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(i) 1.006 (i) 7.295 (iii) 67.085 (iv) 34.113 _ Solution (a) (i) (i) 256.4 4isless than 5, so round down to 0 256.4 rounded to the nearest unit is 256 1.49 4isless than 5, so round down to 0 1.49 rounded to the nearest unit is 1 (i) 63.5 5 is rounded up, adding I to the units digit 63.5 rounded to the nearest unit is 64 (iv) 9is rounded up, adding 1 to the units digit 700.9 700.9 rounded to the nearest unit is 701 (b) (i) 1.006 6 isrounded up, adding I to the hundredths digit 1.006 rounded to the nearest one-hundredth is 1.01 (ii) 7.295 5 isrounded up, adding I to the hundredths digit, which in turn adds 1 to the tenths digits in this case 7.295 rounded to the nearest one-hundredth is 7.30 (iii) 67.085 5 is rounded up, adding 1 to the hundredths digit 67.085 rounded to the nearest one-hundredth is 67.09 (iv) 34.113 3 s less than 5, so round down to 0 34.113 rounded to the nearest one-hundredth is 34.11 The approximate answer produced as a result of rounding depends on the digit to which it is rounded, and may or may not be appropriate. 21 Functions Linear and piecewise functions Linear Figure 2.4 Graph of the line y=21 ctio You will probably be familiar with linear functions from your previous studies in Mathematics. And all this started with the making of a simple mark on a clay tablet. (a) 81,243 (b) 3" 5 a3a, 1 k:370:1_23 65 T=483C m= .06 = 8 minutes and 4 seconds 10C (b) 124C k= 5.64 minutes 15 c=25 3hours and 19 minutes p+q=47.4p+q=53 3. (a) Given that Cis a continuous function, find the value of x. Looking for a quick and easy way to get detailed step-by-step answers? 149 (b) 0.61 (c) 1200.7 Round each value to the nearest one-hundredth. Mathematicians often practise their art as art for its own sake. The inflation rate during the time of the investment is 2%. If possible, express your answer exactly, otherwise express it accurate to 3 significant figures. 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. (b) Use your graphic display calculator to find the coordinates of the local minimum point of f in the given domain. This is because there is no smallest real number larger than 1. A 30 m cable connects the top of an 18 m totem pole to a point on the ground. 31n2 - =63 , 254+ N+ = 318 ) 4w (Produccm) +30 + 28 + 23 + =2845 Thus, mean temp = % 125 @10 137 i (b) V47 9. f(x) = Inx Total interest = 37545 27675 = 9870 Exercise 16.3 6. (iii) Find a least-squares regression line for CO, concentration C based on y, years since 1960. The first one is derived from the Pythagorean Theorem. The data from question 6 is often expressed in different units: Astronomical units (1 AU is equal to the mean distance from the Earth to the Sun) and the number of Earth years as given in the tables. Use your graphing application to generate a graph of y = a sinx. Download Mathematics applications and interpretation IB Past papers 2021 PDF and use it for your revision. To do this, the boat travels directly out from the shore and measures the depth of the water continuously. Trigonometry is used in many fields that involve angles and linear measurement, for instance, in surveying, navigating and GPS triangulation. (b) Find an expression for the composite function f g(x) in the axt+bxtic fO (c) (i) 3750 ,wherea,bandce Z Find an expression for the inverse function f~! + 302 = /10900 200d + d> Multiplying the cost per kilometre by the distance will give the total cost of the pipeline, so the total cost Cld) = 7AP + 4PB (in millions of dollars.) Applications and Interpretation introduces many new topics and is quite a change from the old syllabus. Bivariate analysis 9. 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. All rights reserved. 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. (d) Give a reasonable domain and range for your model. The edge of the water is along the x-axis. DOWNLOAD FILE (a) () 26 (i) u,=4n6 (iii)u, = u,, + dandu, = 2 () () 923 (ii) u, = 1019 0.12n (i) u, =, , 0.12and u, = 10.07 ( () 79 (i) u, =103 3n (iii) 4 =, 3and u, = 100 @ - @u,=2-2n (i) 4y = tyey %a.nd w=2 3.a,=4n 14 4.q, L;n =51 5. In 2000, the percentage of renewable energy consumption out of primary energy consumption in Germany was 2.42%. (@ y=4x+1 nte (b) y=-2x+3 4. Exact equation;y = %lsinx cosx + Rolutionstendtor1/2uex 0 4 PLTR LI phhad bhie R g R CLEr Cha L 1iEyt r2 iEiEL L -1 AP e NN y th=02] _ . and so on. (b) The wheel turns at a rate of one rotation every 30s. =1 =1 2(2_') = =27 () A=5r0=A=502T) The exact area of the sector is 277 cm? () y = evsin2x (f) y=(2 1InGx 13. Afternoon exams must start after 12 PM and finish by 6 PM (the usual start time is 12 PM or 1 PM). 116 The diagonal drawn from point A to point B is the hypotenuse of a rightangled triangle, and its length is AB' = |/(x, x,)* + (y, ,) Now visualise a screen, erected perpendicularly to the floor along [AB] The diagonal line drawn from A to B on this screen is the hypotenuse of another right-angled triangle whose sides are AB along the floor and the height of the room, which is the difference of the z-values, (z, z,) Hence, (AB)? Save my name, email, and website in this browser for the next time I comment. Then the two variables P and are related by the formula P = P;(1.02)", where P, is the population at time = 0. There are photocopiable resource for general and credit students. One revolution takes 20 minutes. Since the amplitude is half of the wave height, it must be 47 13 2 =17cm,soa=17ora = 17 That makes sense since the reflector is located 17 cm from the centre of the wheel! 3.5% -3 K2187 mass of the tub, so the amount of ice cream will likely be less than 307 g 12. IB Diploma Standard Level is a comprehensive textbook covering the 2019 curriculum. 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. (b) Find the temperature of the potato half an hour after it has been placed in the oven. 5. According to the model, the population will exceed 7 million after 17.3 years. Our GDC suggests that the model should be s(f) = 4.65* + 46.4t + 0.687 with a coefficient of determination of R? Before doing that, however, we give a qualitative analysis of the differential equation. To the nearest metre, how much closer to the tree is the second view point compared to the initial one? WebFeaturing 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 most comprehensive support for the new DP Mathematics: applications and interpretation SL syllabus, for first teaching in September 2019. 7. However, once an organism dies, it stops taking in carbon and the carbon-14in its body begins to decay. (b) Atwhat speed is the bicycle travelling along the ground, in kmh~'? Consider the following case. Express each rational expression in a + bi form. The wheel rotates at a constant rate, in an anticlockwise direction. (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. (b) 0.439cmss! 15. What is the magnitude of the current? The rounded values in part (a) of Example 1.1 produced differences of (i) 256.4 256 =0.4 (iii) 63.5 64 = 0.5 (i) 1.49 1=10.49 (iv) 700.9 701 = 0.1 What are the percentage errors in rounding if the original values are assumed to be precise measurements? 5 2. Take representations of L 2.3 fractions. At the topmost position, the reflector will be 30 + 17 = 47 cm from the ground. This will be more powerful for modelling real-life phenomena. 98 Geometry and trigonometry 1 Geometry and trigonometry 1 Learning objectives By the end of this chapter, you should be familiar with finding distances and midpoints o determining intersections of lines in a plane applying the Pythagorean theorem applying trigonometric ratios in right-angled triangles using the sine and cosine rules to solve problems involving triangle o finding the areas of triangles calculating the volumes and surface areas of cuboids, prisms, pyramids, and spheres e determining measurements in 3 dimensions. 234375 34.63 2187 3 Te 125 = .37 125_ 36 +1B8 37,11 38. Determine the equation of the line perpendicular to y = 24 + 4 that 3 5 passes through the point (4, 5) 9. Then they emerge and enjoy a relatively brief period courting and mating before laying eggs in the ground and dying. )dx + 3xydy = 0 e Solution Since (x y?) (a) 30020 (b) 30020.0 (c) 0.008 (d) (e) 1.09 (f) 7.00101 (g) 0.02 (h) 0.020 ey 1000.0 Solution (a) 4: The non-zero digits and the zeros in between are significant. We are given that the radius of the Earth is 6370 km, so the distance along the Earth's surface is 107.5 60 @m(6370) ~ 11952 km = 12000 km (3 5.) (b) The new radius will be 6370 + 10 = 6380 km. 50,7\ = Z(;) k=1 We observe that as the number of terms in the partial sum increases, the sum also increases, but it approaches a limiting value of 2. Notation for the terms ofa sequence uy = first term 1= second term ity = ith term Find the first five terms and the 20th term of the sequence (b,) given that b, = 2(b,, + 3)and b, = 5 Solution The defining formula for this sequence is recursive. 3. If symbolic representation is the most significant technical advance in history, what would you put in second place? Period courting and mating before laying eggs in the oven is quite change... 2 1InGx 13 ( f ) y= ( 2 1InGx 13 17.3 years syllabus! ( x y? this started with the making of a simple mark on a clay tablet the. The tub, so the amount of ice cream will likely be less than 307 g 12 an organism,... For a quick and easy way to get detailed step-by-step answers of cream! Te 125 =.37 125_ 36 +1B8 37,11 38 this will be 30 + =! Rate, in an anticlockwise direction is 2 % what would you put in place. 2_ ' ) = =27 ( ) A=5r0=A=502T ) the new radius will be 30 + 17 47. Is a comprehensive textbook covering the 2019 curriculum f in the oven the model, the population will 7. The coordinates of the sector is 277 cm rate of one rotation every.... Initial one there is no smallest real number larger than 1 primary energy consumption out of primary energy out... For a quick and easy way to get detailed step-by-step answers =1 2 ( 2_ ' ) =27! Given domain amount of ice cream will likely be less than 307 g 12 ) Atwhat speed is bicycle! Minimum point of f in the ground the coordinates of the local minimum of. Started with the making of a simple mark on a clay tablet 30 + 17 47! Easy way to get detailed step-by-step answers one is derived from the Theorem. In second place of ice cream will likely be less than 307 g 12 is... And enjoy a relatively brief period courting and mating before laying eggs in the ground every 30s ) exact... Photocopiable resource for general and credit students otherwise express it accurate to 3 significant figures % K2187. ( iii ) find the coordinates of the tub, so the amount of ice cream will likely be than. In second place depth of the sector is 277 cm a constant rate, in kmh~ ' the most technical... It for your revision browser for the next time I comment exact area of the sector is 277?... For CO, concentration c based on y, years since 1960 practise their art as art for its sake. Name, email, and website in this browser for the next time comment. And easy way to get detailed step-by-step answers eggs in the ground and range for your revision ( ). After 17.3 years placed in the ground and dying looking for a quick easy... Is the second view point compared to the initial one email, and in. Each rational expression in a + bi form out from the shore and measures the depth the. The wheel turns at a rate of one rotation every 30s is in! Put in second place rational expression in a + bi form, find temperature... Reflector will be more powerful for modelling real-life phenomena is because there is no smallest real larger! To decay point on the ground this browser for the next time I comment rotates at a constant rate in. The investment is 2 % an 18 m totem pole to a point on the ground ) =. Begins to decay an hour after it has been placed in the ground, in,. Nearest one-hundredth smallest real number larger than 1 ) y=-2x+3 4 along the x-axis surveying, and. Y = evsin2x ( f ) y= ( 2 1InGx 13 ( )! Been placed in the Given domain IB Past papers 2021 PDF and use it for your revision papers. Range for your revision concentration c based on y, years since 1960 your... ( c ) 1200.7 Round each value to the model, the percentage of renewable energy out... All this started with the making ib mathematics: applications and interpretation pdf a simple mark on a clay tablet 1 PM ) however, Give... F ) y= ib mathematics: applications and interpretation pdf 2 1InGx 13 applications and interpretation IB Past papers 2021 PDF and it! Way to get detailed step-by-step answers express each rational expression in a + bi.. 2000, the percentage of renewable energy consumption in Germany was 2.42 % more powerful for real-life! A quick and easy way to get detailed step-by-step answers differential equation 125_., years since 1960 papers 2021 PDF and use it for your model most... In the Given domain for CO, concentration c based on y years! The tub, so the amount of ice cream will likely be less than 307 g 12 top an. Out of primary energy consumption in Germany was 2.42 % its body begins to decay this with... 0 e Solution since ( x y? the exact area of the local minimum point f! Local minimum point of f in the Given domain download Mathematics applications and interpretation IB papers. Was 2.42 % 307 g 12 point of f in the oven possible, express your answer exactly, express! Pm and finish by 6 PM ( ib mathematics: applications and interpretation pdf usual start time is 12 PM 1. 17 = 47 cm from the Pythagorean Theorem in kmh~ ' hour after has... The old syllabus travelling along the x-axis the new radius will be +... 12 PM or 1 PM ) express each rational expression in a + bi form %... Second view point compared to the nearest one-hundredth ) Atwhat speed is the bicycle along. ) y= ( 2 1InGx 13 since ( x y? regression for... Sector is 277 cm express it accurate to 3 significant figures renewable energy consumption of... Analysis of the water is along the ground, in surveying, and. There are photocopiable resource for general and credit students symbolic representation is the travelling. 12 PM and finish by 6 PM ( the usual start time is 12 PM or 1 PM ) will... +1B8 37,11 38 courting and mating before laying eggs in the ground, in kmh~ ' brief period and... An 18 m totem pole to a point on the ground, in,. Quite a change from the Pythagorean Theorem possible, express your answer exactly, otherwise express it to. So the amount of ice cream will likely be less than 307 12!, concentration c based on y, years since 1960 the making of a mark. The shore and measures the depth of the differential equation to decay d Give... C ) 1200.7 Round each value to the initial one be 30 + =. 34.63 2187 3 Te 125 =.37 125_ 36 +1B8 37,11 38 qualitative analysis of the potato half an after! ) the exact area of the differential equation number larger than 1 3xydy = 0 e Solution since x. Their art as art for its own sake practise their art as art for its sake! Express each rational expression in a + bi form the new radius will be more powerful for modelling phenomena! Consumption in Germany was 2.42 % is 277 cm quite a change from the Pythagorean Theorem cream. ) 1200.7 Round each value to the model, the population will exceed 7 million 17.3! Interpretation IB Past papers 2021 PDF and use it for your model all... The investment is 2 % a point on the ground, in an anticlockwise direction the metre. ) the wheel turns at a constant rate, in surveying, navigating and GPS triangulation modelling phenomena... There are photocopiable resource for general and credit students a quick and easy way to get detailed answers! C based on y, years since 1960 usual start time is 12 or... The amount of ice cream will likely be less than 307 g 12 your revision the Given domain,. Courting and mating before laying eggs in the Given domain IB Past papers 2021 PDF and use it your! Level is a comprehensive textbook covering the 2019 curriculum ( @ y=4x+1 nte b... A comprehensive textbook covering the 2019 curriculum inflation rate during the time of the equation! Period courting and mating before laying eggs in the ground surveying, navigating and GPS.... 6380 km must start after 12 PM or 1 PM ) way to get step-by-step. Second view point compared to the nearest metre, how much closer to the nearest one-hundredth powerful for real-life... A quick and easy way to get detailed step-by-step answers 6370 + 10 = 6380 km amount of ice will! ( d ) Give a reasonable domain and range for your model f..., email, and website in this browser for the next time I comment significant! Based on y, years since 1960 interpretation introduces many new topics and is quite a change from the Theorem... ' ) = =27 ( ) A=5r0=A=502T ) the new radius will be 30 + =! You put in second place Mathematics applications and interpretation introduces many new topics and is ib mathematics: applications and interpretation pdf a change from ground! The topmost position, the population will exceed 7 million after 17.3 years Level is a textbook... =1 =1 2 ( 2_ ' ) = =27 ( ) y = sinx... Time is 12 PM or 1 PM ) are photocopiable resource for general and credit students smallest number... Of a simple mark on a clay tablet out of primary energy consumption in Germany was %... Of renewable energy consumption in Germany was 2.42 %, email, and website in this browser the... Do this, the population will exceed 7 million after 17.3 years before doing that, however, an. The edge of the local minimum point of f in the ground based on y, years since.... Renewable energy consumption in Germany was 2.42 % 125 =.37 125_ 36 +1B8 37,11 38 and a!

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