IB Questionbank Test



Name ___________________________________________________________Exam 5 Paper 21a. [1 mark] The marks obtained by nine Mathematical Studies SL students in their projects (x) and their final IB examination scores (y) were recorded. These data were used to determine whether the project mark is a good predictor of the examination score. The results are shown in the table.Use your graphic display calculator to write down , the mean project mark. 1b. [1 mark] Use your graphic display calculator to write down , the mean examination score. 1c. [2 marks] Use your graphic display calculator to write down r?, Pearson’s product–moment correlation coefficient. 1d. [2 marks] The equation of the regression line y on x is y = mx + c.Find the exact value of m and of c for these data. 1e. [2 marks] Show that the point M (, )?lies on the regression line y on x. 1f. [2 marks] A tenth student, Jerome, obtained a project mark of 17.Use the regression line y on x to estimate Jerome’s examination score. 1g. [2 marks] Justify whether it is valid to use the regression line y on x to estimate Jerome’s examination score. 1h. [2 marks] In his final IB examination Jerome scored 65.Calculate the percentage error in Jerome’s estimated examination score. 2a. [2 marks] 160 students attend a dual language school in which the students are taught only in Spanish or taught only in English.A survey was conducted in order to analyse the number of students studying Biology or Mathematics. The results are shown in the Venn diagram.Set S represents those students who are taught in Spanish.Set B represents those students who study Biology.Set M represents those students who study Mathematics.Find the number of students in the school that?are taught in Spanish. 2b. [2 marks] Find the number of students in the school that study Mathematics in English. 2c. [2 marks] Find the number of students in the school that study both Biology and Mathematics. 2d. [1 mark] Write down?. 2e. [1 mark] Write down . 2f. [2 marks] A student from the school is chosen at random.Find the probability that this student studies Mathematics. 2g. [2 marks] Find the probability that this student studies neither Biology nor Mathematics. 2h. [2 marks] Find the probability that this student is taught in Spanish, given that the student studies Biology. 3a. [2 marks] The final examination results obtained by a group of 3200 Biology students are summarized on the cumulative frequency graph.Find?the median of the examination results. 3b. [3 marks] Find the interquartile range. 3c. [2 marks] 350 of the group obtained the highest possible grade in the examination.Find the final examination result required to obtain the highest possible grade. 3d. [2 marks] The grouped frequency table summarizes the examination results of this group of students.Write down?the modal class. 3e. [1 mark] Write down the mid-interval value of the modal class. 3f. [2 marks] Calculate an estimate of?the mean examination result. 3g. [1 mark] Calculate an estimate of the standard deviation, giving your answer correct to three decimal places. 3h. [3 marks] The teacher sets a grade boundary that is one standard deviation below the mean.Use the cumulative frequency graph to estimate the number of students whose final examination result was below this grade boundary. 4a. [4 marks] Consider the function .Sketch the graph of y = f?(x), for ?4 ≤ x ≤ 3 and ?50 ≤ y ≤ 100. 4b. [1 mark] Use your graphic display calculator to find?the zero of?f?(x). 4c. [2 marks] Use your graphic display calculator to find the coordinates of the local minimum point. 4d. [2 marks] Use your graphic display calculator to find the equation of the tangent to the graph of y = f?(x) at the point (–2, 38.75).Give your answer in the form y = mx + c. 4e. [2 marks] Sketch the graph of the function g?(x) = 10x + 40 on the same axes. 4f. [2 marks] Solve the equation?f?(x) = g?(x). 5a. [3 marks] A flat horizontal area, ABC, is such that AB = 100?m , BC = 50?m and angle AC?B = 43.7° as shown in the diagram.Show that the size of angle BA?C is 20.2°, correct to 3 significant figures. 5b. [4 marks] Calculate the area of triangle ABC. 5c. [3 marks] Find the length of AC. 5d. [5 marks] A?vertical pole, TB, is constructed at point B and has height 25?m.Calculate the angle of elevation of T from, M, the midpoint of the side AC.? 6a. [2 marks] Haruka has an eco-friendly bag in the shape of a cuboid with width 12?cm, length 36?cm and height of 9?cm. The bag is made from five rectangular pieces of cloth and is open at the top.Calculate the area of cloth, in cm2, needed to make Haruka’s bag. 6b. [2 marks] Calculate the volume, in cm3, of the bag. 6c. [2 marks] Nanako decides to make her own eco-friendly bag in the shape of a cuboid such that the surface area is minimized.The width of Nanako’s bag is x?cm, its length is three times its width and its height is y?cm.The volume of Nanako’s bag is 3888?cm3.Use this value to write down, and simplify, the equation in x and y for the volume?of Nanako’s bag. 6d. [2 marks] Write down and simplify an expression in x and y for the area of cloth, A, used to make Nanako’s bag. 6e. [2 marks] Use your answers to parts (c) and (d) to show that. 6f. [3 marks] Find . 6g. [3 marks] Use your answer to part (f) to show that the width of Nanako’s bag is 12?cm. 6h. [2 marks] The cloth used to make Nanako’s bag costs 4 Japanese Yen (JPY) per cm2.Find the cost of the cloth used to make Nanako’s bag.Printed for City Honors ? International Baccalaureate Organization 2019 International Baccalaureate? - Baccalauréat International? - Bachillerato Internacional? ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download