Edexcel Mathematics Foundation Tier, November 2011 (1380/2F) (Paper 2, calculator)

Transcription

1 Link to examining board: This question paper is not yet available to download for free from the Edexcel website. You can purchase your own copy by phoning the Edexcel order line on or you may be able to get a copy from your school. These solutions are for your personal use only. DO NOT photocopy or pass on to third parties. If you are a school or an organisation and would like to purchase these solutions please contact Chatterton Tuition for further details. Question 1 a) 4.3 b) Page 1

2 Question 2 i) first add 1 hour and we get to 18:55 (5 minutes to 7) then add the 20 minutes and we get to 19:15 (quarter past 7) 19:15 ii) we need to know the time elapsed from 17:55 to 18:34 there are 5 minutes until 18:00 then another 34 minutes = 39 minutes Page 2

3 Question 3 a) put them all to 2 decimal places first 13.10, 0.89, 1.20, 7.01 Now it is easier to put them in order 0.89, 1.20, 7.01, b) the smallest number is the biggest negative number -8, -3, 0, 2, 6 c) 15 (4 x (2 + 1)) = 3 15 (4 x 3) = = Page 3

4 Question 4 a) i) we read the x values first, then the y values P = (-4, 3) ii) Q = (0,-2) b) to find the midpoint we add the x values and divide by 2 and add the y values and divide by 2 (or we just see by eye on the diagram) midpoint = (, ) = (, ) = (-2, ) Page 4

5 Question 5 Flavour Number of Angle of children sector Vanilla 12 90⁰ Mint 6 note 1 45⁰ Strawberry ⁰ note 2 Chocolate 16 note 3 120⁰ Total ⁰ 12 children is 90⁰ so we multiply the number of children by 7.5 to get the angle (90 12) And divide the angle by 7.5 to get the number of children Note 1: = 6 Note 2: 14 x 7.5 = 105⁰ Note 3: = 16 To check add up the totals and then 48 x 7.5 = Page 5

6 Question 6 We can just count the number of shaded squares Area = 28 cm Page 6

7 Question 7 a) 8.0 cm b) 50⁰ c) Page 7

8 Question 8 a) Country Tally Frequency England l l l l 5 Ireland l 1 Scotland l l l l l l l l 10 Wales l l 2 Check that we have 18 in total we do. b) Page 8

9 Question 9 a) b) = simply key 3 8 into your calculator c) we can convert all the fractions to 24 th by multiplying the top and the bottom by the same number = = = = = = and = = The fraction that is closest to is Page 9

10 Question 10 a) 6p b) 4m Page 10

11 Question 11 a) we simply multiply the by x 1`.50 = 3 10 x 1.50 = x 1.50 = 75 Pounds ( ) US dollars ($) b) c) draw a horizontal line across from $100 to meet the conversion graph, then drop this down to meet the pounds axis (shown with a red dashed line) $100 = Page 11

12 Question 12 First rewrite with them all in order 90, 91, 92, 93, 93, 93, 95, 97, 98, 99 a) the mode is the most frequent mode = 93 b) the range is the largest take away the smallest range = = 9 c) the mean is the meanest as it is the most work add up all the numbers and divide by the number of them = = 94.1 Mean = Page 12

13 Question 13 a) divide both sides by 4 x = 5 b) multiply both sides by 3 y = Page 13

14 Question 14 i) vertices are the corners vertices = 6 ii) faces are the flat areas (3 rectangles and 2 triangles) faces = 5 iii) edges are the straight lines that join the faces, some of them are shown on the diagram as dashed lines edges = Page 14

15 Question 15 3 kg of potatoes would cost 3 x 1.24 = 3.72 The rest of the cost was for carrots = bought 2 kg of carrots so the cost per kilogram will be half this = 0.68 Carrots cost 68 p per kg Page 15

16 Question 16 Caravan Camping Hotel Total Adult note 1 Child 8 19 note 3 4 note 5 31 note 4 Total 23 note note 6 80 Note 1: = 49 Note 2: = 23 Note 3: 25 6 = 19 Note 4: = 31 Note 5: 31 (8 + 19) = = 4 Note 6: = 32 Check: = Page 16

17 Question 17 Angles in a quadrilateral add up to 360⁰ We have 62⁰, 136⁰ and a right angle which is 90⁰ The missing angle is 360 ( ) = = 72⁰ Angles on a straight line make 180⁰ x = 180 = 72 = 108⁰ Page 17

18 Question 18 A tessellation is where the pattern repeats without any gaps Page 18

19 Question 19 a) b) Page 19

20 Question 20 Interest each year is 2.5% simple. x 3500 = years so multiply by 3 (we can only do this as it is simple interest) 3 x 87.5 = Page 20

21 Question 21 a) i) a factor of 30 is a number that goes exactly into 30 find them in pairs: 1 and 30 2 and 15 3 and 10 5 and 6 1, 2, 3, 5, 6, 10, 15, 30 ii) all the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 The common factors of 24 and 30 are 1, 2, 3, 6 The highest common factor is 6 b) multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60 multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60 multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, is the smallest number that is in all the lists LCM = 60 Alternative method 4 and 5 have no common factors so we know that the LCM must also be a multiple of 20 Now we just need the lowest common multiple of 6 and 20. Easy to see that this is Page 21

22 Question 22 a) angles in a triangle add up to 180⁰ angle ABP = 180 (2x 10 + x + 50) angle ABP = 180 (3x + 40) angle ABP = 180 3x 40 = 140 3x angles on a straight line add up to 180⁰ y = 180 angle ABP y = 180 (140 3x) y = x y = 3x + 40 b) i) y = 145 3x + 40 = 145 Subtract 40 from both sides 3x = 105 Divide both sides by 3 x = 35⁰ ii) angle ABP = = 35⁰ angle BAP = 2x 10 = (2 x 35) 10 = = 60⁰ angle APB = x + 50 = = 85⁰ just check that = 180 it does the largest angle is APB and is 85⁰ Page 22

23 Question 23 When we multiply with powers we add the powers When we divide with powers we subtract the powers = Page 23

24 Question 24 a) -2, -1, 0, 1, 2, 3, 4 b) (x + 5)(x 3) = x x 3x = x 2 + 2x Page 24

25 Question 25 a) 12% of 140 = x 140 = = b) i) 10.5 kg ii) 11.5 kg Page 25

26 Question 26 Melissa Becky Daniel Total x note 1 28 Note 1: Whatever we did to 35 to get to 28 we do to the other ratios. Becky then gives a third to her mother. She gives her mother 3.20 Becky has ( ) 6.40 left Answer = Page 26

27 Question 27 a) 1)We need to have a time frame. Is this number of hours per day, per week or per month for example. 2)There are also lots of overlaps. For example where do we put a response of 10 hours it could fit in either of the two middle boxes. 3) there is no box for those that don t listen to any music b) How many hours a day do you spend listening to music? Tick one box only. 0 hours to less than 1 hour 1 hour to less than 5 hours 5 hours to less than 10 hours 10 hours to less than 20 hours 20 hours or more Page 27

28 Question 28 Area of a triangle is ½ x base x height First we need to find the height of the triangle As we have a right angled triangle we can use Pythagoras Theorem a 2 + b 2 = c 2 where c is the longest side let h be height h = 12 2 h = 144 subtract 36 from both sides h 2 = 108 square root both sides h = base = 6 Area of triangle = ½ x 6 x = cm Page 28

29 Question 29 the diameter of the CD is 12cm we can fit = 8 CDs along the length and we can fit = 4 CDs along the width 8 x 4 = 32 CDs It should be noted that Chatterton Tuition is responsible for these solutions. The solutions have not been produced nor approved by Edexcel. In addition these solutions may not necessarily constitute the only possible solutions. If you found this paper helpful then visit where you will find plenty more Page 29