Mathematics Foundation Tier, June /1F (Paper 1, non-calculator)

Transcription

1 Link to past paper on AQA website: The associated question paper is available to download freely from the AQA website. To navigate around the website, choose QUALIFICATIONS, GCSE, MATHS, MATHEMATICS, MATHEMATICS A (LINEAR), KEY MATERIALS. Question 1 a) a quarter to 3 or 2:45 pm b) i) 45 minutes later the time will be half past three (or 3:30 pm) ii) lesson finishes at 3:30 pm this is the same as 15:30 15:30 Question 2 a)i) the smallest number is 2004 ii) the largest number is 4200 iii) the nearest number to 3000 is 2400 b) i) 7200 x 10 = ii) = Page 1

2 Question 3 a) half of the pie chart is football half of 60 is students play football b) there are 360⁰ in a circle football is 180⁰ basketball is 60⁰ hockey and rugby are the rest 360 ( ) = = 120⁰ x 60 = x 60 = students play hockey or rugby Question 4 a) A and E fit together to make a rectangle A E b) C and D fit together to make a square C D c) just count the squares area D = 8 cm Page 2

3 Question 5 a) AB is not parallel to CD (FALSE) b) angle A = angle C (TRUE) c) the kite does not have two lines of symmetry (FALSE) it has only one line of symmetry d) the diagonals are at right angles to each other (TRUE) Question 6 a) and c) b) midpoint of AB is (7,6) Page 3

4 Question 7 a) the mode is the most often mode is 17 b) we must first put the data in order of size 8, 9, 10, 13, 14, 16, 16, 17, 17, 17, 18 check we still have 11 pieces of data the median is the middle piece of data and in this case will be the sixth piece of data the median is 16 c) the range is the largest take away the smallest range = 18 8 = 10 d) 75% of 20 is 15 marks (75% of 20 = x 20 = x 20) there were 6 students who got a mark of 15 or more 6 students passed the test Question 8 a) b) 5 x 4 x 3 x 2 x 1 = 5 x 24 = Page 4

5 Question 9 a) i) = ii) 30% = = iii) 15% = = 0.15 b) we first need to have them all as fractions, decimals or percentages I am going to convert them all to decimals with 2 decimal places = 75% = = % = 0.70 In order (smallest first) 0.70, 0.75, %,, 0.8 c) of 60 is 60 3 = 20 so of 60 is 2 x 20 = 40 d) to multiply fractions you multiply the top numbers together and multiply the bottom numbers together x = Page 5

6 Question 10 a) = 6 5 x 6 = b) working backwards, take off the 25 from the end we have 42 now we want two numbers that multiply to give 42 where one of them is 1 more than the other 6 x 7 = 42 so our initial tens digit is 6 Our number is = 65 so 55 2 = 3025 Question 11 Overtime rate is 1.5 x 4.80 = = 7.20 For 12 hours: (10 x 4.80) + (2 x 7.20) = = Page 6

7 Question 12 a) b) there are five 8s in the grid out of a possible 36 answers c) there are six numbers in the grid that are 10 or more (10, 11 or 12) out of a possible 36 = Question 13 a) x 3 b) 2x c) x + (x 3) + 2x = 25 x + x + 2x 3 = 25 4x 3 = 25 add 3 to both sides 4x = 28 divide both sides by 4 x = 7 Ann is 7 years old Page 7

8 Question 14 a) 5 x -2 = -10 b) -2 x -4 = 8 c) -4 4 = -1 Question 15 Question 16 a) 2 hours b) from 2 until 6, that is 4 hours c) the car takes 2 hours to travel 60 miles speed = distance time = 60 2 = 30 mph d) the car journey takes 3.5 hours to come back to London and only 2 hours to go from London the distance is the same in both cases so the speed is slower on average on the return journey we can also see this by looking at the relative steepness of the two journeys; the return journey is not so steep so is slower Page 8

9 Question 17 a) x y -3 note Note 1: y = (2 x -3) + 3 = = -3 b) c) 2x + 3 = 0 this is the same as y = 0 so see where the line crosses the x axis (the line y = 0) this happens when x = Page 9

10 Question 18 Teleworld 10% of 480 is 48 40% of 480 will be 4 x 48 = = 288 SuperSave of 420 = = 280 SuperSave is cheaper Question 19 Leah Chloe Maya Total Ratio 2 3 Share ( ) note note Note 1: whatever we did to 2 to get to 90 we do to 3 to get to Chloe s share 90 2 = 45, 3 x 45 = 135 Note 2: 400 ( ) = = 175 Maya s share is 175 Question 20 a) rotation of 90⁰ clockwise about the centre of rotation (1,0) b) if we look at two corresponding points on A and on C (say point (4,1) on A and point (-1,-3) on C) A has moved 5 places to the left and 4 places down Vector translation of Page 10

11 Question 21 a) subtract 2 from both sides 3x 6 divide both sides by 3 x 2 b) integer values means whole numbers divide all 3 parts by 2-2 x 2-2, -1, 0, 1 Question 22 Distance,d, km Frequency Midpoint Frequency x midpoint 0 d d d d d Total mean = = 9.8 km Page 11

12 Question 23 a) the exterior angles for any polygon add up to 360⁰ for a regular pentagon there are 5 sides and 5 exterior angles 1. The exterior angle of a regular pentagon is equal to 360⁰ 5 = 72⁰ b)i) angles on a straight line make 180⁰ interior angle = 180 exterior angle x = = 108⁰ ii) triangle AEF is an isosceles triangle. Both angles EAF and AEF are exterior angles and are equal to 72⁰ = 144 y = = 36⁰ It should be noted that Chatterton Tuition is responsible for these solutions. The solutions have not been produced nor approved by AQA. 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 12