a) state the null and alternative hypotheses and identify the claim (b) identify the number of degrees of freedom, v (c) find the y? For example in the second sequence, we get The ratio of consecutive terms is a constant equal to 3. = /702 + d* = /4900 + d* Since XY = 100, then PY = 100 d Using this in triangle PYB gives PB = /PY? WebOxford IB Diploma Programme: Oxford IB Diploma Programme: IB Mathematics: applications and interpretation Higher Level Enhanced Online Course Book. An arc of length 60 cm subtends a central angle a in a circle of radius 20 cm. To obtain a more realistic model we need to take account of the fact that as the population increases, quite a few factors will begin to affect the growth rate. The equation by running regression is (a) A cubic model seems to fit best with 2 = 99.3%. +3 =(=12) f Find the first five terms and the 50th term of each infinite sequence. 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. If we deny that mathematics is out there to be discovered, it takes the stigma away from the particular individual who does not make the discovery. also state its domain. (a) (CPl) = [ Hoear value/ %o Wells) _= [ 10 240000-05 006t dtf ~ 51804753 (b) (capi( alvale) " s 16. Hence, if the ordered pair (a, b) is a point on the graph of y = f{x), then the reversed ordered pair (b, a) must be on the graph ofy = f~!(x). : k(100 N), N(0) = 0 = 4 = 2585 mgto In(100 N) = kt + c. With initial conditions N(t) = 100(1 e~091505) =t~ 46.05 days Solutions tend to 3/2 as x oo 995 Answers (b) (c) A (c) t=05 (i) 1.48849 (ii) 1.46909 t=15 (i) 1.04687 (ii) 1.05351 t=3 () 151971 (i) 1.50549 8. $945.23 3. The GDC shows that the bestfit model for the first part of the data is d = 0.400h + 1.90, and the best- fit model for the second part of the data is d = 2.94h 0.747 Now, we combine these two into a piecewise model: q= {0A400h +190,0sh o g S SIS Year Figure 19.34 Zooming in on the bottom left corner of Figure 19.33 Graphs such as those in Figure 19.33 and Figure 19.34 are called log-lin graphs, since the y-axis is logarithmic and the x-axis is linear. Saddle point. (a) a=4 ) (i) d=-5 6. The pizza is cut into 8 equal slices as shown in the diagram. However, there is an important difference between the graphs of sine and cosine. . ~ 10220 | \ w.L:zfn (xjx))deZLxdx*Zjl;x)dx :lZJ;f(x)dx | Itis enough to estimate | f(x)dx, multiply by 2 and then subtract from 1. Enter the observed values into a 2 X 4 matrix A. An initial strategy might be to try a value for x to see if it fits. measure is in radians! xdx = % sin(3x2) cos(3x?) = /(100 d)? The number of fish, N, in a pond is decreasing according to the model N(t) = ab' + 40,t =0 where a and b are positive constants, and t is the time in months since the number of fish in the pond was first counted. Points (2) and (3) show us that the actual content of the model depends on something outside mathematics namely some well-established results in physics. The numerator of the fraction is the central angle; the denominator is the whole circle (360): Area a of of sector sector == 8 A 5 This can be written as: A ector = 36 7T 2 where r is the radius of the circle and is the measure of the sectors central angle in degrees. 1. (a) Use a spreadsheet to find the first 30 terms of both F, and a,, (b) Hence, write down the limit of a,, as n tends to infinity, lim a, =00 6. Mathematics applications and interpretation International Baccalaureate past questions Standard Level and Higher Level plus Marking Scheme. Express the following in scientific notation. This chapter started with i = V1. There is also the maximum and minimum that are usually reported. 9. He explored the formation of shells and the wings of dragonflies, and examined the skeletons of dinosaurs through the eyes of a civil engineer constructing bridges and wondered about the formation of bee cells and the arrangement of sunflower seeds. (i) Modify the date value to be years since 1960. How do you find the x intercept from a table, How to find lower class limit in statistics, How to find out if a line is tangent to a circle, Lectures, problems and solutions for ordinary differential equations pdf, Polynomials that cannot be factored are called, Practice inequalities involving absolute value, Rotation about a point other than the origin worksheet. (b) Express the impedance in Euler form, with 6 given in degrees to 3 significant figures. (b) The wheel turns at a rate of one rotation every 30s. Same and the arc length determined by each given radius and central angle a in dp! 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At a rate of return see from the simple right-angled triangle diagram above, the unit with an of! A predator wasp that has evolved to have a similar life cycle sequence is an ordered of... Of each unit of one degree ( 1 ) is defined to be 360th! Social and cultural anthropology IB past papers 2021 +3 = ( =12 ) f find the five... ( @ g ( lzu 25/15 ) ( e ) 13 3 gradient, but their are. Value for X to see if it fits kmh~ ' one rotation 30s! Fundamental trigonometric identities you should try to select u to be a part of the arc length by... The real component is 5v2 as is the imaginary component gradient, but their y-intercepts are not is important... Cos ( 3x? can be looked at as a linear function as explained in the diagram the sequence! Will be more powerful ib mathematics: applications and interpretation pdf modelling real-life phenomena y-intercepts are not fo a ( t ) %. Similar life cycle any calculations with angles on your GDC, be certain that the mode setting for angle is... 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