Calculate the volume of the sphere. Give your answer correct to two decimal places. (3)

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1 1. Let m = and n = Express each of the following in the form a 10 k, where 1 a < 10 and k. mn; m. n (Total 4 marks) 2. The volume of a sphere is V =, where S is its surface area. 36π The surface area of a sphere is 500 cm 2. 3 S Calculate the volume of the sphere. Give your answer correct to two decimal places. Write down your answer to correct to the nearest integer. Write down your answer to in the form a 10 n, where 1 a < 10 and n. 3. The diagram shows the straight lines L 1 and L 2. The equation of L 2 is y = x. IB Questionbank Mathematical Studies 3rd edition 1

2 Find (i) the gradient of L 1 ; (ii) the equation of L 1. Find the area of the shaded triangle. 4. In the diagram, B ÂC = 90. The length of the three sides are x cm, (x + 7) cm and (x + 8) cm. diagram not to scale Write down and simplify a quadratic equation in x that links the three sides of the triangle. Solve the quadratic equation found in part. IB Questionbank Mathematical Studies 3rd edition 2

3 Write down the value of the perimeter of the triangle. 5. A university required all Science students to study one language for one year. A survey was carried out at the university amongst the 150 Science students. These students all studied one of either French, Spanish or Russian. The results of the survey are shown below. French Spanish Russian Female Male Ludmila decides to use the χ 2 test at the 5 % level of significance to determine whether the choice of language is independent of gender. State Ludmila s null hypothesis. Write down the number of degrees of freedom. Find the expected frequency for the females studying Spanish. (d) Use your graphic display calculator to find the χ 2 test statistic for this data. (e) State whether Ludmila accepts the null hypothesis. Give a reason for your answer. (Total 8 marks) IB Questionbank Mathematical Studies 3rd edition 3

4 6. The temperatures in C, at midday in Geneva, were measured for eight days and the results are recorded below. The mean temperature was found to be 7 C. 7, 4, 5, 4, 8, T, 14, 4 Find the value of T. Write down the mode. Find the median. 7. At the end of the year, only seven of the female Science students sat examinations in Science and French. The marks for these seven students are shown in the following table. Science (S) French (F) Using a scale of 2 cm to represent 10 marks for each axis, draw a labelled scatter diagram for this data. (4) Use your graphic display calculator to find (i) S, the mean of S; (ii) F, the mean of F. Plot the point M( S, F ) on your scatter diagram. IB Questionbank Mathematical Studies 3rd edition 4

5 (d) Use your graphic display calculator to find the equation of the regression line of F on S. (e) Draw the regression line on your scatter diagram. Carletta s mark on the Science examination was 44. She did not sit the French examination. (f) Estimate Carletta s mark for the French examination. Monique s mark on the Science examination was 85. She did not sit the French examination. Her French teacher wants to use the regression line to estimate Monique s mark. (g) State whether the mark obtained from the regression line for Monique s French examination is reliable. Justify your answer. (Total 15 marks) IB Questionbank Mathematical Studies 3rd edition 5