Revision, DP16, May 2017

Transcription

1 Revision, DP16, May a. [1 mark] The following Venn diagram shows the relationship between the sets of numbers The number 3 belongs to the set of and, but not, and is placed in the appropriate position on the Venn diagram as an example. Write down the following numbers in the appropriate place in the Venn diagram. 4 1b. [1 mark] 1c. [1 mark] 1

2 1d. [1 mark] 1e. [1 mark] 1f. [1 mark] 2a. [2 marks] The table shows the number of bicycles owned by 50 households. Write down the value of (i) t ; (ii) w. 2b. [4 marks] Indicate with a tick ( ) whether the following statements are True or False. 2

3 3a. [2 marks] The fourth term, u 4, of a geometric sequence is 135. The fifth term, u 5, is Find the common ratio of the sequence. 3b. [2 marks] Find u 1, the first term of the sequence. 3c. [2 marks] Calculate the sum of the first 10 terms of the sequence. 4a. [1 mark] The weights, in kg, of 60 adolescent females were collected and are summarized in the box and whisker diagram shown below. 3

4 Write down the median weight of the females. 4b. [2 marks] Calculate the range. 4c. [1 mark] Estimate the probability that the weight of a randomly chosen female is more than 50 kg. 4d. [2 marks] Use the box and whisker diagram to determine if the mean weight of the females is less than the median weight. Give a reason for your answer. 5a. [2 marks] Neung is going home to Vietnam after working in Singapore. She has 5000 Singapore dollars (SGD) and changes these into American dollars (USD) to take home. The exchange rate between Singapore dollars (SGD) and American dollars (USD) is 1 USD = SGD. There is also a 2.4 % commission on the exchange. 4

5 Calculate the amount of commission on the exchange in SGD. 5b. [2 marks] Calculate the number of American dollars (USD) Neung takes home. Give your answer correct to 2 decimal places. 5c. [2 marks] At the airport in Vietnam, Neung changes 150 USD into Vietnamese dong (VND) to pay for her transport home. The exchange rate between American dollars (USD) and Vietnamese dong (VND) is 1 USD = VND. There is no commission. Calculate the number of Vietnamese dong that Neung receives. Give your answer correct to the nearest thousand dong. 6a. [2 marks] A cuboid has the following dimensions: length = 8.7 cm, width = 5.6 cm and height = 3.4 cm. Calculate the exact value of the volume of the cuboid, in cm 3. 6b. [2 marks] Write your answer to part (a) correct to (i) one decimal place; (ii) three significant figures. 6c. [2 marks] Write your answer to part (b)(ii) in the form, where. 7a. [1 mark] A market researcher surveyed men and women about their preferred holiday destination. The holiday destinations were Antigua, Barbados, Cuba, Guadeloupe and Jamaica. A conducted at the 5 % significance level. test for independence was 5

6 The calculated value was found to be Write down the null hypothesis. 7b. [2 marks] Find the number of degrees of freedom for this test. 7c. [1 mark] Write down the critical value for this test. 7d. [2 marks] State the conclusion of this test. Give a reason for your decision. 8a. [1 mark] Alan s laundry basket contains two green, three red and seven black socks. He selects one sock from the laundry basket at random. Write down the probability that the sock is red. 8b. [2 marks] Alan returns the sock to the laundry basket and selects two socks at random. Find the probability that the first sock he selects is green and the second sock is black. 8c. [3 marks] Alan returns the socks to the laundry basket and again selects two socks at random. Find the probability that he selects two socks of the same colour. 9a. [2 marks] The first term of an arithmetic sequence is 3 and the seventh term is 33. Calculate the common difference; 9b. [2 marks] Calculate the 95 th term of the sequence; 9c. [2 marks] 6

7 Calculate the sum of the first 250 terms. 10a. [2 marks] A group of 33 people was asked about the passports they have. 21 have Australian passports, 15 have British passports and 3 have neither. Find the number that have both Australian and British passports. 10b. [2 marks] In the Venn diagram below, set A represents the people in the group with Australian passports and set B those with British passports. Write down the value of (i) q ; (ii) p and of r. 10c. [2 marks] A group of 33 people was asked about the passports they have. 21 have Australian passports, 15 have British passports and 3 have neither. In the Venn diagram below, set A represents the people in the group with Australian passports and set B those with British passports. 7

8 Find. 11a. [4 marks] The coordinates of point A are ( 4, p) and the coordinates of point B are (2, 3). The mid-point of the line segment AB, has coordinates (q, 1). Find the value of (i) q ; (ii) p. 11b. [2 marks] Calculate the distance AB. Printed for Sannarpsgymnasiet International Baccalaureate Organization 2018 International Baccalaureate - Baccalauréat International - Bachillerato Internacional 8