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STUDY GUIDEIB Math StudiesSummer 2012You will have a paper 1 and a paper 2 test the first week back from break. They will be taken only from the questions in this folder. I will upload explanations via Livescribe on June 4th and 5th. I will also send you a link to the textbook online if you email me at megan.griffith@ .If you know how to do all of these questions, you will get 100. :)1.Let m = 6.0 ×103 and n = 2.4 ×10–5.Express each of the following in the form a ×10k, where 1 ≤ a < 10 and k ? .(a)mn;(b).(Total 4 marks)2.Let x = 6.4 × 107 and y = 1.6 × 108.Find(a)(b)y – 2x,giving your answers in the form a × 10k where 1 ? a < 10 and k ? . (Total 8 marks)7.The heights (cm) of seedlings in a sample are shown below.(a)State how many seedlings are in the sample.(b)Write down the values of(i)the median;(ii)the first and third quartile.(c)Calculate the range.(d)Using the scale below, draw a box and whisker plot for this data.53975022098000 (Total 6 marks)3.The scatter diagram below shows the relationship between the number of vehicles per thousand of population and the number of people killed in road accidents over an eight year period in Calmville. Let x be the number of vehicles per thousand and y be the number of people killed. The following information is known. = 270, = 650sx = 22.3sy = 96.2,sxy = 2077.75(a)(i)Calculate the product–moment correlation coefficient (r).(ii)Explain clearly the statistical relationship between the variables x and y(4) (b)Write the equation of the regression line of y on x, expressing it in the form y = mx + c (where m and c are given correct to 3 significant figures).(4) (c)Use your equation in part (b) to answer the following questions.(i)There were 250 vehicles per 1000 of population. Find the number of people killed.(ii)Explain why it is not a good idea to use the regression line to estimate the number of people killed when the number of vehicles is 150 per thousand.(3)(Total 11 marks)4.A bag containing 60 sweets is opened. The bag contains sweets of the following colours.ColourFrequencyRed18Orange17Green10Purple 9Blue 6According to the manufacturer, the various colours should have the following percentages.ColourPercentageRed35%Orange25%Green20%Purple15%Blue 5% (a)Calculate the expected number of sweets of each colour in a bag containing exactly 60 sweets.(3) Before you can perform the chi-squared test on this data, it is necessary to combine the data for one of the colours with that of another colour.(b)Which colour is this and why is this necessary?(2) (c)Using the chi-squared test at the 5% significance level, investigate the hypothesis that the sweets in the packet may be regarded as a random sample. Remember to state the null hypothesis, the number of degrees of freedom and the critical value of chi-squared.(7)(Total 12 marks)5.For his Mathematical Studies Project a student gave his classmates a questionnaire to fill out. The results for the question on the gender of the student and specific subjects taken by the student are given in the table below, which is a 2 × 3 contingency table of observed values.HistoryBiologyFrenchFemale222018(60)Male20119(40)(42)(31)(27)The following is the table for the expected values.HistoryBiologyFrenchFemalep18.616.2Maleqr10.8(a)Calculate the values of p, q and r.(3)The chi-squared test is used to determine if the choice of subject is independent of gender, at the 5% level of significance.(b)(i)State a suitable null hypothesis H0.(ii)Show that the number of degrees of freedom is two.(iii)Write down the critical value of chi-squared at the 5% level of significance.(3) (c)The calculated value of chi-squared is 1.78. Do you accept H0? Explain your answer.(2)(Total 8 marks)8.For the set of {8, 4, 2, 10, 2, 5, 9, 12, 2, 6}(a)calculate the mean;(b)find the mode;(c)find the median.(Total 4 marks)6.The following are the results of a survey of the scores of 10 people on both a mathematics (x) and a science (y) aptitude test:StudentMathematics (x)Science (y)190852386035878 = 7348570 = 78573656827175680Sx = 16.787390Sy =10.899596Sxy = 100.1108085 (a)Copy the graph below on graph paper and fill in the missing points for students 7–10 on the graph. (4) (b)Plot the point M (, ) on the graph.(1) (c)Find the equation of the regression line of y on x in the formy = ax + b.(2) (d)Graph this line on the above graph.(2)(e)Given that a student receives an 88 on the mathematics test, what would you expect this student's science score to be? Show how you arrived at your result. (2)(Total 11 marks)9.A survey was conducted of the number of bedrooms in 208 randomly chosen houses. The results are shown in the following table.Number of bedrooms123456Number of houses41605232158(a)State whether the data is discrete or continuous.(1)(b)Write down the mean number of bedrooms per house.(2)(c)Write down the standard deviation of the number of bedrooms per house.(1)(d)Find how many houses have a number of bedrooms greater than one standard deviation above the mean.(2) (Total 6 marks)11.The graph of y = x2 – 2x – 3 is shown on the axes below.(a)Draw the graph of y = 5 on the same axes. (b)Use your graph to find:(i)the values of x when x2 – 2x – 3 = 5(ii)the value of x that gives the minimum value of x2 – 2x – 3(Total 4 marks)10.The graph below shows the curve y = k(2x) + c, where k and c are constants.Find the values of c and k.(Total 4 marks)12.Under certain conditions the number of bacteria in a particular culture doubles every 10 seconds as shown by the graph below.(a)Complete the table below.Time (seconds)0102030Number of bacteria1 (b)Calculate the number of bacteria in the culture after 1 minute. (Total 4 marks)13.The following diagrams show the graphs of five functions.Each of the following sets represents the range of one of the functions of the graphs.(a){y ? y ? }(b){y ? y ? 2} (c){y ? y > 0}(d){y ?1 ≤ y ≤ 2}Write down which diagram is linked to each set.(Total 4 marks)14.(a)Represent the function y = 2x2 – 5, where x ? {–2, –1, 0, 1, 2, 3} by a mapping diagram.(b)List the elements of the domain of this function.(c)List the elements of the range of this function.(Total 6 marks)15.The graph of the function f (x) = x2 – 2x – 3 is shown in the diagram below. (a)Factorize the expression x2 – 2x – 3. (b)Write down the coordinates of the points A and B. (c)Write down the equation of the axis of symmetry. (d)Write down the coordinates of the point C, the vertex of the parabola.(Total 8 marks)16.A woman deposits $100 into her son’s savings account on his first birthday. On his second birthday she deposits $125, $150 on his third birthday, and so on.(a)How much money would she deposit into her son’s account on his 17th birthday?(b)How much in total would she have deposited after her son’s 17th birthday?(Total 4 marks)17.(a)Factorize the expression 2x2 – 3x – 5.(b)Hence, or otherwise, solve the equation 2x2 – 3x = 5. (Total 4 marks)18.(a)Solve the equation x2 – 5x + 6 = 0. (b)Find the coordinates of the points where the graph of y = x2 – 5x + 6 intersects the x-axis. (Total 4 marks)19.Jacques can buy six CDs and three video cassettes for $163.17or he can buy nine CDs and two video cassettes for $200.53.(a)Express the above information using two equations relating the price of CDs and the price of video cassettes.(b)Find the price of one video cassette.(c)If Jacques has $180 to spend, find the exact amount of change he will receive if he buys nine CDs.(Total 6 marks)20.A geometric sequence has all its terms positive. The first term is 7 and the third term is 28.(a)Find the common ratio.(b)Find the sum of the first 14 terms.(Total 6 marks)21.The population of Bangor is growing each year. At the end of 1996, the population was 40 000. At the end of 1998, the population was 44 100. Assuming that these annual figures follow a geometric progression, calculate(a)the population of Bangor at the end of 1997;(b)the population of Bangor at the end of 1992.(Total 4 marks)22.Let x = 7.94.(a)Calculate the value of .(b)(i)Give your answer correct to three decimal places.(ii)Write your answer to (b)(i) as a percentage.(c)Give your answer to part (b)(i) in the form a × 10k, where 1? a ?10, k . (Total 6 marks)23.The first four terms of an arithmetic sequence are shown below.1, 5, 9, 13,......(a)Write down the nth term of the sequence.(b)Calculate the 100th term of the sequence.(c)Find the sum of the first 100 terms of the sequence.(Total 4 marks)24.The Venn diagram below shows the universal set of real numbers and some of its important subsets:: the rational numbers,: the integers,: the natural numbers.Write the following numbers in the correct position in the diagram.–1, 1, ?, . (Total 6 marks)25.A problem has an exact answer of x = 0.1265.(a)Write down the exact value of x in the form a×10k where k is an integer and 1 ? a ? 10.(b)State the value of x given correct to two significant figures.(c)Calculate the percentage error if x is given correct to two significant figures.(Total 6 marks)26.(a)Consider the numbers 2, and the sets , , , and .Complete the table below by placing a tick in the appropriate box if the number is an element of the set, and a cross if it is not.(i)2(ii)(iii)(3)(b)A function f is given by f : x ? 2x2 – 3x, x ? {–2, 2, 3}.(i)Draw a mapping diagram to illustrate this function.(ii)Write down the range of function f.(3)(Total 6 marks) ................
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