IB Questionbank Test



Calculator Work1. A class of 13 Mathematics students received the following grades in their final IB examination.3 5 3 4 7 3 2 7 5 6 5 3 4a.For these grades, find the mode;b. For these grades, find the median;c. For these grades, find the upper quartile;d. For these grades, find the interquartile range.2. A study was carried out to determine whether the country chosen by students for their university studies was influenced by a person’s gender. A random sample was taken. The results are shown in the following table.A test was performed at the 1% significance level.The critical value for this test is 9.210.a.State the null hypothesis.b. Write down the number of degrees of freedom.c. Write down(i) the statistic;(ii) the associated p-value.d. State, giving a reason, whether the null hypothesis should be accepted.3. A survey investigated the relationship between the number of cleaners, , and the amount of time, , it takes them to clean a school.a.Use your graphic display calculator to write down the equation of the regression line on .b. Write down the value of the Pearson’s product–moment correlation coefficient, .c. Use your regression equation to find the amount of time 4 cleaners take to clean the school.4. The heights of apple trees in an orchard are normally distributed with a mean of and a standard deviation of .a.Write down the probability that a randomly chosen tree has a height greater than .b. Write down the probability that a randomly chosen tree will be within 2 standard deviations of the mean of .c. Use your graphic display calculator to calculate the probability that a randomly chosen tree will have a height greater than .d. The probability that a particular tree is less than metres high is . Find the value of .5. Two propositions and are defined as follows : Eva is on a diet : Eva is losing weight.a.Write down the following statement in words.b.Write down, in words, the contrapositive statement of .c. Determine whether your statement in part (a) is logically equivalent to your statement in part (b). Justify your answer.Calculator Work1. A class of 13 Mathematics students received the following grades in their final IB examination.3 5 3 4 7 3 2 7 5 6 5 3 4a.For these grades, find the mode;Markscheme3 (A1) (C1)[1 mark]b. For these grades, find the median;Markscheme4 (M1)(A1) (C2)Note: Award (M1) for ordered list of numbers seen.[2 marks]c. For these grades, find the upper quartile;Markscheme5.5 (A1) (C1)[1 mark]d. For these grades, find the interquartile range.For these grades, find the interquartile range.Markscheme5.5 – 3 (M1)Note: Award (M1) for 3 and their 5.5 seen.= 2.5 (A1)(ft) (C2)Note: Follow through from their answer to part (c).[2 marks]2. A study was carried out to determine whether the country chosen by students for their university studies was influenced by a person’s gender. A random sample was taken. The results are shown in the following table.A test was performed at the 1% significance level. The critical value for this test is 9.210.a.State the null hypothesis.MarkschemeCountry chosen and gender are independent. (A1) (C1)Notes: Accept there is no association between country chosen and gender. Do not accept “not related” or “not correlated” or “influenced”.[1 mark]b. Write down the number of degrees of freedom.Markscheme2 (A1) (C1)[1 mark]c. Write down(i) the statistic;(ii) the associated p-value.Markscheme(i) 9.17 (9.16988…) (A1)Notes: Accept 9.169.(ii) 0.0102 (0.0102043…) (A1) (C2)Notes: Award (A1) for 0.010, but (A0) for 0.01.[2 marks]d. State, giving a reason, whether the null hypothesis should be accepted.MarkschemeSince , we accept the null hypothesis. (R1)(A1)(ft)ORSince , we accept the null hypothesis. (R1)(A1)(ft) (C2)Notes: To award (R1) there should be value(s) given in part (c). If a value is given in (c), we do not need it explicitly stated again in (d). It is sufficient to state a correct comparison. e.g. OR Do not award (R0)(A1). Follow through from part (c).[2 marks]3. A survey investigated the relationship between the number of cleaners, , and the amount of time, , it takes them to clean a school.a.Use your graphic display calculator to write down the equation of the regression line on .Markscheme (A1)(A1) (C2)Notes: Award (A1) for and seen, (A1) for an equation involving and .[2 marks]b. Write down the value of the Pearson’s product–moment correlation coefficient, .Markscheme (A2) (C2)Notes: Award (A0)(A1) for .[2 marks]c. Use your regression equation to find the amount of time 4 cleaners take to clean the school.Markscheme (M1)Note: Award (M1) for substitution into their regression equation. (minutes) () (A1)(ft) (C2)Notes: Follow through from their regression equation found in part (a). Accept (minutes) ().[2 marks]4. The heights of apple trees in an orchard are normally distributed with a mean of and a standard deviation of .a.Write down the probability that a randomly chosen tree has a height greater than .Markscheme (A1) (C1)[1 mark]b. Write down the probability that a randomly chosen tree will be within 2 standard deviations of the mean of .Markscheme (A1) (C1)Note: Accept or .[1 mark]c. Use your graphic display calculator to calculate the probability that a randomly chosen tree will have a height greater than .Markscheme (M1)Note: Accept alternative methods. (A1) (C2)[2 marks]d. The probability that a particular tree is less than metres high is . Find the value of .Markscheme (M1)Note: Accept alternative methods. (A1) (C2)[2 marks]5. Two propositions and are defined as follows : Eva is on a diet : Eva is losing weight.a.Write down the following statement in words.MarkschemeIf Eva is losing weight then Eva is on a diet (A1)(A1) (C2)Notes: Award (A1) for If… then…Award (A1) for correct propositions in correct order.[2 marks]b.Write down, in words, the contrapositive statement of .MarkschemeIf Eva is not on a diet then she is not losing weight (A1)(A1) (C2)Notes: Award (A1) for “not on a diet” and “not losing weight” seen, (A1) for complete correct answer. No follow through from part (a).[2 marks]c. Determine whether your statement in part (a) is logically equivalent to your statement in part (b). Justify your answer.MarkschemeThe statements are logically equivalent (A1)(ft)The contrapositive is always logically equivalent to the original statement (R1)(ft)ORA correct truth table showing the equivalence (R1)(ft) (C2)Note: Follow through from their answers to part (a) and part (b).[2 marks] ................
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