ib mathematics: applications and interpretation pdfshrimp toast recipe david chang

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 (a) n=25and a = 0.05, right-tailed (b) n=25and a = 0.05, left-tailed () n=20and a = 0.05, two-tailed (d) n=18and a = 0.01, two-tailed . The number of bacteria in colonyA after hours is modelled by the function A(t) = 12%4 (a) Find the number of bacteria in colonyA after four hours. (a) 27.047 (b) 800.008 (c) 3.14159 (d) 83.47 (d) 0.0009 Give an example that would justify the use of measurements given to the following levels of precision. (b) How much of the blank is wasted? We will show both approaches here. Example 4.21 A bird lands on the zip line in Example 4.19, two-thirds of the way along the line from point M(0, 0, 0) to T(30, 60, 20). (b) Linearise the data using logarithms to find the best-fit model, using P for orbital period and D for average distance from the Sun. We end up with x = 2 orx=1 The equation therefore has three solutions: x = lorx = lorx =2 The history of these problems illustrates the great attraction of pure mathematics. Use the model to calculate the height above sea level of Mt. Your teacher will advise you on the timeline for completing your exploration and will provide critical support during the process of choosing your topic and writing the draft and final versions of your exploration. (e) Describe what happens to the activity of the substance after a long period of time. In 99% of these cases the test does its job and records a negative result. LetA:(3 52 S)andnz(z 15 3),1}15,;3:(3 5 2/\-1 6)(2 3):(0 39) 5/ \-8 25 but BA = -2 3\(3 6 5 2 1 = 9 6 28 16 = AB#BA However, there are some special cases where matrix multiplication is commutative. Unfortunately, this situation makes the y statistic unreliable. Unsere Partner sammeln Daten und verwenden Cookies zur Personalisierung und Messung von Anzeigen. For part (a), the lifeguard can minimise the time it takes to reach the swimmer by running for 281 m and swimming the remaining distance. (a) 26 () 1 () 2. (v) Use your model to predict CO, concentration in the year 2005. (e) Yes.d = 7,usy = 341 2. Calculate the percentage increase by multiplying by 1.045 for each year. The first series, 3251, does not have a limit and we say it diverges. Finally,t everyone lse who picked up looseends while I was otherwise oceupied: thank you for casing the bunden o his tas. 72 ] Solution (a) The amount after 10 years compounding annually is A =1000(1 + 0.06)' = 1790.85 (b) The amount after 10 years compounding quarterly is A= 1000(1 # %) 40 = 1814.02 (c) The amount after 10 years compounding monthly is A= 1000(1 e %) 120 = 1819.40 Example 3.1 can also be solved using the built-in financial package on a graphing calculator. 9. Theres no math without people. 37. ) y= 3le+ &4 then i\] _ 8Wf' forg) lgwaf? Sejah placed a baking tin, that contained cake mix, in a preheated oven 150 T(C) in order to bake a cake. They stay in the ground for 13 years. in the account after t years is is paid 7 times : Since every The amount A A=p(1+0)" Example 3.11 1000 is invested in an account paying compound interest at a rate of 6%. Mathematics uses symbols to describe these amazing structures in the basic language of sets and the mappings between them. (a) 3.09 1 - 20 15. o If0 < a < 1, then as x increases, f decreases. What is the difference between Resistance and Resistivity? A bank pays interest at a rate of 3.5% compounded monthly. We know that the tangent is; defined as tan 6 -= 4% . Note that in Figure 9.44 the graph approaches - but does not intersect the horizontal axis. The proportions of some of the rectangles in this painting is eauty in numbers Keats also put it the other way around: the beautiful is the true. 4 b) T &) _ [-{7% =0=Amop=mgARkv:=0=v=v= () K=2/49 15. 0.1 913 (a) Generate a scatter diagram for the data and describe it. 3% 5,134 19. (b) Find the least-squares regression line for marathon time (M) based on 5km time (7). (a) 1.95m 819 18. A woman, standing 3 m from a ( tan6=1 streetlight, casts a 2-metre shadow on level ground. In this context, the horizontal asymptote is not meaningful because it occurs in negative years since 2018, so there doesn't seem to be a useful interpretation of it. 123.45 has 5 s.f. Figure 5.11 When the radius ris equal to the arc length s, the measure of the angle is 1 radian 131 Geometry and trigonometry 2 The unit circle When an angle is measured in radians it makes sense to draw it, or visualise it, so that it is in standard position. Find the general solution of (x> y? But, how exactly does b affect the period? 821 = 2=1 = [eTdex0477 V2mr 29 13. Find the radius of the circle. How much money will there be in the account at the end of 4 years? Being part of society and culture, its both internal and external: internal to society and culture as a whole, external to the individual, who has to learn it from books and in school. Model Answers. (a) Write down two equations in p and g. (b) Calculate the value of p and of g. (c) Find the number of cells in the culture at 22:00 on Monday. (a) Find a formula for the total number of cases in the first days of the epidemic. 37 L (a) (d) (g) G) 2. What is the difference between a Rhizome and a Tuber? (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. T & Figure 5.6 Angles are not only in triangles - in this section we study angles of rotation, which can be used to describe this snowboarders 3607 jump 129 Geometry and trigonometry 2 Angle Remember than an angle in a plane is made by rotating a ray about its endpoint, called the vertex of the angle. 11. Likewise, you may seey,y,y"" o j, j, j for first, second, and third derivatives, respectively. Lets put some numbers into the problem to illustrate this. Looking again at the solution for Example 13.16, we see that we can choose to express and work out the chain rule in function notation rather than in Leibniz notation. Find the equation of the transformed graph. (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. (a) (i) whend = 110.8 the rate of change is the greatest = day 111 (ii) late April, in the middle of spring (iii) on average, the next day is 0.2C warmer. The lifeguard will leave point L, run along the waters edge (the x-axis) to point C, then swim to the swimmer at point S, as shown below. Recall that the constructivist sees mathematics as a big abstract game played by human beings according to invented rules. (e) Intersecting: their gradients are different. (m) h(u) = 3t1+ 5 () g(6) = ) 3cos0 oM =% 2 cos? O 1(x)=(30-2x) (21-2x) (x) = From the graph shown, we can conclude that the value of x that produces the maximum volume is 4.06 cm. The domain of f " s equal to the range of f; and the range of ~ is equal to the domain off Consider the function fix) = Vx +3,x= -3 (a) Determine the inverse function f~! A parallel AC circuit has two loops. The signs of the terms alternate and there are 99 terms. 5 Figure 9.7 GDC screen for solution to Example 9.4(b) (1.12,56.2) makes sense since we know the maximum height of the ball and we presume the ball does not go underground. o f(1) = log, 1 = 0, so the graph always has an x-intercept at (1, 0) o The graph y = fx) has a vertical asymptote at x = 0 o The domain of fis x > 0 and its range isy R 26 The decibel (dB) is a unit for measuring the relative loudness of sounds. Find the amount of Philippine Pesos she receives. 0.0286m 8. Since mathematical objects are abstract and we cannot point to them, we have to represent them with symbols. The steel frame consists of a rectangular base, two semi-circular ends and two further support rods, as shown in the diagram. _eeeeeeeeeee Solution (a) MCis the rate of change of cost, thus, cost itself is an antiderivative of MC. Find the measure of 3 significant figures. Emerge 7 years later. After 5 years, the deer population is 208. Also, recall that y = fix) 38 flx)=4x8 =x =8 writey = fix) x=4y8 interchange x and y (i.e. Estimate the number of pages in this textbook. 824 10000 (b) Estimate the average distance from the Sun and orbital period for Mercury. (a) (0,7) %(3)2 = % (b) (-2,3) (e) 1-2,0[ 967 Answers 3x2 6x = f3) = () Sce graph. Knowing these four facts can help you to quickly convert between degrees and radians for many common angles. (@) 1+2i (b) 4+ 3i (c) 3/2 +2i 10. V27 - 9V3 12. The difference in decimals is: 1000 000. For the angle 6 in Figure 5.10, Rl it Note that this ratio is an arc length divided by another length (radius), so it is a number without units. Calculate the annual rate of depreciation of the machine. Note that when the common ratio is negative, the sign of the terms in the sequence alternates. 12. The differential equation (1) is separable and can be easily solved. method I frden 1 S 0.2 . The International Baccalaureate, formerly known as the International Baccalaureate Organization, is a nonprofit foundation headquartered in Geneva, Switzerland, and founded in 1968. (d) Calculate the time required for one complete rotation. 68 125 shown in Table 19.16. and radius 6 m (d) Area 40 m and radius 2m (e) Arclength 7577 km and radius 25 km 137 Geometry and trigonometry 2 (f) Arclength %T m and radius 2m (g) Arclength 15cm and radius 5cm (h) Arclength 100 mm and radius 20 mm 39. (a) y=2x b) y=-3 () xy=2 d) x> +y>=4 () y=2x ) y=x2+2 @y =x (0) y=2x20 (i) 2 +y=2 A B 4 2 i Sy =2 B E. 1%> 19 Functions G. 1]A H. 24 = J. o 3 > >4x 74 a 4x K. 1]74 2 \ T 2 > T 4x 0 -4 4] 2. We will talk more about this in the next section, when we will quantify the predictive power of a model. That piece of paper acquires its status ultimately from a whole set of social agreements. = 2u,,3+ 1 andu; =0 (h) a,=a,;+2anda; =1 Find a recursive definition for each sequence. Multiplying a 2 X 3 matrix by a 3 X 2 matrix results in a 2 X 2 product matrix. (a) C=08d+4 (h) x = 3log,y (i) x=2lny o -1 () 5505C @ F= %K 4504 () () 4594F (i) 273C 3. mAn=20j+i+1) But j, i and 1 are all whole numbers so j + i + 1 is also a whole number. Printed in Slovakia by Neografia Acknowledgements The authors and publisher would like to thank the following individuals and organisations for their kind permission to reproduce copyright material. 836 [ 802 [ 779 [ 741 [ 762 [ 770 | 765 | 723 [ 687 ::l:iz;:r:"f::::) 224 | 140 | 138 | 94 | 100 | 95 | 87 | 62 | 79 Speed (kmh~?) also state its domain. Composition with Red, Blue and Yellow (1926) Piet Mondrian. Unstable. But this means that mathematics is really radically different from other areas of knowledge, including the natural sciences. (b) Determine the amount of the substance remaining as t becomes very large. By definition: (c) Anarc oflength t = 7 is equivalent to one-half of the circumference of the unit circle, so it terminates at the point (1, 0). (b) Estimate the length of a 3-year-old Gila Monster. 149 (b) 0.61 (c) 1200.7 Round each value to the nearest one-hundredth. is critical. 19. 3. But, since x = cos (=1,0) Figure 5.21 The Pythagorean Identity and y = sin (), we have xX22=1 (cos 0)2 + (sin )2 = 1 cos?f +sin?6 = 1 This is known as the Pythagorean Identity. Exercise 2.3 L@ (d) 3.98 () 63 @) 1 () @) x @ 1 2x3 (ii) 2. (a) cosB (b) sinC d) B (e) A (c) tan(%) 11. Example 9.8 examines a classic problem. 9. The point estimate is p = 0.5, but the 90% confidence interval is 0.32 < p < 0.68 0 4 8 12162024 28 32 36 40 Number of marked items in the sample Figure 17.7 90% box plots for sample size 40 742 0246 > The results should give reason to ponder the size of the interval. Find the products of each pair of complex numbers. Solution Since the sprinkler sprays an arc of 150, the watered area is % of the total Qo circle area. 2 Period ==~ 12 = 4=2 6] = 27 _ |h|==~== 4 2 Sob:gorb:f;I Finally, we need to decide if a sine or cosine model is better suited for this situation. (f) 2* The bases are the same. Yet mathematics is remarkably useful in this world. derivative changes sign atx = c, then (c, fio) is apoint of inflection. Whereas, if the cicada had a life cycle of 12 years, the prey and predator would meet every cicada cycle. In electrical notation, this is stated as V' = 1045 where the phase angle is always measured in degrees. Postings 0-4 | 5-9 | 10-14 | 15-19 | 20-24 | 25-30 | 31+ | Total Students 2 16 20 23 40 35 12 148 Business owners 5 12 16 18 16 8 4 79 The claim by the business owners is that the distributions are independent of the sample groups. (@) F:C+32 (b) 98.6F ) 5 (d) P=100 (c) 161 years (e) increases towards 100 x 919 Answers 12. (a) Use these values to find a linear function that converts Celsius to Fahrenheit. This suggests that the length of the period and the value of b vary inversely. We write this as S, = =00 lim S, For the above example we have o 1 1 0" lim () 1 =2, since e\ 2 =0 If S, = L, where L is finite, then we say that the infinite series converges to L. 85 Sequences and series % So this particular infinite series converges to 2. WebMathematics - Applications and Interpretation SL - Hodder 2019 - Free ebook download as PDF File (.pdf), Text File (.txt) or read book online for free. (d) Find the maximum height reached by the ball. 5. (a) Write down the temperature of the potato at the moment it is placed in the oven. 1 3 . 138 The trigonometric functions in the unit circle To generalise the definition of the trigonometric ratios, consider an angle of 45 in standard position in the unit circle, as shown in Figure 5.17. So, we can say that x = 0 is not a solution to the equation. 15 In questions 32-33, find the area of the shaded sector. (@) a,=25n u, = (=11 (e) a,=2a,, (b) b,=2 X 3n-1 2 a = @d) a,=n 2n +5anda, () b,=3b,,andb, =2 3. I understand every breakdown. (d) Give a reasonable domain and range for your model. (i) Calculate the required monthly repayment, giving your answer correct to 2 decimal places. We can be challenged by results that seem counter to our intuition, but ultimately, the nature of mathematical proof is that it forces us to accept them nonetheless. (a) Find a linear function to model the cost of model A. (0)) Show that T'= (@ = Or =5~ a7 (@) Find 47 i dr The lobster trap is designed so that the length of steel used in its frame is a minimum. Assume that x is the independent variable and y is the dependent variable. Using the language of limits, we define the sum to infinity, S, as the limit as n tends to infinity of S,. Now we have to use some symbolic rules. Can you think of an example ofa model that does not represent the world well but is nonetheless useful? I wish I found out about it sooner. If you generate many more sets of rolls and record their means, you will eventually have a distribution of sample means. 63 Sequences and series ] Solution (a) Record the differences in an extra row in the table. However, our data indicates that the height of the rocket at time t = 0 is zero, so there must be error present in the data collection or in the model. 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. Fior immediately challenged Tartaglia to a contest. Both estimation and approximation skills are important in mathematics, but they are skills that are practiced every day in many contexts. @ z,=5 ds%ra.nd 2= 3cis 2 () z, = 4C152Tn-and z= 2cisT z 3. (c) Find the minimum average cost, and the number of units produced at that level. 2 (m) not possible (0) 3= logv;(%) (p) 3=log12/2 7. Both Vand V are considered imaginary components, with the symbol j used to denote the imaginary unit in electrical theory. Example 20.5 Sol dy 3x%y V& T 1t 4y Solution First separate the variables 1+ 4y? 31. Assuming the population growth rate remains constant, find: (a) the size of the population in 2021 (b) the number of years until the population exceeds 7 million. Let r be the radius of the circle and x be the side length of the square; we can decide which one should be our independent variable later. (d) The number of fish in the pond will not decrease below p. Write down the value of p. . This indicates that most customers are happy with the company's products or services. 4. Since the triangle has a radius of the unit circle as a hypotenuse, it must be equal to 1. 30 14. (a) their nearest site, there are two largest empty circles, centred at each point, both with radius V65 ~ 8.06. In Figure 5.19, we see these angles shown. (a) Find an estimate of the common difference, by using an average of the differences. (a) Given that fixed costs are 2500, find the cost function, C(x). o The lines have different gradients; hence, they intersect at one point. oo x5 % () 822 o o - (b) 0 % % ,z:;}% o (d) |f e XX 2. emperania] 0) 001 peight m3) (kN 0 9.8050 0.1 9.8052 1 9.8057 4 9.8064 (c) Use your GDC to find an appropriate model for this data, with w as specific weight in terms of temperature T. 10 9.8040 15 9.7980 (d) Use your model to predict the specific weight of water at 12C to 4 significant figures. The variance is unknown. This requires a more abstract and conceptual understanding and it is recommended to students who have a natural mathematical ability and enjoy maths (especially algebra, solving linear and quadratic equations, trigonometry, calculus such as differentiation and integration etc). 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. 2] 5 5 =) v [ 0 ": [~Guadiea o[t | Ouadatc. Interest is earned on each payment at an annual rate of 2% per year, compounded annually. (a) i 4. (e) Since one complete revolution takes 10 minutes, the domain for this model shouldbe 0 < t =< 10 In that time, the person will travel from 12 feet to 212 feet, so the range is 12 < h() < 212 (f) Again, we can use a GDC to solve this, by adding a second function with the constant value of 100. 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. 15. Although the test is quite good, it is not perfect it is only 99% accurate. Diploma Programme In order to account for the rate of inflation, the nominal rate is adjusted to take inflation into account. 400 9. made at the beginning of each year. 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. So, we can find the second term from the first, the third from the second, and so on. Given that fis a one-to-one function and: (a) fl2) = 5, write down f~1(=5) (b) f~(6) = 10, write down f(10) () fi=1) = 13, write down f~1(13) (d) f~'(b) = a, write down fia) 2. The table below indicates their responses. (b) Q) = [r(Hdt = 601n(* + 1) + 3t + c and with initial . 5767162 u .V (n)= V(nMin)= W (n)= 1. (d) On Earth, at sea level, acceleration due to gravity is the constant =9.81ms 2 Compare to the value of a and interpret the difference. There are, to add to the puzzle, none that have cycles of 12, 14, 15, 16 or 18 years. (@) V=49 () V=9-y=T (b) V=18 ) v=12-y=27 2. (a) 3+ 3i (d) 3-3i (b) =3 +3i (e) 5+ 5/3i (c) 33i (f) 5/3 +5i () 5+5/3i (h) 5v3 5i 2. (f) We need to solve the equation % = % Using a GDC we can find the intersection of the curves a(t) = % and _ 80 bt) = = The curves intersect at (1.16, 22.4), so it takes 1.16 days for the activity to be Figure 2.9 GDC screen for the solution to Example 2.4 (f) equal. A goat is tied to the outside corner of a rectangular building, using a 10 m leash. Typically in chess, a move involves the movement of only one piece.

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