IB Mathematics: Applications and Interpretation SL in 70 Pages - May 11 2020 This Find the quotient Zl of these complex numbers and give your answer in the form a + bi 2 (a) z;, = 9cis3T1Tand 2= 3cis% () z,= 2clsandz2 = 4c1sg (b) z, =10 cisSTTrandzl = 2cisg d) z, = lchsZandZ2 = 3c157 17. o flo= = 1, so the graph always has a y-intercept at (0, 1) o Ifa> 1, then as x increases, so doesf. Inflation means an overall rise in the cost of goods and services. To take care of the sign change, we use some power of (1) that will start with a positive value. equal to fu at)dt We use Trap. (d) From the graph we can see that the horizontal asymptote is a = 0 Figure 2.8 GDC screen for the solution to Example 2.4 (c) (e) From part (d) we can deduce that after a long period of time, the activity of the substance tends to zero. (n) h(0) = e cosf) (0) flx) =06+ 2x%? 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. The scalar product of and A is another g . (b) Calculate the value of Pearsons r and interpret it in context. We can do this quickly and efficiently using a GDC or spreadsheet. The Fibonacci sequence F, is defined by Bi= 1B 1andB, B\ /B, .n>2 A second sequence a,, is defined by _ T Tan hW=T7 n n=1, where F, is a member of the Fibonacci sequence. Because of this, scientists can use carbon-14 dating to henra years e have passed since 326 o Substituting into A(f) = ke~ = e 0.000121 L=as P a o St = Therefore, to 3 significant figures, the half-life of carbon-14 is 5730 years. |1 = 20A 8.6250 (0) and (d) (b) 3. 917 Answers 2. Figure 5.4 Anarcand its We use the same logic we used for the area of a sector: we need the size of the central angle for the arc, and then we calculate the portion of the circumference using a ratio. Starting out with the notion of the empty set and the idea that no set can be a member of itself, we can construct the whole number system. The typical way to solve this type of problem is to use what we call a mathematical model. Instead of using a GDC to graph the derivative function, we could analyse the length function directly to find the minimum. and variance o2 737 17 Inferential statistics 5. October 10, 2020 Written by Praveen Shrivastava. (c) At the level of significance of a = 0.01, test the claim. (a) A bank offers loans of $P at the beginning of a particular month at a monthly interest rate of I . The width and length of several leaves from the same tree were measured. 150 = 150"( 17)715017,517 180) ~ 180 6 Given that the radius, r, is 10 cm, substituting into the formula gives The units of the product 1 are equal to the units of rbecause in radian measure has no units. Mathematics and personal i Sometimes our intuition can let us down badly when it comes to making judgments of probability. (a) 3-i ) -53 100 (b) 273 + 4i 9. WebMathematics - Applications and Interpretation SL - Hodder 2019 - Free ebook download as PDF File (.pdf), Text File (.txt) or read book online for free. He can take his medication again when the concentration of medication reaches 0.395 milligrams per litre. 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. =32 s, 2 3 (b) 13v2Ze " 2 2] (W= 1)L+ w+ w2+ w + wh + wS + wo) (i) w1=0andw1%0 C] (*Zx}y'#l S1+w+w+w+witw +wt=0 xy2x+6 b)) p=24 @lfo 12010 73> x2+x*9> BA=( Y -3y6 () Not possible . Then, by using ratios to calculate the measurement of arcs and sectors in a circle, we will develop the definition of radian measure. P(X=10) = 1 P(X = 9) ~0.0139 (a) 0.817 (b) 1 (c) 0.0162 (a) 0.0338 (b) 0.0245 (c) 0.783 (@ 3 (b) 0.101 (c) 0.000215 (a) 0.0025 (b) 0.9826 (c) 0.9999 (a) 0.1396 (b) 0.1912 (c) 0.9576 (a) 0.8187 (b) 0.5488 (a) 0.9877 (b) 0.999998 (c) 0.0000244 (a) 0.0334 (b) 646 (c) 98" P(X=7) =1~ P(X < 7)~0.212 (Note: In a continuous 2.00004 5. A language act would be a registry officer saying I pronounce you married The use of language in a performative manner creates social facts. Einstein suggested that the most incomprehensible thing about the universe was that it was comprehensible. Animal Fruit fly Horse fly Hummingbird Dragonfly Bat Common swift (bird) Flying fish Pintail duck Swan Pelican Length (cm) 02 13 8.1 85 11 17 34 56 120 160 Speed (cms~1) 190 660 1120 1000 690 2550 1560 2280 1880 2280 827 Bivariate analysis (a) Generate a scatter diagram for these data and describe it. An IB education also fosters diversity, curiosity and a healthy appetite for learning. (d) Use your model to predict the depth 500 m from the shore and 1.5 km from the shore. (@ 6+6i (b) 2/3 + 61 (0 13i 7. 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. Method with 1 = 6 and At = . () The method of interchanging domain (x) and range (y) to find the inverse function used in Example 2.9 also gives us a way for obtaining the graph of ! DDT is a toxic insecticide that was widely used in the past. We can use the logic from section 5.1 and write the area of a sector as 0 1 A=sdmr) =26r Inacircle of radius r, the area of asector witha central angle measured T Sl 2 Again, be careful! (a) Write down the temperature of the potato at the moment it is placed in the oven. If the state of the pieces before the move was legitimate and the move was made according to the rules of the game, then the state of the pieces after the move is also legitimate. In AC circuits, impedance (Z) is the measure of resistance that includes reactance due to capacitance (X) and inductance (X;). So, as you see, you can get to the nth term by multiplying u, by r, (n 1) times. 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. GRS sind2 sin75 - C _ 6sin75 sind2 = ~ 8.66cm In Example 4.11, two angles and one side (AAS) were known. Nature has discovered prime numbers through the cicada life cycles by evolutionary trial and error. Using the symmetry shown in Figure 5.19, we can then evaluate the values for the other three angles: 140 sin (135) = Q sin (225) = 7 sin (315) = = cos(135) = -22 cos (2259 = Y22 cos (3157 = 422 tan(135) = 1 tan(225) = 1 tan (315) = 1 2 2 Note that whether the value ofa trigonometric function for a given angle is positive or negative depends on which quadrant the terminal side of theangle ~ isin, because the signs ofx; y, or- change in each quadrant. (a) logsx= 3 1o (b) logxz o (c) log;(x?2x5)=1 11 Given that 2 = 8 and 2" = 16, (a) write down the value of m and of n (b) hence or otherwise solve 82! In a 2017 study, researchers used data from US national heath surveys from 1997 to 2009, involving 333 247 participants, and found that light and moderate consumption of alcohol correlated with fewer deaths from cardiovascular disease. (b) How long does it take for the number of bacteria in colony A to reach 4007 The number of bacteria in colony B after hours is modelled by the function B(f) = 24ek After four hours, there are 60 bacteria in colony B. (a) V2 (e) 13 3. 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). Find the exact angle, in radians, of a sector with these measurements: (a) Area 2577 cm? and radius 5cm (b) Area 3077 m? (b) The temperature in the centre of the cake mix was 18C when placed in the oven. All points on the floor are mapped by the x- and y-axes. V=27 fz xfx)dx; we use Trap. Now we have to use some symbolic rules. 37. Ay Ax In the graph of fix) = 2x 1 we can see that each time increases by 2 units. With 6, = 40 and fit) = = (ksint? All DP mathematics courses serve toaccommodate the range of needs, interests and abilities of students, and to fulfill the requirements of various university and career aspirations. Calculate the percentage error of your prediction. (a) 210 X 8000 (b) 200 X 0.00018 () (2.3 X109 X (8 X 10?) e i EE}E}EFRE on Earth is the naturally Solution isotope cagrbonlz;, the fraction of carbon-14 (a) A half-life is the time taken for the activity of carbon-14 to halve. 1. - )whereOShB (a) Find the greatest volume of liquid that the flask can contain. 1 34. Notes Notes include general information or advice. They are motivated by the internal beauty and elegance of their subject. = Axe* +c The constant cannot be completely arbitrary because 2sinx + C=0 IfC < 2 then 2 sinx + C will always be negative, regardless of the value of x. X )2-i 5. 36 99.4 51 114 (e) Give a reason why your least-squares regression line should not be used to predict solubility of NaNO, at 95C. (b) Give a reason why linearisation using logarithms should not be used for this data. Eigenvalues are purely imaginary; the origin is a stable equilibrium point (but not asymptotically stable). Then the real rate of return is only 4% per year. Interpret the gradient and intercept in context. (a) Find the amount in his account after 5 years. Find the time taken to reach this charge. (a) A =30%c=10cm,and B = 72 (b) A =36%a=8cm,andB = 72 (c) a=6cm,C = 60%and b= 10cm (d) a=12cm, b =18cm, and = 15cm 3. (@) F:C+32 (b) 98.6F ) 5 (d) P=100 (c) 161 years (e) increases towards 100 x 919 Answers 12. (c) At the top of Mt. She has ben my inspiration and motivation for continuing to improve my knowledge and move my career forward. (f) Eigenvalues: L A Vb v v ke . In the scatter diagram itself, we see a strong positive association in the first part and a strong negative association in the second part. (a) The value of Pearson correlation coefficient for the time it takes an athlete to run 5km and the time for her to cycle 30 km is r = 1.21 (b) The fuel economy of passenger cars decreases linearly with the mass of the car with Pearsons r = 0.78 (c) Among mammals, those with greater average body mass have longer life expectancy; the rank correlation coefficient is r, = 0.85 (d) For a set of (x, y) data, the least-squares regression line is y=253.52x with r = 0.64 2. = OO Mark 4 fold lines, equidistant from the edges of the paper. 17. (a) (b) (0 12. The points P, Q and R represent different positions of a seat on the wheel. 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)? () x=-2%2i @ x=2%2i 5. Math ; FREE. Solution To use the formula s = r6, we must first $ convert 150 to radian measure. (a) 104 \{ (d) 20 (e) 1.55,5.21,8.79 (ii) () is not a function, it fails the vertical line test. Lets call this whole number p. 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