An advertising company is comparing published listening figures for different radio stations and podcasts in order to decide where is the best place to put their adverts. The audience figures for the last 20 quarters of radio stations A and B are in Table 1. Table 1 Audience figures in 100 000's of radio stations A and B for the last 20 quarters Radio Station A Radio Station B 109 95 103 98 105 97 110 96 108 97 106 96 105 97 109 95 112 93 112 94 115 95 111 91 113 92 112 96 115 102 105 103 109 100 107 106 105 108 108 104(a) (i) Find the summary values for radio stations A and B, using Dataplotter or otherwise. Copy and complete the table below. Round values, where necessary, to one decimal place. The mean, rounded to one decimal place, is given for you as a check that you have entered the data correctly. Table 2 Summary values of audience figures in 100 090's for radio stations A and B. Radio Station A Radio Station B Min Median Max Mean 109.0 97.8 SD IOR Range (ii) Use the two measures of location to say which radio station, on average, has most listeners. Explain your reasoning. (iii) Use all three measures of spread to say which radio station has the greater variability in the amount of listeners. Explain your reasoning. (b) (i) Create boxplots for these two data sets (either drawn by hand or as a printout from Dataplotter or another suitable computer package). Include all the relevant information required for drawing boxplots as set out in Subsection 1.2 of Unit 11. The summary values can be displayed on the borplots themselves or in a table to the side of the chart, as they appear in Dataplotter. (ii) Use the boxplot for radio station B to say whether the data are symmetric or skewed. If the data are skewed, then state whether they are skewed to the left or skewed to the right. What does this tell you about the spread of the data for radio station B? (iii) The advertising company tries to summarise what the boxplot for radio station A is saying. Are the following statements true or false? In each case justify your answer. (1) About one-quarter of the reporting periods for radio station A had less than 10550 000 listeners. (2) About three-quarters of the reporting periods for radio station A had more than 10900 000 listeners.(c) The advertising company also looked at the two top podcasts available for download from the two radio stations. The summary values are in the table below. Table 3 Summary values for the audience figures for the top podcast from radio stations A and B (1090's). Station A Station B Min 105 274 Median 230.5 290 MAX 450 324 Mean 204.0 204.1 SD 131.3 13.4 IQ range 213 18.5 Range 345 50 (i) State what kind of data these are, discrete or continuous. Justify your answer. (ii) The advertising company creates histograms, shown in Figure 1, for the podcasts data, but forgets to label them. Which histogram represents the data for the podcast from radio station A? Explain your answer. 6- frequency 4 2 200 300 400 500 Audience Figures (1000's) Start Value |0 Interval Use Custom8- frequency 200 300 400 500 Audience Figures (1000's) Start Value |0 Interval 50 Use Custom 2 10 frequency 5 200 300 400 500 Audience Figures (1000's) Figure 1Throughout this question, you should use algebra to work out your answers, showing your working clearly. You may use a graph to check that your answers are correct, but it is not sufficient to read your results from a graph. (a) A straight line passes through the points (3, -? ) and (-3. 4). (i) Calculate the gradient of the line. (ii) Find the equation of the line. (iii) Find the r-intercept of the line. (b) Does the line y - -#7 + 3 intersect with the line that you found in part (a)? Explain your answer. (c) Find the coordinates of the point where the lines with the following equations intersect: Ar + 8y - 32, - 2x +1 - -6. (d) Using a throwing stick, Dominic can throw his dog's ball across the park. Assume that the park is flat. The path of the ball can be modelled by the equation y - -0.02 +x+1.8. where r is the horizontal distance of the ball from where Dominic throws it, and y is the vertical distance of the ball above the ground (both measured in metres). (i) Find the y-intercept of the parabola y - -0.02x + + 1.8 (the point at which the ball leaves the throwing stick). (ii) (1) By substituting r - 20 into the equation of the parabola, find the coordinates of the point where the line x - 20 meets the parabola. (2) Using your answer to part (d) (ii) (1), explain whether the ball goes higher than a tree of height 8.5m that stands 20 m from Dominic and lies in the path of the ball. (iii) (1) Find the r-intercepts of the parabola. Give your answers in decimal form, correct to two decimal places. (2) Assume that the ball lands on the ground. Use your answer from part (d)(iii) (1) to find the horizontal distance between where Dominic throws the ball, and where the ball first lands. (iv) Find the maximum height reached by the ball.You should use algebra in all parts of this question, showing your working clearly. (a) Solve the following equations, giving your answers as integers or as fractions in their simplest form. (i) 7: + 19 -21 -3x (ii) 14 - $19x-2) - 6 +3x 20 (iii) +2 F +8 (b) Factorise the expression r' + 13x -68, and hence solve the equation 1 + 13x -68 - 0. (c) A student was asked to rearrange the formula 100 - = - 2c(6 - d) to make d the subject (assuming that ] + lic / 0). The student's incorrect attempt is shown below. 10a = =-2016-d) Clear the fractions By multiplying By 7 10a=d-206-d' Multiply out the Bracket 10a=d-120-2ed Collect the d terms 10 a +120=d-Zed Factorise 10 a+120 = dil-20) Divide By |-Ze to Give de 10a+2c 1-20 (i) Write out a correct rearrangement of the formula. (ii) Identify and explain, as if directly to the student, two of the mistakes they have made.Throughout this question, take care to explain your reasoning carefully. You should round your answers, where necessary, to two significant figures. Finn is looking into the position and range of 4G mobile towers in his local area. Finn learns that the range of the 4G mobile towers is 50 km, where there are no obstructions. (a) Calculate what area is within the range of a 4G mobile tower where there are no obstructions. (b) Finn looks at a map of 4G mobile towers in his area. There is one at Hollingworth Hill and another at Cleggswood Hill. The top of these towers have heights of 248m and 264m respectively. Let point A be the top of the tower at Hollingworth Hill, point B be the point vertically beneath Cleggswood tower and on a level with the point A and let point C be the top of the tower at Cleggswood Hill. A measurement of I cm on the map represents 1 km on the ground. (i) The horizontal distance between the two locations on the map is 3.5 cm. What is the actual horizontal distance between the masts (the length AB)? (ii) What is the reduction scale factor? Give your answer in standard form. (iii) What is the actual distance between the tops of the two towers, the length AC? (iv) Calculate ZCAB, the angle which is the line of sight from the top of the mast at Hollingworth Hill to the top of the mast at Cleggswood Hill? (c) A third tower is located at Heights Barn Hill. Let DEF represent the points on the map for Cleggswood Hill, Hollingworth Hill and Heights Barn Hill respectively. On the map, DE - 3.5 cm and EF -5.5 cm and ZDEF - 105- (i) Is ZDEF on the map greater than, less than, or the same as the angle between the horizontal line between Cleggswood Hill and Hollingworth Hill and the horizontal line between Hollingworth Hill and Heights Barn Hill in real life? Explain your answer. (ii) Find the length DF. (iii) Find the ZEFD. (iv) Find the area of triangle DEF.(a) A hardware engineer is looking at the temperature of Central Processing Units (CPUs) of different computers. In one experiment, the temperature of the CPU of her own computer can be modelled by the equation 7 - -0.051 +47 (0