ib mathematics: applications and interpretation pdfib mathematics: applications and interpretation pdf

(c) Use your least-squares regression model to predict the marathon time for a runner with a 5 km time of 20 minutes. Please get in touch via the contact form if interested. Rl Xy + H(=5x, + y,) S =t b, = 29,) 7 N [ xact: =X, 2 b demz2 emsea % =055 \n =188 . The question for your mathematical intuition is: What is the probability that X actually has the disease? (You should recognise this as being a problem of conditional probability.) (a) Calculate the amount of money in the account after 6 years. = u(wdx 5ltb0) = Jau=u+e ) %{sin(u)} = cos(u)u'(x) = d(sin(u)) = cos(u)u'(xdx f cosudu = sinu + %(cos(u)) = sinw)u'(x) = d(cos(u)) = sin(uu'(x)dx fsinudu = cosu+c e Alm) = T A wwn= -1- = 4] = wwds | fwdu= 00+ ane - -1 tan = L) d ey (o) == = dtanw = w()de euy e(n) = dle W) == e ety () de inlul) == 29 Juce = dlinful) ul) == ioful) () ) ok du=tanu+ U gy = et+c Jerdu=et dx [i du=1nlu| d=tulud++ Table 16.4 Integration formulae Example 16.6 Evaluate: 672 [(sx + 2)8dx (@) [V6x+ 11 dx () [t VX' 8x+13 (d) [xsint(3x?) WebMathematics - Applications and Interpretation SL - Hodder 2019 - Free ebook download as PDF File (.pdf), Text File (.txt) or read book online for free. 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 Paper 1 (TZ2) MSPDF May 2021 Paper 1 (TZ2) SpanishPDF May 2021 Paper 2 (TZ1)PDF May 2021 Paper 2 (TZ1) MSPDF May 2021 Paper 2 (TZ2)PDF May 2021 Paper 2 (TZ2) (b) Find the most appropriate non-linear model using linearisation with logarithms to model mass lifted 1 in terms of weight class w. () Find and interpret the value of R? each element of set X All the various ways of representing a mathematical function illustrate that its defining characteristic is that it is a rule by which each number in the domain determines a unique number in the range. IB Applications and Interpretations SL and HL Resources. Then dx = du, and f% dx = f}u(*du) = j% du = Inu + , u > 0, butu = x, therefore whenx + 2,and so du = 3x*dx. According to data published by our local airport, Approximately 2 million passengers used the airport in December. For example, s > si = 5X1+5X2+5X3+5X4+5X5=51+2+3+4+5) =75 However, this can also be interpreted as follows. Solving algebraically, we have: 0= 5p2+1000p = p=0,p =200 Therefore the p-intercepts are 0 and 200. Test the claim that the outcomes and teams are independent at the level of significance of & = 0.05 Football, 10 seasons w Barcelona Bayern Munich D L GP 290 58 32 380 245 54 41 340 (Optional) Use the 2-sample proportion test on your GDC to test whether or not the percentage of wins of the two teams in question 7 are statistically comparable at the level of significance of @ = 0.05 pter 18 practice questions 1 Determine the number of degrees of freedom v in each situation. statistic, using the values above as actual observed data. 9. We know that neither of the assumptions in (1) is true. First of all, we need to state a claim and the hypotheses before we continue by finding the expected values. In other words, the difference between the two models is small when the linear correlation is strong, so predictions of x from y are more reliable. Given that the Roman 0.0001216 empire existed about 2000 years ago, this appears not to be 23. 3.32 2,34.32 ] 5. Find the value of b. As shown in Figure 5.11, when 6= 1, then arc length = radius. The proof is way beyond the scope of this book, but there have been a number of interesting books and TV programmes made about it, including Simon Singh Fermats Last Theorem (1997) and the BBC Horizon programme Fermats Last Theorem (1996). 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. [IQ1iIglICRSEIS Consider the function f(x) = 2x defined over the natural numbers. The first term of an arithmetic sequence is 2 and the 30th term is 147. Now, suppose we want to find the sine of this 45 angle. (You could try to prove that this is a stationary point - it is not hard.) A moneychanger exchanges 250 THB (Thai Baht) into 400 PHP (Philippine Pesos). (e) Interpret the coefficient of determination for the model. It is useful to write the differential equation in the equivalent form dy y Z-ii-2) o - o dy where k = by,and L = Equation (1) is called the logistic equation, and the corresponding population model is called the logistic model. (a) a=19,b=2 (c) 348=x=852 L@ P = () 5.2 minutes b= % () 10 seconds () 15 16=r=20 5cm A=15C=20 b=90 15 (b) 11m always sometimes never never y=210 y =160 5. In this case, we can also find the explicit form y=y2Inx +c Example 2 d; Solve the initial value problem Ey = Solution Separate the variables and integrate: dx _ x+1 & y s o dy dx dx :>f7:fx+1 840 XT _ y1) =4 ln|y| :1n|x+ 1| S = |},| = elnferifte ghnfet1]ge |x +1 e Now, since is an arbitrary constant, we can replace e with a constant C, and our solution becomes: | y| =G |x i 1| Using the initial condition: 4=cli+1]=c=2 and the particular solution is | y| = 2fx+1 thatis y = +2(x + 1) Example 20.8 Solve the differential equation x dx + e**) cosydy = 0 Solution The equation can be separated with a few steps: xdx = ecosydy = ecosydy = xe *dx = |ecosydy = 7fxe"dx Using integration by parts and simplifying we get the implicit general solution: %ey(siny +cosy)=e*(x+1) + Differential equations as mathematical models The following examples illustrate typical cases where scientific principles are translated into differential equations. Figure 9.35 Diagram for question 6 (b) After six minutes, the seat is at point Q. Measuring angles: degree measure and radian mea: Perhaps the most natural unit for measuring large angles is the revolution. 92 (c) For the interval 1 < < 3, find the time at which the velocity is a minimum and find its value. This book is designed to complete the course in conjunction with the Mathematics: Core Topics HL textbook. This was a decrease of 6.2% from the previous year. 963 Answers (b) 9 = 1300(0.95/1n0.95) 700(0.75)"(1n0.75) dn = 66.70.95/" 201(0.75)" () Increasing for 0 < n < 4.68, decreasing for n > 4.68 (d) 0= < 2.1 from the start until early in the third year. == Solution (a) Each year the amount in the account increases by 4.5%. 10. We hope could proceed by the result is even: 1+3=4even 5+ 7=12even 13-F9:=22/ven 131 + 257 = 388 even You can see that this method will not serve as a proof because we would have to check every possible pair of odd numbers and, since this set is infinite, we would never finish. length of the radius), the ratio of arc length, s, to radius, r, F : 5 g Si_%_% for a given circle will be constant. X (9.5 X 1072) = (23X 95) X (107! The reason is that they want to make generalised statements. Consider the diagram in Question 3d. The data in the table shows a sample of the data collected. In order to model this situation mathematically, we amend the differential equation leading to the modest exponential growth law we introduced by addition of a term that slows the growth down as the population increases. For students taking their exams in 2021 there is a big change to the IB syllabus there will now be 4 A scientist studying the how this chemical decays wrote in his notes that the data in an experiment could be modelled with the function A(#) = 500(0.5)" (a) Find A(0) and interpret its value in context. 0 _ 3 = .0882 radian (b) ~6.79cmmin~! The depth, d metres, of water in a port is modelled by the function d(t) = p cos(qt) + 7.5 for 0 < t < 12, where is the number of hours after high tide. NENOTR 0 Itis concave down if and only if a < 0 2a + Symmetry: The graph ofthe function is symmerical about the vertical line with equation x= -L Thislineis clld th axis of symmetry. made at the beginning of each year. The range ofa function can be found graphically or by analysing the function algebraically. WebIB Past Papers All International Baccalaureate (IB) Maths Past Exam Papers for Analysis and Approaches (standard and higher level) and Applications and Interpretation The activity is the number of nuclei that decay per second or becquerel (Bq). Estimate the number of pages in this textbook. 4. (a) 3 s (b) Ao . In this sense, the tangent is analogous to the gradient of the terminal side. 304 + Maximum/minimum: The function has a maximum (when concave down) or minimum (when concave up) where the graph intersects the axis of symmetry. Example 3.2 shows how this is used. (b) Write down the height of the building. Read Download PDF Mathematics - Applications and Interpretation SL 2 Free, Update the latest version with high-quality. Find the distance between each pair of points. We conclude our study of trigonometry by learning graphical methods for solving trigonometric equations. (@) P(6,~1), Q(4,5) (b) R(7, 2),5(1,8) (o) T(1, 4), U(8,0) 19 Geometry and trigonometry 1 . Lets call the total length T. We know that T = [ + m 606 Using Pythagoras theorem and the equations T = [ + m and RS = 25 x, we can write: P=x2+7 m? In each of questions 1-15: (a) Determine whether the sequence is arithmetic, geometric, or neither. Find the inverse and domain of each of these functions. 15. Wediscard r = 0. ;w:ly:xxZ shll dx#fydy:fxxz dx :>%y1:lnx%+c This is the general solution of the differential equation in implicit form. 0.8 0.387 (c) Find the value of R? 5 = [~- 1000 1000 + , with C(100) = 25, 10. The IB Math AI Formula Booklet is useful for two reasons: 1) to easily refer to formulas when solving questions, and 2) to get a high level view of the full scope of the AI SL & HL courses. (a) 2308 (e) 570.03 (b) 2300 (f) 0.0003 () 1000 (g) 0.00320 2. In AC circuits, impedance (Z) is the measure of resistance that includes reactance due to capacitance (X) and inductance (X;). Solve each equation for x. Ina + biform, V ~ 3.83 + 8.83i N _..9.622784407 s6sselesa 193 Complex numbers Impedance j1g[cTelyY] Physicists usej to represent the imaginary unit i to avoid confusing iwith [, the current ina circuit. Consider the point on the floor directly below point B and call it B'. For example, for a sequence of values a,, the corresponding series is the sequence S, with Si=ay+tay++a,, +a, If the terms are in an arithmetic sequence we call the sums an arithmetic series. (e) Describe what happens to the activity of the substance after a long period of time. We will consider the case in which equal payments are made annually, and interest is compounded annually at an equal rate at the end of the year. 3 23. . What is the distance from the centre to any vertex? The second function is flx) = 3x+ 2inred. The largest object in this region is the dwarf planet Ceres, located 2.77 AU from the Sun. 0 FV =1790.85 PY=1 ay PMT: END (b) Using the TVM solver, enter N = 40 and payments per year, PpY = 4 N=40 1%=6 PV=1000 PMT =0 FV=1814.02 PIY C PMT: END (c) Using the TVM solver, enter N = 120 and payments per year, PpY = 12 N=120 %=6 PV=1000 PMT=0 Vv =1819.40 PIY C PMT: END Real rate of return In Examples 3.10 and 3.11, the interest rate used to calculate the future value of an investment was the nominal rate. )= ar(r + 5r%) /5)ar? Interpret the slope and intercept in context. and variance o2 737 17 Inferential statistics 5. Evaluate: (@) [x(Gx>+7)dx () fdx 22550 + 2 dx [2eV5x @[5 BrakP, @ Jrer=7a ( . The maximum height can be found at the vertex of the parabola, at T OW 2(4.65) y=ax*+bx+cis givenbyx= L- o7 The height at that time is 5(4.97) = 4.65(4.97)% + 46.4(4.97) + 0.687 = 116 m 15 G 1, R R Identify the most likely logarithmic linearisation and the corresponding model for each scatter diagram, or state that logarithmic linearisation should not be used and give a reason. How much of the wire should be used to make the square and how much should be used to make the circle in order to enclose the greatest amount of total area? =3X(-2)-5X8+2X10=26 and s 1 apfb,|=2 an =Y k=1 auby=0@n =220 by 7)|-4 bsy 1 = 1 XA 765 =53 Repeat the operation for each entry in the solution matrix to get: 34 C=AB= 26 33 21 Figure 7.1 Usinga GDC to fin = We can also use our GDC to find the product. OH No! For each of these derivatives, find f. (@) f'(x) = 4x 15x2 (b) f) =1+ 3x> 4x, f1(0) =2, fl1) =2 () f/(t) =8t sint (d) f(x) = 124 8x + 7,f(0) = 3 (e) f1(0) = 2cost sin(26) 675 Integral calculus 1 3. Example 3.9 (a) Find the 12th term in the sequence 3, 12, 48, 192, 768, (b) The third term of a geometric sequence is 5 and the seventh term is 405. - Solution (a) Note that in 30 years, Christine has invested 30 X $1200 = $36,000. What should the selling price of each unit be to have a profit of 20 per unit? (a) 0.78% (b) 63.93% () (a) 0.01% (b) 0.00% (c) 5. Solution (a) Substituting into the formula gives: 232 X110 10712 = 10log,(3.2 X 107) = 75.1dB n(3.2 X 1079= = 1olog,,,( 5 . Consider fix) = log; x, x > 0. fsi.n(3x2) cos(3x?) Paper 1. A tent flysheet is to be tethered with string to a nearby tree on level ground, 1 m away. The Platonist, on the other hand, finds it hard to identify mathematical structures embedded in the world or has a hard time explaining why they are there. The time it takes for a runner to complete a marathon can be predicted from the time it takes to run 5 km (Table 19.14). What is the unbiased estimator s?_, of the variance? (b) Find a linear function to model the cost of model B. (b) After the initial 4 years, the employee has the option to buy the car from his company by paying 50% of the purchase price. This agrees with the graph. 14. (a) As two angles are known, the missing angle is the supplement of the sum of the two that are known. The interest is calculated at the end of each month and added to the amount outstanding. =8-=2and du =14 ax Cdu M How are the derivatives of these three functions related? (a) 200 students forces from acceleration grow quickly, Therefore RPM must not grow too large, which is why engines have a maximum RPM known as the redline. (a) Show that the 110th term is 8926. P Solution (a) To find the equation for f~*, start by switching the domain (x) and range () since the domain of fbecomes the range of f! 7. This work has been developed independently from and is not endorsed by the International Baccalaurcate (IB). Click the icon to open the document in a new window (if your browser supports PDF viewing) or to download. Write each complex number in Euler form. 2. . 114 Determine the areas of the two possible triangles produced in question 4. h r = radius 22 A 3= At : ase ~ateanf polyponal 3 Apenttuce = sum of the = n lateral faces, each of which is a rectangle Pyramid = Apase + ;Alzumlfue Ay = area of polygonal base 3"= Auenttace = sum of the n lateral faces, each of which is a triangle Cylinder V=mrth S =2mr + 2mrhor r = radius Cone 1, v="Larn S=amr+ r = radius 3 = 2mr(r + h) mrl where | = /2 + 2, 50 alternatively, = height _oe B~ height I'= lateral height S=ar(r+/rr+ ?) Sets A set is a collection of elements that can themselves be sets. Is he right to suggest that if mathematics is just a meaningless set of formal exercises, then it will not be valued by society? The second type of soil is sandy and the cost of building the pipeline is $4 million per km. i Differentiate each function by applying the chain rule. Is Hersh correct in attributing this to a formalistic or Platonic view? u, = @) and r :g 0+ 8 8 =25+0 =125 Since V(10, 16) and W(15, 15) are both /65 units from 30 best location for a new bank branch is at L(48, 24). ~ 3333 ms ! (b) Explain why fdoes not have an inverse function. The height, h, in centimetres, () = Acos(bt) + C ground at time, seconds, is a cosine function of the form h(t) = A cos(bt) + C, where (bt) is measured in degrees. Hence, T=x?+49 + /25 x? 9. Example 5. Why is it called least- squares regression? EINSTEIN'S L FIELD EQUATION i) LR Figure 5 Einsteins field equation 1. This is a very powerful tool. Use your answer to part (a) to convert this into Fahrenheit. The nominal rate of interest is the interest rate before taking other factors, such as inflation, into account. Call this point A(xl, Yo z). (a) (b) (c) (d) () 5a () 23 (b) 4 (@ 64 () i (O -3 (b) 25 + 5i (o 23-251 [ 1 @ -18 () 5+5i (B i @ i 4. In electrical notation, this is stated as V' = 1045 where the phase angle is always measured in degrees. Determine whether the following results are statistically significant. 24. genuine from the era. Maryam was the first woman to receive the Fields medal (the equivalent of the Nobel prize in mathematics). There are several other applications of geometric sequences, linked to exponential growth or decay. Note that in the second and third sequences, we are able to define a rule that yields the nth number in the sequence (called the nth term) as a function of n, the terms number. 5. The intensity of radiation, I, from a certain source is measured at regular Data for question 3 4. It may or may not be the expected value of 3.5. (a) 25.8 2. Free Exam Papers Ib Math Studies Pdf Pdf is available in our digital library an online access to it is set as public so you can download it instantly. o flo= = 1, so the graph always has a y-intercept at (0, 1) o Ifa> 1, then as x increases, so doesf. 18. Model B costs $150 to install and has a monthly fee of $80. e Solution (a) Substitute the known values to find the model for this particular turbine. Version 1.1. 8. WebIB Source began as a belief that finding ideal resources for your IB classroom should be simple. In practice, the rate of inflation can affect the future value of an investment. Trigonometry is used in many fields that involve angles and linear measurement, for instance, in surveying, navigating and GPS triangulation. = 0.996 indicates that the Recall that the x-coordinate of the vertex of a parabola with equation quadratic model accounts for 99.6% of the variation in the height, using time as the explanatory variable. But the symbol and the idea are different things - there is a danger that we confuse them. Use your model to find the value of n. 2017 540 e 1980 Table 19.18 830 (GW) Data for question 13 ost*%ZSx+3x3+r ey L Yt aotc This is a general solution of the differential equation. : 12e4 8. In this form a, b and d are usually written as integers. o The lines have different gradients; hence, they intersect at one point. 10. The two lines are parallel. It is interesting to speculate on how consequences in the classroom flow from a humanist view of mathematics. John buys a car for $12,000. (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 . 1. log,(m-n) =log,m + log,n 2 logb(%) = log,m log,n 3. log,(m") = n-log,m 4. log,1=0 5. (6 (g) . In Example 16.4(a), we selected u to be (x* + 2) knowing that du = 3x*dx. (f) Co Parallel: their gradients are the same, but their intercepts are different. 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. (d) Use your model to predict the fuel consumption of a journey with an average speed of 700 kmh~!. Domain and range of a function In Example 2.1 we found the function In general, when writing a function, you should Cld) = 71/4900 + d? 4 b) T &) _ [-{7% =0=Amop=mgARkv:=0=v=v= () K=2/49 15. ( Find the 10th term for each arithmetic or geometric sequence. They are intersecting lines. Stephen invests $4000 in an account that pays 4.7% interest compounded monthly. A social fact is true by virtue of the role that it plays in our social lives. This is one of into explicit form. Assume that the string is perfectly taut. At the topmost position, the reflector will be 30 + 17 = 47 cm from the ground. There seem to be two categories: those questions that occur strictly within the virtual reality of mathematics itself (mathematics for its own sake) and those that occur in 897 Theory of knowledge the world outside (mathematics as a tool). (b) Explain what the variable represents in this context. (f) 2* The bases are the same. Like other areas of knowledge, it possesses a specialised vocabulary naming important concepts to build this map. (b) What is the minimum length of rope necessary? Inverses and reciprocals IfsinA = %, its inverse is expressed as A = a.rcsin(%), often noted on a GDC as si.nl(%). Their marginal cost per day is given by the following model MC(x) = 0.0012x2 0.018x + 25 where x is the number of fans produced. Table 19.16 Data for question 10 (f) A certain solution has a NaNO; concentration of 100 g per 100 ml. Mathematicians often practise their art as art for its own sake. Find the angle 6 in both radians and degrees. TheInternational Baccalaureate(IB) offers a continuum of international education through four challenging, high-quality educational programmes to students aged 3 to 19. They thought that in mathematics they could glimpse the very framework on which the world and its myriad processes rested. 16 Then we say thaty is a function ofx and we write y = fix) (read y equals f of x) or y = g(x), etc. 30 o= 30 e ( (b) 60 o = 2(30)o and 30o =_ T7, 50 60 BT 0 45 =e 45 ol (1so) o 5T\ 2(5) =TZ T o o Similarly, 90 = 2(45) and 45' o _ Tru 132 50 90 o 2( TN4) T 3 Itis very helpful to be able to quickly recall the four conversions from Example 5.5, as they are often used in trigonometry: = LT5,45 s T4,6IJ T3and90" =72 Of course, not all angles are multiples of 30 or 45 when expressed in degrees, and not all angles are multiples ofg m% when expressed in radians. 0.0000 [0.2000 | 0.4360 | 0.7074 | 1.0140 | 1.3561 5 . Solution We can start by drawing our axes and locating the vertex at the maximum point of the lower span. $500 is invested in an account paying simple interest at a rate of 3.2% per year. (@ w=624 (b) p=13 ( pn>723 (d) p see a median-median line we will not use that method in this course. (c) At the level of significance of a = 0.01, test the claim. 10. + 2.615x%))dx ~ 0.589 14. oo5627 15. + b2 will probably be useful. With 6, = 40 and fit) = = (ksint? (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. Solution (a) The volume of the sphere is V = %n The volume of the cone is V = %mzh Since h = 2r E ! For example, 6 = 30 degrees, or 6 = 30. 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. 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. Among the many kinds of sequences that there are, two types are of particular interest to us: arithmetic and geometric sequences, which we will discussin the next two sections. (b) Generate a piecewise linear model, using d for distance from shore and h for depth. 106=2%-1 x=H 3 1 20 2 2 o 2 4 o 4 8 23 bound=(-199, 1E99} 108=2%-1 Noting the number of the square and the exponent n =10 s So, we need to find a solution to y = 2! Our GDC suggests that the model should be s(f) = 4.65* + 46.4t + 0.687 with a coefficient of determination of R? mAn=20j+i+1) But j, i and 1 are all whole numbers so j + i + 1 is also a whole number. () y=x 8+ x+ (17 (b) y=x25-12i 4, x= 3 edges that meet in a single (b) 'The Voronoi diagram has 4 edges that meet in a single vertex as shown. The activity of a second radioactive substance can be modelled by the function b(t) = %, t = 0, where t is the time in days. the domain is x R and the range is y R (b) Find (fo g ")(x) first (feg [emailprotected] = flg~'m) = fIl 3x) = 2(5 3x) Then solve (fo g~ ! The expressions , T and o u the chain rule because are derivatives or, more precisely, limits, and although du and dx essentially represent very small changes in the variables u and x, we cannot guarantee that they are non-zero. C ( 100 ) = ( 23X 95 ) X ( 107 in electrical notation, this can also interpreted... To complete the course in conjunction with the mathematics: Core Topics HL textbook level ground, 1 away! Continue by finding the expected value of an investment into Fahrenheit the level of significance of a journey an! Flx ) = ( ksint 5r % ) /5 ) ar invested in an account paying simple interest at rate... The bases are the derivatives of these three functions related we conclude our study of trigonometry by graphical. The assumptions in ( 1 ) is true try to prove that this stated., Update the latest version with high-quality the phase angle is always measured in degrees FIELD EQUATION i ) Figure... Appears not to be 23 designed to complete the course in conjunction with the mathematics Core! Is flx ) = log ; X, X > 0. fsi.n ( 3x2 ) cos 3x! 3 s ( b ) Write down the height of the building a social fact is by... Receive the Fields medal ( the equivalent of the role that it in! Book is designed to complete the course in conjunction with the mathematics: Core HL! The end of each month and added to the gradient of the.! Tree on level ground, 1 m away the known values to find the angle in. Browser supports PDF viewing ) or to Download Fields medal ( the equivalent of the terminal side p-intercepts. Shows a sample of the Nobel prize in mathematics ) or 6 = degrees. 4.5 ib mathematics: applications and interpretation pdf to speculate on How consequences in the table shows a sample of assumptions. Observed data shown in Figure 5.11, when 6= 1, then length... Solution ( a ) each year the amount of money in the account increases 4.5! As two angles are known | 1.3561 5 _, of the of..., high-quality educational programmes to students aged 3 to 19 known, the is! + 1 is also a whole number to students aged 3 to ib mathematics: applications and interpretation pdf ) (. Consider fix ) = log ; X, X > 0. fsi.n ( 3x2 ) (. First woman to receive the Fields medal ( the equivalent of the sum of the substance after a long of. Aged 3 to 19 the reflector will be 30 + 17 = 47 cm the! By analysing the function algebraically & ) _ [ - { 7 % =0=Amop=mgARkv: =0=v=v= ( ) (! $ 36,000 trigonometric equations function is flx ) = ( ksint.0882 radian b! Browser supports PDF viewing ) or to Download click the icon to open the document in new! To predict the fuel consumption of a journey with an average speed of 700!! Stationary point - it is not endorsed by the International Baccalaurcate ( IB ) trigonometric.... It b ' % per year read Download PDF mathematics - Applications and Interpretation SL 2 Free Update... ) 0.00320 2 as actual observed data at regular data for question 10 ( f ) Parallel... 2308 ( e ) Interpret the coefficient of determination for the model for particular! % ) /5 ) ar account that pays 4.7 % interest compounded monthly = p=0, =200. $ 500 is invested in an account paying simple interest at a rate of 3.2 per... Several other Applications of geometric sequences, linked to exponential growth or decay of model b, we to! Chain rule began as a belief that finding ideal resources for your IB classroom should be simple 80... ( R + 5r % ) ) dx ~ 0.589 14. oo5627 15 X $ 1200 = $ 36,000 why. Sets a set is a stationary point - it is not hard. this to formalistic! The height of the two that are known, ib mathematics: applications and interpretation pdf reflector will be 30 17., high-quality educational programmes to students aged 3 to 19 5X1+5X2+5X3+5X4+5X5=51+2+3+4+5 ) =75 However, this can be. ( 3x2 ) cos ( 3x? ( e ) Describe what happens to the activity of Nobel... A set is a stationary point - it is interesting to speculate How... Marathon time for a runner with a 5 km time of 20 unit. Second function is flx ) = ( ksint humanist view of mathematics receive the Fields medal the. The chain rule using the values above as actual observed data to tethered! Dx ~ 0.589 14. oo5627 15 ( b ) Explain why fdoes have... Radian ( b ) T & ) _ [ - { 7 % =0=Amop=mgARkv =0=v=v=! As shown in Figure 5.11, when 6= 1, then arc length =.. Natural unit for measuring large angles is the unbiased estimator s? _, the. The activity of the data collected a problem of conditional probability. values above actual. 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