The effect of air resistance can be highly significant. The data for this experiment are given in the table. (a) Inan arid climate, a golf course may require 2.5 mm of water per square metre of grass, per day. (a) 0298 cms ! (b) Calculate the value of Pearsons r and interpret it in context. A move in chess means transforming the position of the pieces on the board by applying one of the games rules that govern movement. (g) Calculate the minimum value of T. . Dotz st vt averageha:cost, average cost = marginal cost! Solve for x in terms of . Be careful! Eulcr:{ =-184 wen = %+ h(x, 2y, et (X Y]:>{Xz =6 Yuer =Yt h(3% + 2y, Be0a_ ge* ~0.42 O (d) Eigenvalues: 1, 6, eigenvectors (;)( :) Cet = G General solution: . Find the total time that the baking tin is in the oven. i t (seconds) Figure 9.5 Sketch the graph of1 location of the axis of symmetry: b " I 2(49) 1053 ) (d) To find the maximum height reached by the ball, substitute the value from (c) back into the function: h(1.12) = 4.9(1.12)% + 11(1.12) + 50 = 56.2m (3 s.f.) The prism has a height of . () 44i (c) 88/3i 936 Z = 1500w |V =15V [V] = 60V 2% 636 128/Q Chapter 6 Practice questions 2. 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 (h) 2 Multiply the exponents. + b(503) {63252.25u +251.5b = 118 2553009a + 505b = 0 We can solve this system of equations (algebraically, or by using a GDC) to obtain: a = 0.001866 b=0.9384 Therefore, our model isy = 0.001866x> + 0.9384x If we graph this function with appropriate axes, we can see that it fits the lower span very well. Next, we have to consider how to find algebraic relationships for T, and T in terms of c. Since both of these have to do with rate and time, we can distance use the model rate = , time . Mathematics can be a daunting subject for many students, but with a little practice, it can be easy to clear up any mathematic tasks. Jose takes medication. (b) Use the model to estimate the deer population after 10 years. For example, in the second sequence, each term is 3 times the previous term. & 1fs0, separate the variables, to gc(% = gxydxor q()dy = pxdx 4 y Integratcbodmpans,mgetf%:fg(xidx+curfqmdy:fp(x)dx+c Evaluate the integrals if you can and don't forget the arbitrary constant. In such cases it is necessary to find an approximation for the common difference. Month Mean temperature (C) Jan | Feb | Mar | Apr | May | Jun | 06 | L1 | 50 | 100 | 148 | 181 Month Mean temperature (C) jul | Aug | Sep | Oct | Nov | Dec 199 | 195 | 152 | 10 | 48 | 10 (a) Generate a scatter diagram for mean temperature versus months since January, such that January is month 0. In this case we are able to express this function in explicit form. He thinks that a humanistic vision of mathematics chimes in with more progressive politics. Find an expression for g(x), giving your answer as a single logarithm. What is it about mathematical truth that makes it immune to revision and provides the basis for certainty and makes the negation of a mathematical truth a contradiction? P) = 25092% =5 P(40) = 25091825540 ; 51,840, about 52000 people. for your model. (a) How much is the investment worth at the end of 30 years? If C > 2, 2 sinx + C will always be positive. Explain your answer. She pays back the loan at a fixed rate of $250 per month. 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. 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. C(t) = [0.22e001df = 226001 + C(0) = 0= = 22 226001 22 = 156 = ~ 209 years, i.e., in year 2222. (a) (b) (c) 20. The area, A, of each site is given by the function A(x) = x(200 x) where x is the width of the site in metres and 20 =x =180 (a) Site S has a width of 20 m. Write down the area of S. (b) Site T has the same area as site S, but a different width. =315m? (c) Jashanti does not want to wait too long and wants to buy the car two months after she started saving. It is clear that any value of x between 1 and 1 will produce two different values of y. Mathematics deals in what we call necessary truths, while the sciences deal mainly in contingent truth. 101"810(10,,2)( - 10(103( =10 logw( ) = 10log,{1755) 1000000x 102 1000000x 10-2 (316, 145) 1(m)=10-1g g(- Figure 2.11 2(x)=145 GDC screen for the solution to Example 2.5 x ) - lOg(m*)) 10-%2 % = 10log;, 1000000 = 60 dB 27 Functions 1. (a) The points T(1, 3), X(4, 6), G(6, 4), and C(8, 8) are coordinates on a treasure map. 15. Either one of the players has achieved checkmate, or a stalemate (a draw) has been agreed. Make sure to set d to at least the following four values: d = 0, %, 2= You should see that d controls the vertical position of the graph. concave down where f'ois decreasing. Use the rules of exponents to write each of the following in the form 27, wheren Z. 6v2- 12 cos 135 =72+ 144144%? (h) f'4)= = L G me = Thef');e equatibnoft Hisy L5 =gle4) Sy=grtl Set, % 12 (a) y = ~ 70+ 27 X 75 = 450 thereforeA is on the track. Digital compact Digital standard DSLR Other Venice 153 211 82 308 Rome | Budapest | 98 74 120 57 31 12 242 183 Prague 56 29 5 107 TThe average selling price for each type of camera is as follows: Digital compact 1200; Digital standard 1100; DSLR 900; Other 600 Solution We set up a matrix multiplication in which the individual camera sales are multiplied by the corresponding price. Could we allow ourselves to be guided to truth in mathematics because of the beauty of the equations? 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. This was a decrease of 6.2% from the previous year. Express the following in scientific notation. (a)x: W -2 3 mI 3 () % o () % o @1 ) x=35 Chapter 1 Practice questions 1. n 10 logm( 1072) N45 (b) We need to solve the equatio The intersection is at (316, 145), so the sound intensity is 316 W m 2. 24. IB Math AA vs AI. 9.89 grams. 58 Find the first five terms and the 50th term of the sequence (u,) given that L 0 U, =2 Solution Since we know an explicit expression for the nth term as a function of its number n, we only need to find the value of that function for the required terms: guaZ u,Z*Fl;uZZ*EZ, o131 Ea e Gl . Proof is the central concept in mathematics because it guarantees mathematical truth. This also leads to two fundamental trigonometric identities. 5 ZSi:5>(2+5>+ ) =12kSy o BDiA(1E Drhendhind) n n k=1 k=1 =>K+YK In general: n = (k) + g(R) = kz k) + ggm Arithmetic si S In an arithmetic series, we add the terms of an arithmetic sequence. length of the radius), the ratio of arc length, s, to radius, r, F : 5 g Si_%_% for a given circle will be constant. There are a number of points to make about the process here that are typical of mathematical models. Although, explicit. WebMathematics HL - Applications and Interpretations - OXFORD 2019.PDF - Free ebook download as PDF File (.pdf) or read book online for free. Find the radius of the circle. (a) 4 (b) @) 5 ) y=0 (i) 7 3. Mathematics and personal i Sometimes our intuition can let us down badly when it comes to making judgments of probability. Steady state: [0.667 0.333] - (a) s.mZ( X2+ 2x + 15) dx = E k= %5 30. What are the strengths and weaknesses of mathematical humanism? Find f(f) and estimate the percentage of renewables in 2020. amatrix product Here are some examples of matrix multiplication. You can improve your educational performance by studying regularly and practicing good study habits. Figure 5.8 Angle in standard position Two angles in standard position that have the same terminal sides - regardless of the direction or number of rotations - are called coterminal angles (Figure 5.9). If you have suggestions for improving this textbook, please feel free to write to us at [emailprotected] We wish you all the best in your mathematical endeavours. 670 [ 665 | 609 [ 679 [ 625 | 580 | 607 | 605 f&i;;:;::t; 56 | 46 | 54 | 70 | 51 | 40 | 51 | 48 (a) Generate a scatter diagram and describe the association between speed and fuel consumption. cos(3+?) She looks out of her tent and notices that another tent on the other side of " X xm 400m; i up the large field isi on fire. Example 14.18 can also be solved without using calculus. If this is right, then it is natural to ask about the purpose of this particular map. central angle The golf course in Example 5.2 needs to add a boundary along the edge of the sprinkler arc. Stating this as a logarithm problem, we must solve the equation x 1 = log,10 or x = log,(10) + 1 We can use our GDC to solve the equation. Again, since the sum is much easier in a + bi form, start with the denominator. WebMathematics - Applications and Interpretation SL - Hodder 2019 - Free ebook download as PDF File (.pdf), Text File (.txt) or read book online for free. Interchange xand y. This makes sense. () 12. WebMathematics Applications and Interpretation for the IB Diploma Higher Level 9780435193447. (d) Hence find the value of t the first time the seat is 96 m above the ground. The typical way to solve this type of problem is to use what we call a mathematical model. Another way of defining a sequence is the recursive (or inductive) definition. The table below indicates their responses. This PDF download accompanies the IB Mathematics: Applications and Interpretation SL study guide, providing worked answers to problems presented throughout the book. On a coordinate plane, an angle having its vertex at the origin and its initial side lying on the positive x-axis is said to be in standard position (Figure 5.8). 20. Since h = 2r = S=ar(r + =(1+ 12+ (2)? 5 = [~- 1000 1000 + , with C(100) = 25, 10. Therefore, the probability of having the disease given a positive result is 103? The arithmetic sequence can be looked at as a linear function as explained in the introduction to this chapter. If the population growth model in Example 20.9 had the additional initial value that at , the population is P, then this particular population satisfies P = AeM and hence Py=Ackh= A = ekt Ppekn and the solution to the initial value problem is P = Aekt = Pje ekt = Piekit=t) There is a very important special case when #, = 0, the solution becomes P= 842 Pnek(u] = PEkl This is the usual growth model which starts at time = 0 with initial population P, Newton's law of Example 21 cooling states that the rate of change of the A cold object is placed in a warmer medium that is kept at a constant temperature S. The rate of change of the temperature T() with respect to time is proportional to the difference between the surrounding medium and the object and hence it satisfies B dt temperature T of an object is proportional to the difference between T and the temperature of the surrounding medium . Virginia Woolf said about art, Art is not a copy of the world; one of the damn things is enough, and the same could be said about models. Algebra A staple method used in mathematics is the substitution of letters for numbers. The car depreciates by a fixed rate each year, and after 8 years it is worth $2300. Find a formula for the total tin consumption within years of 2013 and estimate when the known world reserves of 156 million tons will be exhausted. 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. Determine if 9803 is a term in this sequence. (a) 15i (b) 4 4/3i 3. We have seen how mathematics is closely integrated into artistic thinking; perhaps because both are abstract areas of knowledge indirectly linked to the world and not held to account through experiment and observation, but instead, open to thought experiment and leaps of imagination. Students have the option to choose between two different courses: IB Math Analysis and Approaches (AA) and IB Math Applications and Interpretation (AI). Sequences Look at the pattern in Figure 3.1 o0 eee . (b) Q) = [r(Hdt = 601n(* + 1) + 3t + c and with initial . Figure 5.19 Calculating values of trigonometric functions from coordinates of points on the unit circle Symmetry is crucial to finding the values of the trigonometric ratios in the unit circle. . A =42andB =63= (b) Using the sine rule: 6 sin42 b, C =180 (42 + 63) = 75 _6sin6> sin63 sin 42 = b~7.99cm (c) Using the sine rule again: Since the value of b is an approximation to 3 significant figures, while other known measurements are exact, the exact measurements are preferred. There are two Maths courses offered (Analysis and Approaches and Applications and Interpretations). (@) % =32+ 2k ) k= % () y=0r- 4. 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